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<journal-id journal-id-type="publisher-id">Front. Polit. Sci.</journal-id>
<journal-title>Frontiers in Political Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Polit. Sci.</abbrev-journal-title>
<issn pub-type="epub">2673-3145</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
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<article-meta>
<article-id pub-id-type="doi">10.3389/fpos.2025.1500403</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Political Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>The quantitative and qualitative allocation of ministerial portfolios to European radical right parties</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name><surname>Tan</surname> <given-names>Tian</given-names></name>
<xref ref-type="corresp" rid="c001"><sup>&#x0002A;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/2843897/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-review-editing/"/>
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<aff><institution>The Law School, Tohoku University</institution>, <addr-line>Sendai</addr-line>, <country>Japan</country></aff>
<author-notes>
<fn fn-type="edited-by"><p>Edited by: Stylianos Ioannis Tzagkarakis, Hellenic Open University, Greece</p></fn>
<fn fn-type="edited-by"><p>Reviewed by: Fred Paxton, University of Glasgow, United Kingdom</p>
<p>Angela Kahil, Holy Spirit University of Kaslik, Lebanon</p></fn>
<corresp id="c001">&#x0002A;Correspondence: Tian Tan <email>tian.tan.b2&#x00040;tohoku.ac.jp</email></corresp>
</author-notes>
<pub-date pub-type="epub">
<day>16</day>
<month>06</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>7</volume>
<elocation-id>1500403</elocation-id>
<history>
<date date-type="received">
<day>23</day>
<month>09</month>
<year>2024</year>
</date>
<date date-type="accepted">
<day>08</day>
<month>05</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x000A9; 2025 Tan.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Tan</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/"><p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p></license>
</permissions>
<abstract>
<p>This paper examines the ministerial portfolio allocation to European Radical Right Parties (RRPs) in coalition governments, focusing on both quantitative and qualitative aspects. Ministerial portfolio allocation, essential for policy implementation and government stability, typically follows the proportionality principle, aligning ministerial portfolios with seat share. Meanwhile, traditional mainstream parties often secure ministerial portfolios that match their electoral programs. This study investigates whether RRPs&#x02014;long regarded as &#x0201C;pariah parties&#x0201D;, despite their increasing participation in coalition governments since the early twenty-first century, often entering as weak junior partners and maintaining a hostile stance toward liberal democracy&#x02014;follow these allocation patterns. Our analysis shows that while RRPs exhibit a proportional seat-to-portfolio share relationship, their allocations are more strongly influenced by bargaining power. Moreover, RRPs often fail to obtain ministerial portfolios aligned with their electoral priorities. Thus, while RRPs appear normalized in terms of quantitative allocation, they continue to face significant qualitative challenges.</p></abstract>
<kwd-group>
<kwd>European radical right party</kwd>
<kwd>ministerial portfolio allocation</kwd>
<kwd>proportionality principle</kwd>
<kwd>bargaining power</kwd>
<kwd>policy salience</kwd>
<kwd>mainstreaming</kwd>
<kwd>normalization</kwd>
</kwd-group>
<contract-sponsor id="cn001">Tohoku University<named-content content-type="fundref-id">10.13039/501100006004</named-content></contract-sponsor>
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<fig-count count="2"/>
<table-count count="5"/>
<equation-count count="1"/>
<ref-count count="113"/>
<page-count count="18"/>
<word-count count="15116"/>
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<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Elections and Representation</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>The study of coalition governments is one of the most advanced and progressive areas in political science (Druckman and Roberts, <xref ref-type="bibr" rid="B39">2008</xref>, p. 101). Research on coalition governments encompasses several important classic themes, including the composition, duration, fulfillment of electoral pledges, decision-making processes, and the allocation of ministerial portfolios. Among these topics, the ministerial portfolio allocation is the least studied (M&#x000FC;ller and Str&#x000F8;m, <xref ref-type="bibr" rid="B83">1999</xref>; Mershon, <xref ref-type="bibr" rid="B76">2001a</xref>, p. 278; Ecker et al., <xref ref-type="bibr" rid="B41">2015</xref>, p. 802). However, ministerial portfolio allocation is one of the most critical aspects of coalition bargaining and formation (B&#x000E4;ck et al., <xref ref-type="bibr" rid="B7">2011</xref>, p. 441), representing the bottom line of the political process in parliamentary democracy (Laver and Schofield, <xref ref-type="bibr" rid="B62">1990</xref>, p. 164; Laver and Shepsle, <xref ref-type="bibr" rid="B63">1996</xref>).</p>
<p>This is because, on the one hand, ministerial portfolios are typically the pinnacle of a political career for politicians and one of the most crucial resources for parties to provide rents and patronage (Druckman and Warwick, <xref ref-type="bibr" rid="B40">2005</xref>; Verzichelli, <xref ref-type="bibr" rid="B110">2008</xref>, p. 237; Saijo, <xref ref-type="bibr" rid="B92">2020</xref>, p. 4). On the other hand, ministers, as the most important policymakers in parliamentary democracy, are the most tangible manifestations of policy payoffs. Controlling relevant ministerial portfolios in the government is a crucial intervening link between party policy and government action, giving a party a significant advantage in implementing its preferred policies in the relevant sector and bargaining capital to trade with parties controlling other issue areas. This, in turn, affects the overall policy output of the government and ultimately has a profound impact on the stability of the government itself (Browne and Franklin, <xref ref-type="bibr" rid="B19">1973</xref>; B&#x000E4;ck et al., <xref ref-type="bibr" rid="B7">2011</xref>; B&#x000E4;ck and Carroll, <xref ref-type="bibr" rid="B6">2020</xref>). Therefore, regardless of a party&#x00027;s strategic goals&#x02014;whether office-seeking, policy-seeking, or vote-seeking&#x02014;all parties should be highly concerned with both the quantitative (i.e., how many ministerial portfolios they can secure) and qualitative (i.e., what types of ministerial portfolios they can obtain) aspects of ministerial portfolio allocation (Budge and Keman, <xref ref-type="bibr" rid="B22">1990</xref>, p. 89; Str&#x000F8;m and M&#x000FC;ller, <xref ref-type="bibr" rid="B102">1999</xref>; Verzichelli, <xref ref-type="bibr" rid="B110">2008</xref>, p. 238; B&#x000E4;ck and Carroll, <xref ref-type="bibr" rid="B6">2020</xref>, p. 314).</p>
<p>Many past studies have shown that traditional mainstream parties strictly adhere to the principle of proportionality in the quantitative allocation of ministerial portfolios. This means that the share of ministerial portfolios they receive closely corresponds to their share of seats in the coalition government, maintaining an almost one-to-one relationship. This proportionality is largely unaffected by factors such as each party&#x00027;s bargaining power or the varying importance or policy salience of different ministerial portfolios. Regarding the qualitative allocation of ministerial portfolios, traditional mainstream parties are also often seen as being able to secure the ministerial portfolios they desire.</p>
<disp-quote><p><italic>Do the characteristics displayed by traditional mainstream parties in the quantitative and qualitative allocation of ministerial portfolios also apply to Radical Right Parties<xref ref-type="fn" rid="fn0001"><sup>1</sup></xref> (RRPs), which are often defined by their core ideological features of nativism, authoritarianism, and populism (Mudde, <xref ref-type="bibr" rid="B80">2007</xref>, <xref ref-type="bibr" rid="B82">2019</xref>)?</italic></p></disp-quote>
<p>While postwar RRPs differ in many respects from the fascist movements of the interwar era, continuities in historical context and ideology can no longer be overlooked&#x02014;particularly in terms of socio-economic conditions marked by widening class inequality and rising economic distress, policy orientations toward protectionism and authoritarian, xenophobic agitation, and political emotions fueled by anti-establishment sentiment and demands for radical change. Accordingly, the current surge of RRPs has been described by scholars of fascism as a period of &#x0201C;post-fascism&#x0201D; (e.g., Traverso, <xref ref-type="bibr" rid="B104">2017</xref>). RRPs have also traditionally been treated as &#x0201C;pariah parties&#x0201D;, excluded from coalition politics due to their perceived threat to parliamentary democracy (van Spanje and van der Brug, <xref ref-type="bibr" rid="B109">2007</xref>; B&#x000E4;ck et al., <xref ref-type="bibr" rid="B8">2024</xref>; Calvo et al., <xref ref-type="bibr" rid="B24">2024</xref>). Consequently, they have long been subject to political (Downs, <xref ref-type="bibr" rid="B37">2002</xref>) and societal cordons sanitaires (Art, <xref ref-type="bibr" rid="B5">2011</xref>). Only in the twenty-first century did they begin to normalize and gradually gain mainstream acceptance, leading to a growing number of RRPs entering coalition governments (Mudde, <xref ref-type="bibr" rid="B82">2019</xref>, p. 3). However, within such coalitions, RRPs are almost always weak junior partners (McDonnell and Newell, <xref ref-type="bibr" rid="B73">2011</xref>, p. 448&#x02013;449). Moreover, due to their hostility toward liberal democracy (Mudde, <xref ref-type="bibr" rid="B80">2007</xref>, p. 155&#x02013;157, <xref ref-type="bibr" rid="B82">2019</xref>, p. 113&#x02013;128), they are seen not only as undermining democratic</p>
<p>quality at the national level but also as posing significant risks to European and North Atlantic integration (Liang, <xref ref-type="bibr" rid="B65">2007</xref>). These features raise reasonable doubts as to whether RRPs follow the same patterns as traditional mainstream parties in the quantitative and qualitative allocation of ministerial portfolios. Yet this important question has received surprisingly limited scholarly attention.</p>
<p>To address this issue, this paper aims to compare the characteristics and differences between RRPs and traditional mainstream parties in both the quantitative and qualitative allocation of ministerial portfolios. It does so by constructing a more comprehensive and transparent dataset, applying widely accepted and standardized methodological approaches, adopting a pan-European perspective while remaining attentive to the political, economic, and cultural differences between Eastern and Western Europe, and combining primarily quantitative analysis with qualitative insights. In doing so, the paper contributes to the broader literature on ministerial portfolio allocation, RRPs, and the interrelationships between them.</p>
<p>This study finds that, regardless of whether ministerial portfolio importance is considered, and across all of Europe, Western Europe, and Eastern Europe, similar to other traditional mainstream parties, the seat share of RRPs shows an imperfect but still strong proportional relationship with their ministerial portfolio shares. However, though seat share shows higher explanatory power, the power index/vote weight of RRPs demonstrates a better proportional relationship with their ministerial portfolio shares than does their seat share. Particularly when considering ministerial portfolio importance, there is an almost perfect proportional relationship between the power index/vote weight of RRPs and their ministerial portfolio shares in all of Europe, Western Europe, and Eastern Europe. This indicates that, unlike traditional mainstream parties, for RRPs, bargaining power has a stronger proportional relationship with the ministerial portfolio shares they receive in coalition governments compared to their seat share.</p>
<p>Meanwhile, the ministerial portfolio shares that RRPs receive in coalition governments are often less than their seat share. However, the proportional relationship between seat share and ministerial portfolio share for RRPs in Eastern Europe is stronger than that for RRPs in Western Europe, regardless of whether ministerial portfolio importance is considered. Lastly, unlike traditional mainstream parties, RRPs often do not secure the ministerial portfolios they desire when entering coalition governments. Nonetheless, Eastern European RRPs still find it somewhat easier to obtain specific ministerial portfolios they prioritize compared to their Western counterparts, whereas Western European RRPs rely more heavily on their &#x0201C;hard power&#x0201D; (i.e., seat share) to secure specific ministerial portfolios than their Eastern counterparts. All in all, while RRPs have largely achieved normalization/mainstreaming in the quantitative allocation of ministerial portfolios, they still have a considerable way to go in the qualitative allocation before fully reaching that status.</p>
<p>In the next section, we will first provide an overview of the quantitative and qualitative theory of ministerial portfolio allocation, summarizing their longstanding key conclusions and highlighting the importance of studying the ministerial portfolio allocation to RRPs. In Section 3, we will explore the potential characteristics of ministerial portfolio allocation to RRPs, present our hypotheses, and critically assess the conclusions of the limited existing research. In Section 4, after introducing the dependent, independent, and control variables, we test each hypothesis using ordinary least squares regression and conditional logit regression, followed by a concise comparative case study to provide a more robust empirical foundation for the analysis. Finally, Sections 5 and 6 will discuss the empirical analysis results, highlight the academic contributions and limitations of this paper, and conclude with suggestions for future research directions.</p></sec>
<sec id="s2">
<title>2 The quantitative and qualitative theory of ministerial portfolio allocation</title>
<p>Regarding the quantitative allocation of ministerial portfolios (i.e., how many ministerial portfolios each coalition party secures), Gamson (<xref ref-type="bibr" rid="B49">1961</xref>, p. 376, p. 379) proposed over 60 years ago: &#x0201C;Any participant will expect others to demand from a coalition a share of the payoff proportional to the amount of resources which they contribute to a coalition&#x0201D;, meaning parties&#x00027; demands reflect the proportion of resources they control.</p>
<p>The primary resource for each party is its seat share. Browne and Franklin (<xref ref-type="bibr" rid="B19">1973</xref>, p. 457) argued, &#x0201C;The percentage share of ministries received by a party participating in a governing coalition and the percentage share of that party&#x00027;s coalition seats will be proportional on a one-to-one basis&#x0201D;, meaning &#x0201C;the percent ministries received by parties in governing coalitions is directly proportional to the percent seats they contribute to the coalition&#x0201D; (Browne and Franklin, <xref ref-type="bibr" rid="B19">1973</xref>, p. 467). Their calculations confirm this, showing a correlation coefficient of 0.926 between seat share and ministerial portfolio share, and a simple regression analysis (ministerial portfolio share as dependent variable, seat share as independent variable) yielding a constant of &#x02212;0.01 and regression coefficient of 1.07 (Browne and Franklin, <xref ref-type="bibr" rid="B19">1973</xref>, p. 460). Hence, Browne and Franklin&#x00027;s (<xref ref-type="bibr" rid="B19">1973</xref>) one-to-one proportionality hypothesis is supported.<xref ref-type="fn" rid="fn0002"><sup>2</sup></xref></p>
<p>Since ministerial portfolio allocation visibly reflects the outcome of bargaining processes (Schofield, <xref ref-type="bibr" rid="B94">1976</xref>, p. 36; Falc&#x000F3;-Gimeno, <xref ref-type="bibr" rid="B44">2011</xref>, p. 393), bargaining theory&#x02014;which analyzes how coalition gains are distributed among parties with conflicting preferences (Lasswell, <xref ref-type="bibr" rid="B59">1936</xref>)&#x02014;is often viewed as challenging Gamson&#x00027;s proportionality principle. However, empirical studies comparing seat share with the &#x0201C;power index/vote weight&#x0201D;&#x02014;a widely used proxy for bargaining power, measuring how often a party is pivotal in coalition orderings&#x02014;that is, when it transforms a losing coalition into a winning one (Shapley and Shubik, <xref ref-type="bibr" rid="B97">1954</xref>; Banzhaf, <xref ref-type="bibr" rid="B13">1965</xref>)&#x02014;consistently find that seat share provides stronger explanatory power for ministerial portfolio allocation, both substantively and statistically. Bargaining power only occasionally slightly distorts proportionality<xref ref-type="fn" rid="fn0003"><sup>3</sup></xref> (Mershon, <xref ref-type="bibr" rid="B76">2001a</xref>; Warwick and Druckman, <xref ref-type="bibr" rid="B112">2006</xref>; Ennser-Jedenastik, <xref ref-type="bibr" rid="B43">2013</xref>; Falc&#x000F3;-Gimeno and Indridason, <xref ref-type="bibr" rid="B45">2013</xref>; Ceron, <xref ref-type="bibr" rid="B27">2014</xref>; Cutler et al., <xref ref-type="bibr" rid="B31">2014</xref>), and in fact, differences in bargaining power frequently reinforce proportionality (Martin and Vanberg, <xref ref-type="bibr" rid="B71">2020</xref>).</p>
<p>Another challenge is posed by importance/salience theory. Coalition parties negotiate not only over the number of ministerial portfolios but also over specific ministries (Browne and Franklin, <xref ref-type="bibr" rid="B19">1973</xref>, p. 458). This occurs because certain ministerial portfolios are inherently more critical (e.g., Prime Minister), or because particular ministries become especially significant in specific contexts (e.g., the Finance Ministry after a financial crisis) (de Mesquita, <xref ref-type="bibr" rid="B33">1979</xref>; Druckman and Warwick, <xref ref-type="bibr" rid="B40">2005</xref>). Thus, ministerial portfolio allocation among parties may vary according to the relative importance or salience of individual ministries or policy domains.</p>
<p>These assumptions appear reasonable, yet empirical studies find that the impact of these factors on the quantitative allocation of ministerial portfolios is minimal. Even when considering variations in the importance or policy salience of ministerial portfolios, their quantitative allocation still largely adheres to the proportionality principle (Browne and Franklin, <xref ref-type="bibr" rid="B19">1973</xref>, p. 465; Warwick and Druckman, <xref ref-type="bibr" rid="B111">2001</xref>; Indridason, <xref ref-type="bibr" rid="B56">2015</xref>, p. 21; Martin, <xref ref-type="bibr" rid="B69">2016</xref>, p. 26&#x02013;27; Martin and Vanberg, <xref ref-type="bibr" rid="B71">2020</xref>). Some scholars further argue that despite methodological variations, research approaches emphasizing qualitative dimensions consistently support Gamson&#x00027;s proportionality principle (Raabe and Linhart, <xref ref-type="bibr" rid="B87">2013</xref>, p. 482).</p>
<p>Besides bargaining model theory and importance/salience theory, even when considering factors such as geographical context&#x02014;Eastern or Western Europe (Druckman and Roberts, <xref ref-type="bibr" rid="B38">2005</xref>)&#x02014;time spent in opposition (Falc&#x000F3;-Gimeno, <xref ref-type="bibr" rid="B44">2011</xref>), voter perceptions (Lin et al., <xref ref-type="bibr" rid="B66">2017</xref>), or examining different actors such as intra-party factions (Mershon, <xref ref-type="bibr" rid="B76">2001a</xref>,<xref ref-type="bibr" rid="B77">b</xref>; Ceron, <xref ref-type="bibr" rid="B27">2014</xref>), junior ministers (Manow and Zorn, <xref ref-type="bibr" rid="B68">2004</xref>), the European Commission (Franchino, <xref ref-type="bibr" rid="B47">2009</xref>), regional party branches (Ennser-Jedenastik, <xref ref-type="bibr" rid="B43">2013</xref>), or regional coalition governments (Raabe and Linhart, <xref ref-type="bibr" rid="B87">2013</xref>), Gamson&#x00027;s proportionality principle maintains robust statistical significance.<xref ref-type="fn" rid="fn0004"><sup>4</sup></xref> Therefore, there is no compelling methodological or empirical reason to question the validity of this proportionality principle (de Mesquita, <xref ref-type="bibr" rid="B33">1979</xref>, p. 62&#x02013;63).</p>
<p>This principle, applicable to all aspects of coalition payoffs (Browne and Frendreis, <xref ref-type="bibr" rid="B20">1980</xref>, p. 753; Schofield and Laver, <xref ref-type="bibr" rid="B95">1985</xref>, p. 158), is among the most reliable, widely recognized, and robust empirical regularities. It is described as the &#x0201C;Nash equilibrium&#x0201D; and &#x0201C;iron law&#x0201D; in parliamentary democracies (De Winter, <xref ref-type="bibr" rid="B34">2001</xref>, p. 190; Verzichelli, <xref ref-type="bibr" rid="B110">2008</xref>, p. 239; B&#x000E4;ck et al., <xref ref-type="bibr" rid="B9">2009</xref>, p. 28), coalition studies since the 1970s (Carroll and Cox, <xref ref-type="bibr" rid="B26">2007</xref>, p. 300), comparative politics (Lin et al., <xref ref-type="bibr" rid="B66">2017</xref>, p. 915), political science (Budge and Keman, <xref ref-type="bibr" rid="B22">1990</xref>, p. 105; Laver, <xref ref-type="bibr" rid="B61">1998</xref>, p. 7), and even across social sciences broadly (Laver and Schofield, <xref ref-type="bibr" rid="B62">1990</xref>, p. 171; Warwick and Druckman, <xref ref-type="bibr" rid="B111">2001</xref>, p. 627, <xref ref-type="bibr" rid="B112">2006</xref>, p. 635).</p>
<p>In addition to the quantitative theory, the qualitative theory (i.e., what types of ministerial portfolios coalition parties can obtain) is another critical area of research. Qualitative theory argues that coalition parties not only seek ministerial portfolios proportional to their seat share but also target specific ministerial portfolios that are significant, govern salient policy areas (as noted earlier), or align closely with their ideological and policy priorities. Securing these ministerial portfolios enables parties to implement preferred policies or fulfill campaign promises (Budge and Keman, <xref ref-type="bibr" rid="B22">1990</xref>).</p>
<p>Although these factors may not substantially influence the proportionality principle in the quantitative allocation of ministerial portfolios, numerous studies have found that parties emphasizing specific ministerial portfolios in their electoral programs or belonging to party families traditionally associated with particular ministerial portfolios have a higher likelihood of obtaining those ministerial portfolios (B&#x000E4;ck et al., <xref ref-type="bibr" rid="B7">2011</xref>; Raabe and Linhart, <xref ref-type="bibr" rid="B87">2013</xref>; Ecker et al., <xref ref-type="bibr" rid="B41">2015</xref>; Greene and Jensen, <xref ref-type="bibr" rid="B51">2016</xref>; Saijo, <xref ref-type="bibr" rid="B92">2020</xref>; D&#x000E4;ubler et al., <xref ref-type="bibr" rid="B32">2024</xref>).</p>
<p>For example, Socialist parties typically obtain ministerial portfolios such as Social Affairs, Health, and Labor; Conservative parties commonly secure Interior, Foreign Affairs, and Defense portfolios; Liberal parties frequently receive Finance, Economy, and Justice portfolios; and Agrarian and Green parties usually hold Agriculture and Environment portfolios, respectively<xref ref-type="fn" rid="fn0005"><sup>5</sup></xref> (Browne and Feste, <xref ref-type="bibr" rid="B18">1975</xref>; B&#x000E4;ck et al., <xref ref-type="bibr" rid="B7">2011</xref>).</p>
<p>The characteristics of quantitative or qualitative ministerial portfolio allocation discussed above are, to our knowledge, almost non-existent when applied to RRPs, with very few exceptions (e.g., Bichay, <xref ref-type="bibr" rid="B16">2021</xref>). However, this issue is very important for several reasons. First, RRPs have traditionally been regarded as &#x0201C;pariah parties&#x0201D;, viewed by traditional mainstream parties as posing serious threats to parliamentary democracy and therefore considered non-coalitionable (van Spanje and van der Brug, <xref ref-type="bibr" rid="B109">2007</xref>; B&#x000E4;ck et al., <xref ref-type="bibr" rid="B8">2024</xref>; Calvo et al., <xref ref-type="bibr" rid="B24">2024</xref>). As a result, they have long faced cordons sanitaires in both political systems (Downs, <xref ref-type="bibr" rid="B37">2002</xref>) and social life (Art, <xref ref-type="bibr" rid="B5">2011</xref>). It was only after entering the twenty-first century that they began to normalize and gradually achieve mainstream status, leading to an increasing number of RRPs participating in coalition governments<xref ref-type="fn" rid="fn0006"><sup>6</sup></xref> (Mudde, <xref ref-type="bibr" rid="B82">2019</xref>, p. 3). These innovative governing formulae (Mair, <xref ref-type="bibr" rid="B67">1997</xref>, p. 209) involving RRPs are widely regarded as a reluctant outcome of strategies&#x02014;such as co-optation, collaboration (Downs, <xref ref-type="bibr" rid="B36">2001</xref>), accommodation (Meguid, <xref ref-type="bibr" rid="B74">2008</xref>), or adoption (Bale et al., <xref ref-type="bibr" rid="B12">2010</xref>)&#x02014;that traditional mainstream parties were compelled to pursue after becoming unable to bear the high costs of continually excluding RRPs from coalition governments (Backlund, <xref ref-type="bibr" rid="B10">2023</xref>, p. 894). Therefore, there is good reason to believe that the quantitative and/or qualitative allocation of ministerial portfolios to RRPs may significantly deviate from previously established patterns.</p>
<p>Second, there are marked regional differences in RRPs&#x00027; government participation: over half of the cabinets involving RRPs are in Eastern Europe<xref ref-type="fn" rid="fn0007"><sup>7</sup></xref> (about 52.7%), followed by Southern Europe (about 23%), Western Europe (about 16.2%), and the least in Northern Europe (about 8.1%)<xref ref-type="fn" rid="fn0008"><sup>8</sup></xref> (see also <xref ref-type="fig" rid="F1">Figure 1</xref>, <xref ref-type="supplementary-material" rid="SM1">Appendix 1</xref>). This suggests that political institutions or issue salience in different regions significantly impact RRPs&#x00027; government participation. Third, RRPs in coalition governments are always typically weak junior partners (McDonnell and Newell, <xref ref-type="bibr" rid="B73">2011</xref>, p. 448&#x02013;449). During coalition formation or to maintain coalition stability, RRPs generally make significant concessions to senior partners (Heinisch, <xref ref-type="bibr" rid="B53">2003</xref>). Furthermore, considering the characteristic of RRPs being adversaries of Liberal Democracy (Mudde, <xref ref-type="bibr" rid="B80">2007</xref>, p. 155&#x02013;157, 2019, p. 113&#x02013;128), it is highly questionable whether other coalition partners would be willing to allocate important ministerial portfolios&#x02014;such as Justice, Interior, Economic Affairs, and Immigration&#x02014;to RRPs, even if these are highly desired by them.</p>




<fig id="F1" position="float">
<label>Figure 1</label>
<caption><p>Government participation of RRPs (1993.10&#x02013;2024.01).</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fpos-07-1500403-g0001.tif"/>
</fig>


<p>Therefore, given the unique nature of RRPs, potential regional differences in institutional or issue salience, and their weaker position in coalition governments, the purpose of this paper is clear and straightforward: <italic>to examine whether the ministerial portfolio allocation to RRPs follows the same quantitative and qualitative patterns as those for traditional mainstream parties</italic>.</p></sec>
<sec id="s3">
<title>3 Radical right parties and the ministerial portfolio allocation</title>
<p>Many scholars have long argued that, due to the populist nature of RRPs, these parties&#x02014;even when they enter coalition governments&#x02014;struggle to implement their often unrealistic policy promises, which were primarily designed to attract votes. As a result, the policy influence of RRPs has generally been considered quite limited in the past (Canovan, <xref ref-type="bibr" rid="B25">1999</xref>, p. 12; M&#x000E9;ny and Surel, <xref ref-type="bibr" rid="B75">2002</xref>, p. 18; Heinisch, <xref ref-type="bibr" rid="B53">2003</xref>, p. 123&#x02013;124; Taggart, <xref ref-type="bibr" rid="B103">2004</xref>, p. 270; Hopkin and Ignazi, <xref ref-type="bibr" rid="B55">2008</xref>, p. 61; McDonnell and Newell, <xref ref-type="bibr" rid="B73">2011</xref>, p. 448&#x02013;449; Mudde, <xref ref-type="bibr" rid="B81">2013</xref>, p. 13&#x02013;14).</p>
<p>However, in recent years, as RRPs have more frequently entered coalition governments, some of these parties are even considered to have gained sustainable governance capabilities (Albertazzi and McDonnell, <xref ref-type="bibr" rid="B3">2015</xref>, p. 165&#x02013;166). These parties are increasingly exerting significant policy influence in the areas they govern or are concerned about. For instance, scholars have pointed out that under coalition governments involving RRPs, criminal policies have become stricter (Bale, <xref ref-type="bibr" rid="B11">2003</xref>); immigration, refugee, and integration policies have become more stringent (Schain, <xref ref-type="bibr" rid="B93">2006</xref>; Bale et al., <xref ref-type="bibr" rid="B12">2010</xref>; van Spanje, <xref ref-type="bibr" rid="B108">2010</xref>; Akkerman, <xref ref-type="bibr" rid="B1">2012</xref>; Akkerman and De Lange, <xref ref-type="bibr" rid="B2">2012</xref>); language, education, and cultural policies have become more conservative, foreign policies have become more aggressive (Minkenberg, <xref ref-type="bibr" rid="B79">2015</xref>); and welfare policies have become more restrictive (Schumacher and van Kersbergen, <xref ref-type="bibr" rid="B96">2016</xref>; Falkenbach and Greer, <xref ref-type="bibr" rid="B46">2018</xref>; Chueri, <xref ref-type="bibr" rid="B28">2021</xref>).</p>
<p>The influence of RRPs on these policies can, of course, be indirect&#x02014;such as through blackmailing or bargaining with other parties to achieve their policy goals&#x02014;but it can also be direct, such as by controlling ministerial portfolios that oversee these policy areas. Especially as RRPs gain more experience and governance capabilities through repeated participation in coalition governments, they are increasingly likely to independently manage a ministerial portfolio and exert greater policy influence within its domain.</p>
<p>In this context, Nicolas Bichay made a valuable initial contribution to the study of RRPs&#x00027; ministerial portfolio allocation. In a short article, he noted that RRPs consistently secure a ministerial portfolio share proportional to their seat share in the coalition government. Moreover, RRPs often succeed in obtaining the ministerial portfolios they prioritize (Bichay, <xref ref-type="bibr" rid="B16">2021</xref>). Therefore, building on the conclusions of scholars presented in Section 2 and Bichay&#x00027;s preliminary observations on RRPs, it seems reasonable to assume that RRPs, like traditional mainstream parties, align with existing research findings on the quantitative and qualitative theories of ministerial portfolio allocation. More specifically<xref ref-type="fn" rid="fn0009"><sup>9</sup></xref>:</p>
<list list-type="simple">
<list-item><p>Quantitative Hypothesis 1: RRPs display strong proportionality between their seat share and ministerial portfolio share, even when ministerial portfolio importance is considered.</p></list-item>
<list-item><p>Quantitative Hypothesis 2: RRPs display stronger proportionality between their seat share and ministerial portfolio share than between their bargaining power and ministerial portfolio share, with seat share providing greater explanatory power.</p></list-item>
<list-item><p>Qualitative Hypothesis: The more RRPs emphasize specific policy areas, the greater the likelihood of securing ministerial portfolios overseeing those policy areas.</p></list-item>
</list>
<p>However, the hypotheses outlined above are not necessarily valid, as certain characteristics of RRPs cast doubt on them. For instance, under the governance of RRPs, minority rights, judicial and central bank independence, and freedoms of expression, press, association, and research have been undermined, leading to varying degrees of democratic backsliding in countries like Hungary, Poland, and Slovakia (Rosenbluth and Shapiro, <xref ref-type="bibr" rid="B91">2018</xref>, p. 214&#x02013;228; Batory and Svensson, <xref ref-type="bibr" rid="B15">2019</xref>; Norris and Inglehart, <xref ref-type="bibr" rid="B84">2019</xref>, p. 183&#x02013;185). Furthermore, the rule of RRPs not only undermines the quality of democracy domestically but also negatively impacts international politics, as RRPs are often regarded as pursuing self-centered and sovereignty-focused foreign policies. This tendency results in actions that exclusively consider national interests and contradict the principles of liberal democracy on the international stage (Rathbun, <xref ref-type="bibr" rid="B88">2004</xref>, p. 197&#x02013;198, p. 213&#x02013;214). Consequently, although RRPs do not share a uniform or monolithic set of foreign policy preferences, the main features of their foreign policy&#x02014;characterized by nativism, anti-pluralism, anti-globalism, and anti-establishment sentiments (Destradi et al., <xref ref-type="bibr" rid="B35">2021</xref>, p. 665, p. 671&#x02013;676; Ostermann and Stahl, <xref ref-type="bibr" rid="B86">2022</xref>, p. 5)&#x02014;are widely seen as posing significant risks to European and North Atlantic integration (Liang, <xref ref-type="bibr" rid="B65">2007</xref>).</p>
<p>Given the above, coalition partners are likely reluctant to allocate ministerial portfolios that oversee critical domestic and/or international policy areas to RRPs, which are considered adversaries of liberal democracy. This reluctance may impact the quantitative and/or qualitative allocation of ministerial portfolios to RRPs. In other words, although the normalization/mainstreaming of RRPs has become more frequent and significant in the twenty-first century, the allocation of ministerial portfolios to these parties may not follow the established patterns and principles of quantitative and/or qualitative allocation observed for other traditional mainstream parties.</p>
<p>Simultaneously, although Bichay&#x00027;s research fills an important gap in the study of ministerial portfolio allocation to RRPs, we cannot conclude that his findings are entirely accurate for several reasons: First, Bichay does not provide the source or detailed content of the dataset used, which raises concerns about data transparency and reliability. Second, in his analysis of the quantitative allocation of ministerial portfolios to RRPs, Bichay does not employ the most standard and widely accepted method in ministerial portfolio allocation research&#x02014;ordinary least-squares linear regression (Indridason, <xref ref-type="bibr" rid="B56">2015</xref>, p. 10, p. 15; Martin, <xref ref-type="bibr" rid="B69">2016</xref>, p. 18). Third, his study focuses only on the seven most common ministerial portfolios<xref ref-type="fn" rid="fn0010"><sup>10</sup></xref> shared among European governments, overlooking other significant ministerial portfolios such as Social Welfare, Health, Labor, Economic Affairs, and Culture, which are also often assigned to RRPs. Fourth, some of Bichay&#x00027;s specific conclusions regarding the qualitative allocation of ministerial portfolios to RRPs are inaccurate. For instance, he claims that RRPs are most likely to control the Defense and Justice portfolios and almost never manage the Ministry of Foreign Affairs. However, as demonstrated in <xref ref-type="supplementary-material" rid="SM1">Appendices 1</xref>, <xref ref-type="supplementary-material" rid="SM2">2</xref>,<xref ref-type="fn" rid="fn0011"><sup>11</sup></xref> these assertions do not hold. One of the main reasons for this inaccuracy appears to be Bichay&#x00027;s failure to account for the significant East&#x02013;West divide in ministerial portfolio allocation to RRPs. The differences between Eastern and Western Europe in this regard can be attributed to a variety of factors&#x02014;including, but not limited to, their distinct political, economic, and cultural contexts.</p>
<p>Lastly, Bichay did not take into account the potential influence of bargaining model theory and/or importance/salience theory. While previous research has shown that a party&#x00027;s seat share is crucial for dividing ministerial portfolios within coalition governments, this logic may not necessarily apply to RRPs. In particular, for RRPs operating in highly unfavorable contexts&#x02014;such as in Nordic countries like Sweden or in Germany&#x02014;seat share alone may carry less weight. Instead, the key factor may be whether these parties can convince traditional mainstream parties that their inclusion would enhance the coalition government&#x00027;s policy viability. In other words, bargaining power may replace seat share as the decisive factor (Martin and Vanberg, <xref ref-type="bibr" rid="B70">2014</xref>)&#x02014;especially when the importance or policy salience of specific ministerial portfolios is considered (Bassi, <xref ref-type="bibr" rid="B14">2017</xref>)&#x02014;not only in determining RRPs&#x00027; ministerial portfolio allocation, but also in whether mainstream parties are willing to collaborate with them in the first place (Backlund, <xref ref-type="bibr" rid="B10">2023</xref>). In summary, the hypothesis that RRPs have achieved normalization/mainstreaming in the quantitative and qualitative allocation of ministerial portfolios warrants further investigation.</p>
<p>While the critiques mentioned above may seem overly stringent for research that is less methodologically rigorous, Bichay (<xref ref-type="bibr" rid="B16">2021</xref>) still deserves high praise for addressing the research gap in the quantitative and qualitative allocation of ministerial portfolios to RRPs. Building on this perspective, this paper aims to advance the research in this area by creating a more comprehensive and transparent dataset, incorporating a broader range of variables, and applying more standardized research methods. In doing so, it seeks to make a further contribution to the study of ministerial portfolio allocation, RRPs, and the relationship between the two.</p></sec>
<sec id="s4">
<title>4 Empirical analysis</title>
<sec>
<title>4.1 Data and methods</title>
<p>When testing Quantitative Hypotheses, we use ordinary least-squares linear regression, the most standard and widely accepted method. The independent variables are the seat share of RRPs in coalition governments (Siaroff, <xref ref-type="bibr" rid="B98">2019</xref>; European Journal of Political Research Political Data Yearbook<xref ref-type="fn" rid="fn0012"><sup>12</sup></xref>) and their bargaining power, measured as the power index/vote weight (Shapley and Shubik, <xref ref-type="bibr" rid="B97">1954</xref>). As previously noted, the power index/vote weight measures how often a given party transforms a losing coalition into a winning one&#x02014;that is, how often its inclusion secures a parliamentary majority (i.e., typically 50% &#x0002B; 1 seat).</p>
<p>The formula is:</p>
<disp-formula id="E1"><mml:math id="M1"><mml:mtable columnalign='left'><mml:mtr><mml:mtd><mml:mtext>power&#x000A0;index/vote&#x000A0;weight&#x000A0;of&#x000A0;party&#x000A0;</mml:mtext><mml:mi>i</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mtext>Number&#x000A0;of&#x000A0;orderings&#x000A0;in&#x000A0;which&#x000A0;party&#x000A0;</mml:mtext><mml:mi>i</mml:mi><mml:mtext>&#x000A0;is&#x000A0;pivotal</mml:mtext></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>!</mml:mo></mml:mrow></mml:mfrac></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>n</italic> represents the number of parties, and <italic>n</italic>! is the total number of all possible orderings of those <italic>n</italic> parties.<xref ref-type="fn" rid="fn0013"><sup>13</sup></xref></p>
<p>Additionally, as shown in Section 3, scholars have observed that the normalization/mainstreaming of RRPs have become increasingly frequent and significant over time. Therefore, to examine whether the analysis results on the ministerial portfolio allocation to RRPs change when time is considered as a factor, we will conduct additional regression analyses with time included as a control variable.</p>
<p>The dependent variable is the share of ministerial portfolios held by RRPs in coalition governments. The data source is the database of &#x0201C;WHO governs in Europe and beyond&#x0201D;.<xref ref-type="fn" rid="fn0014"><sup>14</sup></xref> This database contains information about cabinet duration, the names of various ministerial portfolios and the individuals appointed to them, and the partisan affiliation of each minister at the time a particular cabinet is appointed in 48 European democratic states.<xref ref-type="fn" rid="fn0015"><sup>15</sup></xref> We extracted data from 13 European countries, covering 22 RRPs and 74 coalition governments, spanning from October 1993 (Slovakia) to January 2024 (Switzerland) (see also <xref ref-type="supplementary-material" rid="SM1">Appendix 1</xref>).<xref ref-type="fn" rid="fn0016"><sup>16</sup></xref></p>
<p>When considering the importance of ministerial portfolios, we need to weigh the different ministerial portfolios held by RRPs.<xref ref-type="fn" rid="fn0017"><sup>17</sup></xref> We utilize the Portfolio Importance Scores for Western European countries (Druckman and Warwick, <xref ref-type="bibr" rid="B40">2005</xref>) and Eastern European countries (Druckman and Roberts, <xref ref-type="bibr" rid="B39">2008</xref>), derived from large-scale expert surveys.<xref ref-type="fn" rid="fn0018"><sup>18</sup></xref></p>
<p>While most democracies include a set of core ministerial portfolios&#x02014;such as head of government, Foreign Affairs, and Finance&#x02014;the structure and composition of additional ministerial portfolios vary significantly across countries. Even within parliamentary cabinet systems, differences in coalition dynamics, administrative traditions, and institutional rules lead to considerable variation in how responsibilities are distributed, ministerial portfolios are reshaped and renamed, and ministries are reorganized. These variations introduce complexities that can obscure cross-national comparisons (see also text footnote 11). In such cases, like Druckman and Warwick (<xref ref-type="bibr" rid="B40">2005</xref>) and Druckman and Roberts (<xref ref-type="bibr" rid="B39">2008</xref>), the importance of a ministerial portfolio formed by combining two or more posts was calculated as the sum of the mean importance scores of the separate posts. When obtaining separate scores for different posts combined into a single ministerial portfolio, the total mean score was evenly divided among them (see also Bucur, <xref ref-type="bibr" rid="B21">2016</xref>, p. 6) (for the Portfolio Importance Scores of ministerial portfolios across different cabinets in various countries, see <xref ref-type="supplementary-material" rid="SM3">Appendix 3</xref>).</p>
<p>In testing the Qualitative Hypothesis, we will employ a conditional logit regression analysis, following the approach of B&#x000E4;ck et al. (<xref ref-type="bibr" rid="B7">2011</xref>). The data are divided into 20 groups, each representing a different ministerial portfolio (details provided later).<xref ref-type="fn" rid="fn0019"><sup>19</sup></xref> The dependent variable is a binary indicator of whether an RRP obtained a specific ministerial portfolio (1 = obtained, 0 = not obtained). The seat share of RRPs in the coalition government and their power index/vote weight are included as control variables. Meanwhile, similar to the analysis of the quantitative allocation of ministerial portfolios to RRPs, we will also conduct additional analyses to examine the potential impact of time on the qualitative aspect, including time as a control variable.</p>
<p>The independent variable is the policy salience assigned to each specific ministerial portfolio by RRPs. To measure this, the study also draws on the research by B&#x000E4;ck et al. (<xref ref-type="bibr" rid="B7">2011</xref>) and utilizes data from the Comparative Manifesto Project (Lehmann et al., <xref ref-type="bibr" rid="B64">2024</xref>). This salience-based approach is well-suited for examining whether RRPs, like traditional mainstream parties, exhibit a pattern where greater emphasis on specific policy areas in their electoral programs corresponds to a higher likelihood of securing ministerial portfolios governing those areas.</p>
<p>As mentioned earlier, ministerial portfolios often have different names in different countries, and the policy jurisdictions of ministerial portfolios may vary substantially across countries. Therefore, when examining the qualitative allocation of ministerial portfolios, B&#x000E4;ck et al. (<xref ref-type="bibr" rid="B7">2011</xref>, p. 453) suggested a &#x0201C;maximalist approach&#x0201D;, which involves using a large number of categories in different combinations, allowing the repetition of categories for several ministerial portfolios. This approach maximizes the information available in the CMP dataset and provides the widest possible picture of the policy jurisdiction of ministerial portfolios (see also D&#x000E4;ubler et al., <xref ref-type="bibr" rid="B32">2024</xref>).</p>
<p>B&#x000E4;ck et al. (<xref ref-type="bibr" rid="B7">2011</xref>) identified 13 general categories of the most important ministerial portfolios in Western European countries.<xref ref-type="fn" rid="fn0020"><sup>20</sup></xref> However, this paper takes a pan-European perspective and considers all the ministerial portfolios that RRPs have held to date (see also <xref ref-type="supplementary-material" rid="SM1">Appendix 1</xref>). Therefore, we have made some adjustments to the 13 general categories, resulting in 20 general categories (For details on the specific assignment of CMP categories to ministerial portfolios, see <xref ref-type="supplementary-material" rid="SM4">Appendix 4</xref>):</p>
<list list-type="simple">
<list-item><p>(1) Foreign Affairs</p></list-item>
<list-item><p>(2) Interior</p></list-item>
<list-item><p>(3) Justice</p></list-item>
<list-item><p>(4) Finance</p></list-item>
<list-item><p>(5) Economic Affairs</p></list-item>
<list-item><p>(6) Defense</p></list-item>
<list-item><p>(7) Health, Labor, Social affairs, Social Security, Welfare</p></list-item>
<list-item><p>(8) Education</p></list-item>
<list-item><p>(9) Agriculture, Fisheries, Food, Forestry</p></list-item>
<list-item><p>(10) Infrastructure</p></list-item>
<list-item><p>(11) Natural Resources, Environment</p></list-item>
<list-item><p>(12) Family, Generations, Birth, Equal Opportunity</p></list-item>
<list-item><p>(13) Integration, Immigration</p></list-item>
<list-item><p>(14) Public Administration</p></list-item>
<list-item><p>(15) Culture, Public Services, Sports, Tourism</p></list-item>
<list-item><p>(16) Transport, Innovation, Technology, Communication</p></list-item>
<list-item><p>(17) Development Cooperation, Foreign Trade</p></list-item>
<list-item><p>(18) Posts and Telecommunications</p></list-item>
<list-item><p>(19) Petroleum, Energy</p></list-item>
<list-item><p>(20) Regional Affairs and Autonomies</p></list-item>
</list></sec>
<sec>
<title>4.2 Analysis outcomes of quantitative hypotheses</title>
<p><xref ref-type="table" rid="T1">Table 1</xref> presents the descriptive statistics for the ordinary least-squares linear regression, while <xref ref-type="table" rid="T2">Tables 2</xref> and <xref ref-type="table" rid="T3">3</xref> present the results of the ordinary least-squares linear regression without and with consideration of ministerial portfolio importance, respectively. The results from models (1), (3), and (5) support the first part of Quantitative Hypothesis 1, confirming the strong proportionality between RRPs&#x00027; seat share and ministerial portfolio share. The seat share coefficients are all highly significant at the 1% level and generally within the expected proportional range, though varying in their proximity to 1 (see also text footnote 9). The constant terms remain relatively close to zero, reinforcing the proportional relationship. Similarly, the results from models (7), (9), and (11) support the latter part of Quantitative Hypothesis 1, confirming that the proportionality between RRPs&#x00027; seat share and ministerial portfolio share holds even when ministerial portfolio importance is considered. The seat share coefficients are all highly significant at the 1% level and generally within the expected proportional range, though their proximity to 1 varies. The constant terms remain relatively close to zero, further reinforcing the proportional relationship.</p>
<table-wrap position="float" id="T1">
<label>Table 1</label>
<caption><p>Descriptive statistics A.</p></caption>
<table frame="box" rules="all">
<thead>
<tr style="background-color:#919498;color:#ffffff">
<th valign="top" align="left"><bold>Statistic</bold></th>
<th valign="top" align="left"><bold><italic>N</italic></bold></th>
<th valign="top" align="center"><bold>Mean</bold></th>
<th valign="top" align="left"><bold>St. Dev</bold>.</th>
<th valign="top" align="center"><bold>Min</bold></th>
<th valign="top" align="center"><bold>Max</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Total number of ministerial portfolios</td>
<td valign="top" align="left">87</td>
<td valign="top" align="center">17.253</td>
<td valign="top" align="left">5.138</td>
<td valign="top" align="center">7</td>
<td valign="top" align="center">26</td>
</tr> <tr>
<td valign="top" align="left">The number of ministerial portfolios held by RRPs</td>
<td valign="top" align="left">87</td>
<td valign="top" align="center">3.253</td>
<td valign="top" align="left">1.844</td>
<td valign="top" align="center">1</td>
<td valign="top" align="center">10</td>
</tr> <tr>
<td valign="top" align="left">The proportion of ministerial portfolios held by RRPs</td>
<td valign="top" align="left">87</td>
<td valign="top" align="center">0.197</td>
<td valign="top" align="left">0.106</td>
<td valign="top" align="center">0.048</td>
<td valign="top" align="center">0.5</td>
</tr> <tr>
<td valign="top" align="left">The weighted proportion of ministerial portfolios held by RRPs</td>
<td valign="top" align="left">54</td>
<td valign="top" align="center">0.179</td>
<td valign="top" align="left">0.109</td>
<td valign="top" align="center">0.051</td>
<td valign="top" align="center">0.433</td>
</tr> <tr>
<td valign="top" align="left">The total number of seats held by coalition partners</td>
<td valign="top" align="left">86</td>
<td valign="top" align="center">162.395</td>
<td valign="top" align="left">114.18</td>
<td valign="top" align="center">21</td>
<td valign="top" align="center">368</td>
</tr> <tr>
<td valign="top" align="left">The number of coalition seats held by RRPs</td>
<td valign="top" align="left">86</td>
<td valign="top" align="center">41.93</td>
<td valign="top" align="left">38.868</td>
<td valign="top" align="center">2</td>
<td valign="top" align="center">138</td>
</tr> <tr>
<td valign="top" align="left">The proportion of coalition seats held by RRPs</td>
<td valign="top" align="left">86</td>
<td valign="top" align="center">0.247</td>
<td valign="top" align="left">0.11</td>
<td valign="top" align="center">0.056</td>
<td valign="top" align="center">0.502</td>
</tr> <tr>
<td valign="top" align="left">The power index/vote weight of RRPs within the coalition government</td>
<td valign="top" align="left">86</td>
<td valign="top" align="center">0.146</td>
<td valign="top" align="left">0.095</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0.415</td>
</tr></tbody>
</table>
</table-wrap>

<table-wrap position="float" id="T2">
<label>Table 2</label>
<caption><p>Results of ordinary least-squares linear regression (unweighted).</p></caption>
<table frame="box" rules="all">
<thead>
<tr style="background-color:#919498;color:#ffffff">
<th/>
<th valign="top" align="left" colspan="6"><bold>Ministerial Portfolio Shares</bold></th>
</tr>
</thead>
<tbody>
<tr style="background-color:#919498;color:#ffffff">
<td/>
<td valign="top" align="left" colspan="2"><bold>Europe</bold></td>
<td valign="top" align="left" colspan="2"><bold>Western Europe</bold></td>
<td valign="top" align="left" colspan="2"><bold>Eastern Europe</bold></td>
</tr>
 <tr style="background-color:#919498;color:#ffffff">
<td/>
<td valign="top" align="left"><bold>Model (1)</bold></td>
<td valign="top" align="left"><bold>Model (2)</bold></td>
<td valign="top" align="left"><bold>Model (3)</bold></td>
<td valign="top" align="left"><bold>Model (4)</bold></td>
<td valign="top" align="left"><bold>Model (5)</bold></td>
<td valign="top" align="left"><bold>Model (6)</bold></td>
</tr> <tr>
<td valign="top" align="left">Seat share</td>
<td valign="top" align="left">0.677<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">0.604<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">1.171<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
</tr>
 <tr>
<td/>
<td valign="top" align="left">(0.075)</td>
<td/>
<td valign="top" align="left">(0.102)</td>
<td/>
<td valign="top" align="left">(0.129)</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Power index/vote weight</td>
<td/>
<td valign="top" align="left">0.724<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">0.627<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">1.255<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="left">(0.093)</td>
<td/>
<td valign="top" align="left">(0.125)</td>
<td/>
<td valign="top" align="left">(0.172)</td>
</tr> <tr>
<td valign="top" align="left">Constant</td>
<td valign="top" align="left">0.029</td>
<td valign="top" align="left">0.090<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">0.036</td>
<td valign="top" align="left">0.098<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">&#x02212;0.057<sup>&#x0002A;&#x0002A;</sup></td>
<td valign="top" align="left">0.041<sup>&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td valign="top" align="left">(0.02)</td>
<td valign="top" align="left">(0.016)</td>
<td valign="top" align="left">(0.032)</td>
<td valign="top" align="left">(0.027)</td>
<td valign="top" align="left">(0.028)</td>
<td valign="top" align="left">(0.022)</td>
</tr> <tr>
<td valign="top" align="left">Observations</td>
<td valign="top" align="left">86</td>
<td valign="top" align="left">86</td>
<td valign="top" align="left">42</td>
<td valign="top" align="left">42</td>
<td valign="top" align="left">44</td>
<td valign="top" align="left">44</td>
</tr> <tr>
<td valign="top" align="left">Adjusted <italic>R</italic><sup>2</sup></td>
<td valign="top" align="left">0.487</td>
<td valign="top" align="left">0.411</td>
<td valign="top" align="left">0.454</td>
<td valign="top" align="left">0.369</td>
<td valign="top" align="left">0.655</td>
<td valign="top" align="left">0.548</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p><sup>&#x0002A;</sup>p &#x0003C; 0.1; <sup>&#x0002A;&#x0002A;</sup>p &#x0003C; 0.05; <sup>&#x0002A;&#x0002A;&#x0002A;</sup>p &#x0003C; 0.01.</p>
</table-wrap-foot>
</table-wrap>

<table-wrap position="float" id="T3">
<label>Table 3</label>
<caption><p>Results of ordinary least-squares linear regression (weighted).</p></caption>
<table frame="box" rules="all">
<thead>
<tr style="background-color:#919498;color:#ffffff">
<th/>
<th valign="top" align="left" colspan="6"><bold>Ministerial Portfolio Shares</bold></th>
</tr>
</thead>
<tbody>
<tr style="background-color:#919498;color:#ffffff">
<td/>
<td valign="top" align="left" colspan="2"><bold>Europe</bold></td>
<td valign="top" align="left" colspan="2"><bold>Western Europe</bold></td>
<td valign="top" align="left" colspan="2"><bold>Eastern Europe</bold></td>
</tr>
 <tr style="background-color:#919498;color:#ffffff">
<td/>
<td valign="top" align="left"><bold>Model (7)</bold></td>
<td valign="top" align="left"><bold>Model (8)</bold></td>
<td valign="top" align="left"><bold>Model (9)</bold></td>
<td valign="top" align="left"><bold>Model (10)</bold></td>
<td valign="top" align="left"><bold>Model (11)</bold></td>
<td valign="top" align="left"><bold>Model (12)</bold></td>
</tr> <tr>
<td valign="top" align="left">Seat share</td>
<td valign="top" align="left">0.653<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">0.560<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">0.808<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
</tr>
 <tr>
<td/>
<td valign="top" align="left">(0.095)</td>
<td/>
<td valign="top" align="left">(0.161)</td>
<td/>
<td valign="top" align="left">(0.185)</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Power index/vote weight</td>
<td/>
<td valign="top" align="left">1.043<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">0.942<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">1.018<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="left">(0.131)</td>
<td/>
<td valign="top" align="left">(0.201)</td>
<td/>
<td valign="top" align="left">(0.261)</td>
</tr> <tr>
<td valign="top" align="left">Constant</td>
<td valign="top" align="left">0.012</td>
<td valign="top" align="left">0.032</td>
<td valign="top" align="left">0.046</td>
<td valign="top" align="left">0.058</td>
<td valign="top" align="left">&#x02212;0.022</td>
<td valign="top" align="left">0.024</td>
</tr>
 <tr>
<td/>
<td valign="top" align="left">(0.026)</td>
<td valign="top" align="left">(0.021)</td>
<td valign="top" align="left">(0.053)</td>
<td valign="top" align="left">(0.038)</td>
<td valign="top" align="left">(0.034)</td>
<td valign="top" align="left">(0.027)</td>
</tr> <tr>
<td valign="top" align="left">Observations</td>
<td valign="top" align="left">53</td>
<td valign="top" align="left">53</td>
<td valign="top" align="left">30</td>
<td valign="top" align="left">30</td>
<td valign="top" align="left">23</td>
<td valign="top" align="left">23</td>
</tr> <tr>
<td valign="top" align="left">Adjusted <italic>R</italic><sup>2</sup></td>
<td valign="top" align="left">0.468</td>
<td valign="top" align="left">0.544</td>
<td valign="top" align="left">0.278</td>
<td valign="top" align="left">0.418</td>
<td valign="top" align="left">0.451</td>
<td valign="top" align="left">0.392</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p><sup>&#x0002A;</sup>p &#x0003C; 0.1; <sup>&#x0002A;&#x0002A;</sup>p &#x0003C; 0.05; <sup>&#x0002A;&#x0002A;&#x0002A;</sup>p &#x0003C; 0.01.</p>
</table-wrap-foot>
</table-wrap>




<p>Even when time is included as a control variable (<xref ref-type="supplementary-material" rid="SM5">Appendix 5</xref>), the analysis results remain largely unchanged from those presented above. Therefore, regardless of whether ministerial portfolio importance is considered, whether the analysis focuses on All Europe, Western Europe, or Eastern Europe, or whether the time variable is controlled, RRPs, like other traditional mainstream parties, demonstrate a strong proportional relationship between their seat share and ministerial portfolio share in coalition governments. Thus, seat share is a highly reliable predictor of ministerial portfolio share,<xref ref-type="fn" rid="fn0021"><sup>21</sup></xref> and Quantitative Hypothesis 1 is supported.</p>
<p>However, it is also important to note that while RRPs exhibit a strong proportional relationship between their seat share in coalition governments and their ministerial portfolio share, as mentioned earlier, this relationship is not perfect. Except for model (5), RRPs often need to contribute a larger seat share to secure a comparable return in terms of ministerial portfolio share. Additionally, compared to Western RRPs, Eastern RRPs show a more proportional relationship between their seat share and ministerial portfolio share in coalition governments, regardless of whether ministerial portfolio importance is considered.<xref ref-type="fn" rid="fn0022"><sup>22</sup></xref></p>
<p>The conclusions regarding Quantitative Hypothesis 2 are somewhat mixed. On one hand, seat share generally shows higher adjusted <italic>R</italic><sup>2</sup> values compared to the power index/vote weight, indicating that seat share tends to have stronger explanatory power for ministerial portfolio shares in most cases. On the other hand, except for model (6), the regression coefficients of the power index/vote weight are generally closer to one compared to those of seat share. Particularly when considering ministerial portfolio importance, RRPs&#x00027; power index/vote weight shows an almost perfect proportional relationship with their ministerial portfolio shares in All Europe, Western Europe, and Eastern Europe. This indicates that, unlike traditional mainstream parties, for RRPs, the power index/vote weight, which represents bargaining power, has a stronger proportional relationship with the ministerial portfolio shares they receive in coalition governments compared to their seat share. Similarly, even when controlling for the time variable, the results remain nearly identical (<xref ref-type="supplementary-material" rid="SM5">Appendix 5</xref>), indicating that the power index/vote weight also proves to be a more reliable predictor of RRPs&#x00027; ministerial portfolio shares than seat share. Therefore, Quantitative Hypothesis 2 is only partially supported.</p></sec>
<sec>
<title>4.3 Analysis outcomes of qualitative hypothesis</title>
<p><xref ref-type="table" rid="T4">Table 4</xref> presents the descriptive statistics for the conditional logit regression. From the results of the conditional logit regression (<xref ref-type="table" rid="T5">Table 5</xref>), since policy salience does not show statistical significance, RRPs, unlike other traditional mainstream parties, do not necessarily secure the ministerial portfolios they emphasize in their electoral manifestos when entering coalition governments. <xref ref-type="fig" rid="F2">Figure 2</xref> further confirms the robustness of the conditional logit regression results. In <xref ref-type="fig" rid="F2">Figure 2</xref>, the vertical and horizontal dashed lines represent the mean values of the policy salience of ministerial portfolios and the probability of ministerial portfolio allocation, respectively. These two lines divide the 20 ministerial portfolios into four categories:</p>
<list list-type="bullet">
<list-item><p>The top-left quadrant includes five ministerial portfolios with low policy salience but high allocation probability.</p></list-item>
<list-item><p>The bottom-left quadrant includes seven ministerial portfolios with both low policy salience and low allocation probability.</p></list-item>
<list-item><p>The bottom-right quadrant includes four ministerial portfolios with high policy salience but low allocation probability.</p></list-item>
<list-item><p>The top-right quadrant includes four ministerial portfolios with both high policy salience and high allocation probability.</p></list-item>
</list>

<table-wrap position="float" id="T4">
<label>Table 4</label>
<caption><p>Descriptive statistics B.</p></caption>
<table frame="box" rules="all">
<thead>
<tr style="background-color:#919498;color:#ffffff">
<th valign="top" align="left"><bold>Statistic</bold></th>
<th valign="top" align="left"><bold><italic>N</italic></bold></th>
<th valign="top" align="center"><bold>Mean</bold></th>
<th valign="top" align="left"><bold>St. Dev</bold>.</th>
<th valign="top" align="center"><bold>Min</bold></th>
<th valign="top" align="center"><bold>Max</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Ministerial portfolios</td>
<td valign="top" align="left">720</td>
<td valign="top" align="center">0.178</td>
<td valign="top" align="left">0.383</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">1</td>
</tr> <tr>
<td valign="top" align="left">Policy salience</td>
<td valign="top" align="left">720</td>
<td valign="top" align="center">9.123</td>
<td valign="top" align="left">9.393</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">57.692</td>
</tr> <tr>
<td valign="top" align="left">Seat share</td>
<td valign="top" align="left">720</td>
<td valign="top" align="center">0.261</td>
<td valign="top" align="left">0.107</td>
<td valign="top" align="center">0.08</td>
<td valign="top" align="center">0.5</td>
</tr> <tr>
<td valign="top" align="left">Power index/vote weight</td>
<td valign="top" align="left">720</td>
<td valign="top" align="center">0.164</td>
<td valign="top" align="left">0.101</td>
<td valign="top" align="center">0.019</td>
<td valign="top" align="center">0.415</td>
</tr></tbody>
</table>
</table-wrap>

<table-wrap position="float" id="T5">
<label>Table 5</label>
<caption><p>Results of conditional logit regression.</p></caption>
<table frame="box" rules="all">
<thead>
<tr style="background-color:#919498;color:#ffffff">
<th/>
<th valign="top" align="left" colspan="6"><bold>Ministerial Portfolio Acquisition (1</bold> = <bold>Yes, 0</bold> = <bold>No)</bold></th>
</tr>
</thead>
<tbody>
<tr style="background-color:#919498;color:#ffffff">
<td/>
<td valign="top" align="left" colspan="2"><bold>All Europe</bold></td>
<td valign="top" align="left" colspan="2"><bold>Western Europe</bold></td>
<td valign="top" align="left" colspan="2"><bold>Eastern Europe</bold></td>
</tr>
 <tr style="background-color:#919498;color:#ffffff">
<td/>
<td valign="top" align="left"><bold>Model (1)</bold></td>
<td valign="top" align="left"><bold>Model (2)</bold></td>
<td valign="top" align="left"><bold>Model (3)</bold></td>
<td valign="top" align="left"><bold>Model (4)</bold></td>
<td valign="top" align="left"><bold>Model (5)</bold></td>
<td valign="top" align="left"><bold>Model (6)</bold></td>
</tr> <tr>
<td valign="top" align="left">Policy salience</td>
<td valign="top" align="left">0.011</td>
<td valign="top" align="left">0.011</td>
<td valign="top" align="left">0.009</td>
<td valign="top" align="left">0.008</td>
<td valign="top" align="left">0.013</td>
<td valign="top" align="left">0.013</td>
</tr>
 <tr>
<td/>
<td valign="top" align="left">(0.015)</td>
<td valign="top" align="left">(0.014)</td>
<td valign="top" align="left">(0.023)</td>
<td valign="top" align="left">(0.021)</td>
<td valign="top" align="left">(0.025)</td>
<td valign="top" align="left">(0.025)</td>
</tr> <tr>
<td valign="top" align="left">Seat share</td>
<td valign="top" align="left">4.947<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">4.422<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">6.567<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
</tr>
 <tr>
<td/>
<td valign="top" align="left">(1.013)</td>
<td/>
<td valign="top" align="left">(1.405)</td>
<td/>
<td valign="top" align="left">(2.094)</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Power index/vote weight</td>
<td/>
<td valign="top" align="left">3.512<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
<td/>
<td valign="top" align="left">2.072</td>
<td/>
<td valign="top" align="left">7.814<sup>&#x0002A;&#x0002A;&#x0002A;</sup></td>
</tr>
 <tr>
<td/>
<td/>
<td valign="top" align="left">(0.975)</td>
<td/>
<td valign="top" align="left">(1.278)</td>
<td/>
<td valign="top" align="left">(2.546)</td>
</tr> <tr>
<td valign="top" align="left">Observations</td>
<td valign="top" align="left">720</td>
<td valign="top" align="left">720</td>
<td valign="top" align="left">380</td>
<td valign="top" align="left">380</td>
<td valign="top" align="left">340</td>
<td valign="top" align="left">340</td>
</tr> <tr>
<td valign="top" align="left">Log likelihood</td>
<td valign="top" align="left">&#x02212;254.575</td>
<td valign="top" align="left">&#x02212;260.87</td>
<td valign="top" align="left">&#x02212;133.679</td>
<td valign="top" align="left">&#x02212;137.888</td>
<td valign="top" align="left">&#x02212;90.3</td>
<td valign="top" align="left">&#x02212;90.667</td>
</tr> <tr>
<td valign="top" align="left">McFadden&#x00027;s Pseudo <italic>R</italic><sup>2</sup></td>
<td valign="top" align="left">0.048</td>
<td valign="top" align="left">0.024</td>
<td valign="top" align="left">0.040</td>
<td valign="top" align="left">0.010</td>
<td valign="top" align="left">0.053</td>
<td valign="top" align="left">0.049</td>
</tr> <tr>
<td valign="top" align="left">AIC</td>
<td valign="top" align="left">513.149</td>
<td valign="top" align="left">525.740</td>
<td valign="top" align="left">271.358</td>
<td valign="top" align="left">279.777</td>
<td valign="top" align="left">184.6</td>
<td valign="top" align="left">185.333</td>
</tr> <tr>
<td valign="top" align="left">BIC</td>
<td valign="top" align="left">518.853</td>
<td valign="top" align="left">531.444</td>
<td valign="top" align="left">276.097</td>
<td valign="top" align="left">284.516</td>
<td valign="top" align="left">188.384</td>
<td valign="top" align="left">189.117</td>
</tr> <tr>
<td valign="top" align="left">% Correctly predicted</td>
<td valign="top" align="left">82.361</td>
<td valign="top" align="left">83.056</td>
<td valign="top" align="left">81.316</td>
<td valign="top" align="left">81.579</td>
<td valign="top" align="left">85.294</td>
<td valign="top" align="left">84.706</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p><sup>&#x0002A;</sup>p &#x0003C; 0.1; <sup>&#x0002A;&#x0002A;</sup>p &#x0003C; 0.05; <sup>&#x0002A;&#x0002A;&#x0002A;</sup>p &#x0003C; 0.01.</p>
</table-wrap-foot>
</table-wrap>



<fig id="F2" position="float">
<label>Figure 2</label>
<caption><p>Policy salience and the probability of ministerial portfolio allocation.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fpos-07-1500403-g0002.tif"/>
</fig>




<p>This pattern reveals that while RRPs are relatively likely to be allocated ministerial portfolios they assign high policy salience to&#x02014;such as those responsible for Social Affairs, Interior, Culture, and Justice&#x02014;they often fail to secure others they also consider highly salient, such as ministerial portfolios covering Family Policy, Economic Affairs, Public Administration, and especially Immigration policy, which ranks highest in policy salience. At the same time, RRPs are frequently allocated ministerial portfolios they assign relatively low policy salience to, such as those responsible for Defense, Agriculture, Transport, and Education. Therefore, the Qualitative Hypothesis must be rejected.</p>
<p>Moreover, except for model (4), the seat share of RRPs in coalition governments and their power index/vote weight both demonstrate strong statistical significance. This indicates that, compared to the salience RRPs assign to specific policy areas, seat share and bargaining power remain the more influential factors in determining whether RRPs can secure a particular ministerial portfolio. Once again, even when controlling for the time variable, the results remain nearly identical (<xref ref-type="supplementary-material" rid="SM5">Appendix 5</xref>), further confirming the consistently strong association between seat share, power index/vote weight, and RRPs&#x00027; qualitative allocation of ministerial portfolios.<xref ref-type="fn" rid="fn0023"><sup>23</sup></xref></p>
<p>Additionally, the regression coefficients for seat share and power index/vote weight in Eastern Europe are noticeably higher than those in Western Europe, indicating that the influence of seat share and bargaining power on the allocation of specific ministerial portfolios is more pronounced for RRPs in Eastern Europe compared to Western Europe. Interestingly, the regression coefficients for seat share are higher than those for power index/vote weight for RRPs in Western Europe, whereas the opposite is true for RRPs in Eastern Europe. This suggests that the impact of seat share and power index/vote weight on the qualitative allocation of ministerial portfolios to RRPs varies across regions.</p></sec>
<sec>
<title>4.4 Robustness check: comparative case studies of Austria&#x00027;s FP&#x000D6; in 2017 and Slovakia&#x00027;s SR in 2020</title>
<p>To provide a more robust empirical foundation for the preceding analysis, this section presents a concise comparative case study of Austria&#x00027;s Freiheitliche Partei &#x000D6;sterreichs (FP&#x000D6;) in 2017 and Slovakia&#x00027;s Sme Rodina (SR) in 2020. These two cases were selected based on two key considerations. First, at the national level, Austria and Slovakia are neighboring countries with historically close ties. Importantly, while Austria represents Western Europe and Slovakia post-communist Eastern Europe, both countries operate under similar multi-party parliamentary cabinet systems and have experienced substantial influence from RRPs in their political landscapes. Second, at the party level, FP&#x000D6; and SR are not only members of the same RRP party family but also part of the Identity and Democracy political group in the European Parliament. Ideologically, the two parties are often seen as closely aligned (Antal, <xref ref-type="bibr" rid="B4">2023</xref>, p. 33). Both have benefited from &#x0201C;reputational shields&#x0201D; (Ivarsflaten, <xref ref-type="bibr" rid="B58">2006</xref>), have been centered around charismatic leadership figures (Heinz-Christian Strache for FP&#x000D6; and Boris Koll&#x000E1;r for SR), and entered coalition governments as junior partners after spending more than a decade in opposition, each doing so as the third-largest party in parliament at the time. Given these parallels, the two cases are particularly well suited for a comparative analysis based on the most similar systems design.</p>
<p>Austria held its legislative election on October 15, 2017, in which the FP&#x000D6; secured 25.97% of the vote, becoming the third-largest party, just behind the Sozialdemokratische Partei &#x000D6;sterreichs (SP&#x000D6;) at 26.86%. Subsequently, in mid-December of the same year, the FP&#x000D6; officially joined the coalition government led by the first-place &#x000D6;sterreichische Volkspartei (&#x000D6;VP, 31.47%), forming the Kurz I cabinet. According to Twist (<xref ref-type="bibr" rid="B106">2019</xref>, p. 74&#x02013;76), despite not having governed together with the FP&#x000D6; for more than a decade, the &#x000D6;VP&#x00027;s decision to form a coalition government with the FP&#x000D6;&#x02014;rather than with its traditional partner, the SP&#x000D6;&#x02014;was grounded in the belief that such an alliance would allow the &#x000D6;VP to pursue more of its policy objectives. One of the key issues in the campaign was immigration and asylum, historically a core issue for the FP&#x000D6;. However, under Sebastian Kurz&#x00027;s leadership and the rebranding of the &#x000D6;VP as the &#x0201C;new People&#x00027;s Party&#x0201D;, the &#x000D6;VP increasingly encroached upon the FP&#x000D6;&#x00027;s issue ownership in this area, adopting many of its positions during the campaign. Conversely, in response to the growing importance of tax reduction as a campaign issue, the FP&#x000D6; strategically expanded its focus on economic matters in order to strengthen its bargaining position. It even released a dedicated economic platform during the election campaign. The convergence of &#x000D6;VP and FP&#x000D6; policy preferences was later reflected in the coalition agreement (Heinisch and Werner, <xref ref-type="bibr" rid="B54">2021</xref>), which emphasized shared priorities on fiscal, immigration, and European issues&#x02014;including income and tax cuts, reduced benefits and tighter asylum regulations, and rejection of Turkey&#x00027;s EU accession (Bodlos and Plescia, <xref ref-type="bibr" rid="B17">2018</xref>, p. 1360&#x02013;1361).</p>
<p>Under this coalition agreement, the FP&#x000D6;&#x02014;with 51 parliamentary seats, accounting for 45.1% of the coalition government&#x00027;s seat share and a power index/vote weight of 0.333&#x02014;was allocated 5 out of 14 ministerial portfolios, or 35.7% of the total, a distribution more closely aligned with its power index/vote weight than with its seat share. The five ministerial portfolios were: (1) Vice-Chancellor and Minister of Civil Service and Sport, and the Ministries of (2) Interior, (3) National Defense, (4) Health and Social Affairs, and (5) Infrastructure. Among these, the FP&#x000D6; secured the highly salient Ministry of the Interior (policy salience = 26.77), a key ministerial portfolio for controlling immigration and asylum policies. However, the reputational benefits of controlling this issue area were arguably diminished by the &#x000D6;VP&#x00027;s parallel appropriation of the same issue. While the FP&#x000D6; also obtained the Ministry of Health and Social Affairs (policy salience = 25.89), it failed to secure other ministerial portfolios it rated as highly salient, such as the Ministry of Justice (policy salience = 22.12) and the Ministry of Women, Family and Youth (policy salience = 12.17). Instead, it was allocated ministerial portfolios with lower salience for the party, including National Defense and Infrastructure (both at 4.87) (Lehmann et al., <xref ref-type="bibr" rid="B64">2024</xref>). Given that even the SP&#x000D6; had expressed openness to forming a coalition government with the FP&#x000D6; prior to the election (Bodlos and Plescia, <xref ref-type="bibr" rid="B17">2018</xref>, p. 1360; Twist, <xref ref-type="bibr" rid="B106">2019</xref>, p. 81), the eventual distribution of ministerial portfolios appears underwhelming in light of the FP&#x000D6;&#x00027;s relatively strong strategic position during the coalition negotiations.</p>
<p>Slovakia held its legislative election on February 29, 2020. Founded in 2011, SR surprised many by securing 8.24% of the vote, becoming the third-largest party. Later that March, it officially joined the Matovi&#x0010D; Cabinet&#x02014;a coalition government led by the largest party, Oby&#x0010D;ajn&#x000ED; ludia a nez&#x000E1;visl&#x000E9; osobnosti (OLaNO, 25.3%). The 2020 election was dominated by two long-standing themes in Slovak politics: corruption and redistribution. On the one hand, corruption had been a persistent concern since the early 1990s, gaining renewed salience in the late 2010s. On the other hand, since the early 2000s, party competition had increasingly centered on socio-economic questions, particularly regarding how to structure the economy to promote growth and how to equitably distribute its benefits. The ability to mobilize voters around these two themes was a decisive factor in OLaNO&#x00027;s electoral success (Haughton et al., <xref ref-type="bibr" rid="B52">2022</xref>). SR emerged in this same political context, presenting a platform that combined concrete policy priorities&#x02014;such as reforming Slovakia&#x00027;s poorly managed governance, fighting corruption, maintaining a strong anti-immigrant stance, and improving public services like healthcare and education&#x02014;with a broader socio-political agenda focused on supporting low-income families and individuals, explicitly aiming to place social protection at the center of its program. These positions won the party substantial support among low-income and less-educated groups&#x02014;particularly the working poor and so-called &#x0201C;precariat&#x0201D; (&#x00160;kolkay and &#x0017D;&#x000FA;borov&#x000E1;, <xref ref-type="bibr" rid="B101">2019</xref>, p. 20&#x02013;21; Sirov&#x000E1;tka et al., <xref ref-type="bibr" rid="B100">2022</xref>, p. 29; Antal, <xref ref-type="bibr" rid="B4">2023</xref>, p. 35&#x02013;36).</p>
<p>Upon entering the coalition government, SR held 17 parliamentary seats&#x02014;accounting for 17.9% of the coalition&#x00027;s seat share&#x02014;and had a power index/vote weight of 0.1. In return, it was allocated 2 out of 15 ministerial portfolios (13.3%), a share more closely aligned with its power index/vote weight than with its seat share. These included (1) Deputy Prime Minister and (2) Minister of Labor, Social Affairs and Family. The latter reflects the party&#x00027;s core emphasis on social welfare, while the former, which oversees legislation and strategic planning, aligns with SR&#x00027;s calls to reform public governance. During coalition negotiations, SR leader Boris Koll&#x000E1;r also proposed an ambitious housing initiative&#x02014;constructing 25,000 affordable rental units for low-income residents (Sirotnikova, <xref ref-type="bibr" rid="B99">2020</xref>). While SR did not formally obtain the Ministry of Transport and Construction, which would oversee such a project, it reportedly secured the appointment of an ally to that post (L&#x000E1;&#x00161;tic, <xref ref-type="bibr" rid="B60">2021</xref>, p. 353). Given SR&#x00027;s relatively weak position in the coalition government&#x02014;especially compared to OLaNO&#x00027;s 53 seats&#x02014;and the party&#x00027;s reputational vulnerabilities, including alleged ties to organized crime and its association with conspiracy theories, disinformation, and anti-immigrant rhetoric (Sirotnikova, <xref ref-type="bibr" rid="B99">2020</xref>), its performance in securing key ministerial portfolios can be considered notably successful.</p>
<p>The brief comparative analysis of FP&#x000D6; and SR further reinforces the robustness of the findings presented in Sections 4.2 and 4.3. Specifically, it supports the following conclusions: (1) Seat share maintains a generally strong, though not perfect, proportional relationship with ministerial portfolio share; (2) Bargaining power exhibits a stronger proportional relationship with ministerial portfolio share than seat share does; (3) RRPs frequently receive a smaller ministerial portfolio share than their seat share would suggest; and (4) RRPs often fail to secure the specific ministerial portfolios they prioritize&#x02014;though Eastern European RRPs appear somewhat more successful in doing so. The case of SR exemplifies this dynamic well: despite its comparatively weaker position relative to FP&#x000D6; during the same period, it nonetheless performed notably well in ministerial portfolio allocation. This may suggest that Eastern European RRPs rely more on &#x0201C;soft power&#x0201D;&#x02014;including bargaining power&#x02014;rather than &#x0201C;hard power&#x0201D; such as seat share. While these two cases do not fully illustrate the fifth finding from Section 4.2&#x02014;namely, (5) that the proportional relationship between seat share and ministerial portfolio share is stronger for Eastern European RRPs than for their Western counterparts&#x02014;there is indirect support for this conclusion. The proportional ratios (i.e., ministerial portfolio share divided by seat share) are relatively close across regions (West: 0.79 vs. East: 0.74), and given the significant disparity in party strength between FP&#x000D6; and SR, the fact that SR achieved comparable outcomes lends some additional credibility to this argument. The differences in ministerial portfolio allocation between FP&#x000D6; and SR&#x02014;despite their strong similarities&#x02014;may be attributed to a range of factors, including, but not limited to, the differing political, economic, and cultural contexts of Eastern and Western Europe. The following section will offer a more detailed discussion.</p></sec></sec>
<sec id="s5">
<title>5 Discussion and limitations</title>
<p>Ministerial portfolio allocation is one of the most critical aspects of coalition formation, representing the foundation of the political process in parliamentary democracies. The study of ministerial portfolio allocation generally focuses on two dimensions: quantitative and qualitative. The quantitative allocation of ministerial portfolios examines how many ministerial portfolios each party receives, while the qualitative allocation focuses on which specific ministerial portfolios are assigned to each party. In terms of the former, the proportionality principle is regarded as one of the most reliable, well-known, and strongest empirical relationships in social science. As for the latter, scholars have argued that the more a coalition party emphasizes specific ministerial portfolios in its electoral program, the higher the likelihood that the party will secure those ministerial portfolios.</p>
<p>This paper explores the characteristics of the quantitative and qualitative allocation of ministerial portfolios to RRPs, which were once considered &#x0201C;pariah parties&#x0201D;. However, since the early twenty-first century, they have gradually undergone a process of normalization/mainstreaming. Increasingly, RRPs have entered coalition governments, accumulated governing experience, and begun to exert significant policy influence. Some RRPs are even seen as having achieved sustainable governance capabilities. Nevertheless, it is undeniable that in countries governed by RRPs, there has been a varying degree of democratic backsliding. Additionally, RRPs are perceived as significant threats and challenges to European and North Atlantic integration in international politics. Given that RRPs are typically junior partners in coalition governments, other coalition partners might be reluctant to allocate important ministerial portfolios overseeing domestic and/or international policy areas to them, or even to ministerial portfolios that RRPs themselves desire. This may result in the quantitative and/or qualitative allocation of ministerial portfolios to RRPs differing from that of traditional mainstream parties.</p>
<p>Based on the results of this paper&#x00027;s analysis, we find that regardless of whether ministerial portfolio importance is considered, and across all of Europe, Western Europe, and Eastern Europe, seat share shows imperfect but still strong proportional relationships with ministerial portfolio shares. However, while seat share typically shows higher adjusted <italic>R</italic><sup>2</sup> values compared to power index/vote weight, the regression coefficients of power index/vote weight are generally closer to one than those of seat share. Especially when considering ministerial portfolio importance, whether in all of Europe, Western Europe, or Eastern Europe, the power index/vote weight of RRPs shows an almost perfect proportional relationship with their ministerial portfolio shares. This indicates that, unlike traditional mainstream parties, for RRPs, bargaining power has a stronger proportional relationship with the ministerial portfolio shares they receive in coalition governments compared to their seat share. This result somewhat confirms our previous conjecture: because RRPs in coalition governments are always typically weaker junior partners&#x02014;and particularly given their anti-liberal democratic tendencies and their incomplete mainstreaming (see also text footnote 6), that is, operating within highly unfavorable contexts&#x02014;their ability to obtain ministerial portfolios proportional to their contributions depends more on their bargaining power.</p>
<p>Moreover, RRPs often receive fewer ministerial portfolio shares in coalition governments than their seat shares would suggest&#x02014;a pattern that runs counter to the classic &#x0201C;relative weakness effect&#x0201D; (see also text footnote 2) and may further reflect the unique ideological and reputational features of RRPs. However, Eastern European RRPs show a better proportional relationship between their seat shares and ministerial portfolio shares in coalition governments than Western European RRPs, regardless of whether ministerial portfolio importance is considered. This implies that, compared to Western Europe, Eastern European RRPs encounter fewer obstacles on their path to normalization/mainstreaming&#x02014;possibly due to the region&#x00027;s distinct post&#x02013;World War II history, the challenges of nation-building amid ethnic diversity, limited democratic experience, the rapid transition from state socialism to a market economy, and a relatively less institutionalized and more fluid party system (Minkenberg, <xref ref-type="bibr" rid="B78">2002</xref>; Bu&#x00161;t&#x000ED;kov&#x000E1;, <xref ref-type="bibr" rid="B23">2018</xref>). Therefore, although Eastern European RRPs are generally less successful overall than their Western counterparts (see also <xref ref-type="fig" rid="F1">Figure 1</xref>), their characteristics in quantitative ministerial portfolio allocation more closely resemble those of traditional mainstream parties.</p>
<p>Finally, the Qualitative Hypothesis of this paper is found to be unsupported. This result confirms our earlier conjecture that coalition partners are often reluctant to grant ministerial portfolios that are likely related to critical domestic and/or international policy areas, or even the ministerial portfolios RRPs desire&#x02014;such as those responsible for Family Policy, Economic Affairs, Public Administration, and especially Immigration policy. This conjecture is also partially supported by Kimberly A. Twist&#x00027;s research. By examining six traditional mainstream right parties and the coalition governments they participated in across five countries&#x02014;Austria, Denmark, Italy, the Netherlands, and Norway&#x02014;she found that these parties tend to hold slightly more key ministerial portfolios in coalitions with RRPs than in those without them, regardless of the role of policy preferences (Twist, <xref ref-type="bibr" rid="B106">2019</xref>, p. 25&#x02013;26).<xref ref-type="fn" rid="fn0024"><sup>24</sup></xref></p>
<p>Furthermore, the influence of seat share and power index on the allocation of specific ministerial portfolios is more pronounced for RRPs in Eastern Europe compared to Western Europe. At the same time, seat share, as a form of &#x0201C;hard power&#x0201D;, plays a more crucial role than bargaining power, considered &#x0201C;soft power&#x0201D;, in determining whether RRPs in Western Europe can secure specific ministerial portfolios. In contrast, the reverse is true for RRPs in Eastern Europe. These observations further highlight that, although Eastern European RRPs are relatively weaker than their Western counterparts, they face fewer barriers to normalization/mainstreaming&#x02014;potentially making it somewhat easier for them to secure the specific ministerial portfolios they prioritize.</p>
<p>Taken together, the above findings are further corroborated by the concise comparative case studies presented in this paper, which reinforce the empirical credibility of the results. In summary, although RRPs have made notable progress toward normalization/mainstreaming in the quantitative allocation of ministerial portfolios, they continue to encounter substantial challenges in the qualitative allocation, where normalization/mainstreaming remain largely unrealized.</p>
<p>This paper makes significant contributions to advancing research on ministerial portfolio allocation, RRPs, and the relationships between them. However, we also acknowledge some limitations. First, since RRPs&#x00027; participation in government has increased only gradually since the early twenty-first century, this study, being a &#x0201C;small-N&#x0201D; study, employs the most traditional and straightforward analytical methods. As the sample size increases, however, it is reasonable to expect that previous results&#x02014;particularly those from the conditional logit regression&#x02014;may change. At the same time, this study does not incorporate control variables in the quantitative analysis that could also potentially influence the quantitative and/or qualitative allocation of ministerial portfolios to RRPs&#x02014;such as a communist past, the duration of democratic rule, the length of EU membership, prior electoral success or government participation, and the policy distance between coalition partners.</p>
<p>Second, although the significant development of RRPs&#x00027; normalization/mainstreaming over time has been confirmed by previous scholarly research, the additional analyses conducted in this paper, which included time as a control variable, found that time was not statistically significant (<xref ref-type="supplementary-material" rid="SM5">Appendix 5</xref>). This result could be attributed to a small sample size or other technical factors, but it may also be because time represents only the visible tip of the iceberg, while the potential control variables mentioned earlier constitute the massive, hidden iceberg beneath the surface. We encourage other scholars to utilize the publicly available dataset (<xref ref-type="supplementary-material" rid="SM1">Appendices 1</xref>, <xref ref-type="supplementary-material" rid="SM3">3</xref>, <xref ref-type="supplementary-material" rid="SM4">4</xref>) to replicate this study, evaluate its findings, and refine its conclusions using alternative research methods.</p>
<p>Third, compared to more meticulous case studies, this study, being a &#x0201C;large-N&#x0201D; study, may overlook important national contexts, such as Switzerland&#x00027;s &#x0201C;magic formula,&#x0201D; the oversized coalitions in Southern European countries, the tradition of minority coalitions in Northern European countries, or the &#x0201C;red-brown alliance&#x0201D; in Central and Eastern European countries. These factors are also likely to influence the quantitative and/or qualitative allocation of ministerial portfolios to RRPs.</p>
<p>Fourth, some crucial variables related to political party interactions could also impact the quantitative and/or qualitative allocation of ministerial portfolios to RRPs. For instance, the willingness of other parties to govern with RRPs. Given that policies adopted in parliamentary systems reflect a compromise among the policy positions of coalition parties, and that coalition parties may allocate ministerial portfolios with future policy-making in mind, RRPs&#x00027; non-cooperative nature or their excessive policy distance from other coalition parties in certain policy areas (e.g., immigration) could significantly affect their coalitionability (Martin and Vanberg, <xref ref-type="bibr" rid="B70">2014</xref>; Bassi, <xref ref-type="bibr" rid="B14">2017</xref>; Backlund, <xref ref-type="bibr" rid="B10">2023</xref>). Another example is the RRPs&#x00027; willingness to enter a coalition government. If RRPs are unlikely to obtain their desired ministerial portfolios, why would they choose to join a coalition government in the first place? Could it be, as Riker (<xref ref-type="bibr" rid="B89">1962</xref>, p. 22) argued, that gaining access to power is the ultimate goal in party politics&#x02014;leading RRPs to accept concessions in ministerial portfolio allocation as the price for entering government? The case of the Rassemblement National (RN) in France appears to support this view. Since 2011, the RN has pursued a strategy of &#x0201C;d&#x000E9;diabolisation&#x0201D;&#x02014;aimed at gaining governmental credibility&#x02014;by making significant efforts to moderate its rhetoric and policies in pursuit of its long-term ambition of assuming government power, even going so far as to soften its stance on core issues such as immigration (Ivaldi, <xref ref-type="bibr" rid="B57">2016</xref>). It is therefore conceivable that, in order to join a coalition government (as forming a government alone remains unimaginable), the RN would be willing to forgo some ministerial portfolios it considers important. Beyond these factors, instances where coalition entry is enforced due to sheer party size (Tronconi, <xref ref-type="bibr" rid="B105">2015</xref>) could also influence the quantitative and/or qualitative allocation of ministerial portfolios to RRPs. The factors mentioned above warrant further investigation.</p></sec>
<sec id="s6">
<title>6 Conclusion</title>
<p>This paper may also offer potential directions for future research. First, do the characteristics of ministerial portfolio allocation to RRPs in national governments also apply to RRPs in regional governments? Given the lower importance and sensitivity of ministerial portfolio allocation in regional governments, will RRPs be more similar to other traditional mainstream parties in receiving a better proportional allocation of ministerial portfolios and/or obtaining the ministerial portfolios they desire? Second, can specific case studies further substantiate or refute the important conclusions of this paper, such as &#x0201C;RRPs need to rely more on their own bargaining power&#x0201D; or &#x0201C;coalition partners are often unwilling to allocate ministerial portfolios related to important domestic and/or international policy areas to RRPs&#x0201D;? Third, do the characteristics of ministerial portfolio allocation to RRPs apply to Radical Left Parties like Syriza, Podemos, and the Socialist People&#x00027;s Party of Denmark, or Valence Populist Parties like Italy&#x00027;s Movimento 5 Stelle (Zulianello and Larsen, <xref ref-type="bibr" rid="B113">2024</xref>), which, like RRPs, are increasingly entering coalition governments? What are the similarities and differences in ministerial portfolio allocation to these different types of parties that are in the process of normalization/mainstreaming? Fourth, a more important and challenging question concerns the role of these diverse radical and populist parties after entering government: How do they influence policy-making? What kinds of policy outcomes do they produce? What impact do they have on the overall quality of democracy? Exploring these questions through the lenses of historical political culture, institutional structures, media discourse, and elite behavior could prove especially useful in explaining cross-national variation and differences across party families. We believe that pursuing these research avenues would significantly advance the broader scholarly understanding of ministerial portfolio allocation, RRPs, and their interplay with democratic governance.</p></sec>
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<sec sec-type="data-availability" id="s7">
<title>Data availability statement</title>
<p>The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/<xref ref-type="sec" rid="s11">Supplementary material</xref>.</p>
</sec>
<sec sec-type="author-contributions" id="s8">
<title>Author contributions</title>
<p>TT: Writing &#x02013; original draft, Writing &#x02013; review &#x00026; editing.</p>
</sec>
<sec sec-type="funding-information" id="s9">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article. This research was funded by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (Grant Number: 23K18755).</p>
</sec>
<ack><p>A draft of this research was presented at the 2024 Annual Meeting of the Japanese Association of Comparative Politics (Session: Open Theme C) on June 22, 2024, in Osaka, Japan. This research has greatly benefited from the generous support of many scholars, including Mitsuo Koga (Chuo University), Takako Imai (Seikei University), Takeshi Hieda (Osaka Metropolitan University), and Serika Atsumi (Tokyo University). The author also extends heartfelt gratitude to the reviewers for their highly professional, detailed, and actionable feedback, which has significantly enhanced the readability and scientific rigor of this paper. Any remaining errors and shortcomings are entirely the responsibility of the author.</p>
</ack>
<sec sec-type="COI-statement" id="conf1">
<title>Conflict of interest</title>
<p>The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x00027;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec sec-type="supplementary-material" id="s11">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fpos.2025.1500403/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fpos.2025.1500403/full#supplementary-material</ext-link></p>
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<supplementary-material xlink:href="Data_Sheet_2.pdf" id="SM2" mimetype="application/pdf" xmlns:xlink="http://www.w3.org/1999/xlink"/>
<supplementary-material xlink:href="Data_Sheet_3.pdf" id="SM3" mimetype="application/pdf" xmlns:xlink="http://www.w3.org/1999/xlink"/>
<supplementary-material xlink:href="Data_Sheet_4.pdf" id="SM4" mimetype="application/pdf" xmlns:xlink="http://www.w3.org/1999/xlink"/>
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<fn-group>
<fn id="fn0001"><p><sup>1</sup>In this paper, the term RRPs is used in a broad sense to refer to parties that are positioned further to the right than traditional mainstream right-wing parties, such as conservatives or liberals. While RRPs accept the essence of democracy, they are considered anti-system parties, meaning that they are hostile to fundamental elements of liberal democracy, such as minority rights and the rule of law (Mudde, <xref ref-type="bibr" rid="B82">2019</xref>, p. 7&#x02013;8).</p></fn>
<fn id="fn0002"><p><sup>2</sup>As shown by the regression coefficient here, the proportionality principle is not strictly followed in ministerial portfolio allocation. Over the years, many researchers have identified a small deviation in which smaller parties tend to receive additional or &#x0201C;bonus&#x0201D; ministries beyond their proportional shares, while larger parties tend to give up such ministries. This deviation is commonly referred to as the &#x0201C;relative weakness effect&#x0201D; (Browne and Franklin, <xref ref-type="bibr" rid="B19">1973</xref>, p. 460; Schofield, <xref ref-type="bibr" rid="B94">1976</xref>, p. 34; de Mesquita, <xref ref-type="bibr" rid="B33">1979</xref>, p. 71; Browne and Frendreis, <xref ref-type="bibr" rid="B20">1980</xref>, p. 767; Raabe and Linhart, <xref ref-type="bibr" rid="B87">2013</xref>, p. 487; Martin, <xref ref-type="bibr" rid="B72">2018</xref>, p. 1184).</p></fn>
<fn id="fn0003"><p><sup>3</sup>It should be noted that the bargaining model theory posits that parties with a higher power index/vote weight have a more advantageous position in coalition government negotiations. Consequently, these parties can leverage their superior bargaining power to secure more ministerial portfolios than what the proportionality principle would suggest. This view has been supported under certain specific conditions or contexts, such as in less-advanced Eastern European countries (Druckman and Roberts, <xref ref-type="bibr" rid="B38">2005</xref>), the absence of a vote of no confidence (Golder and Thomas, <xref ref-type="bibr" rid="B50">2012</xref>), the intra-party factions of the Liberal Democratic Party of Japan (Ono, <xref ref-type="bibr" rid="B85">2012</xref>) or Italian parties (Ceron, <xref ref-type="bibr" rid="B27">2014</xref>), the regional branches of the German Social Democratic Party (Ennser-Jedenastik, <xref ref-type="bibr" rid="B43">2013</xref>), and the sequential allocation process (Ecker et al., <xref ref-type="bibr" rid="B41">2015</xref>).</p></fn>
<fn id="fn0004"><p><sup>4</sup>The statistical significance of the proportionality principle can be even stronger in certain specific contexts, such as political systems characterized by a small number of parties and connected coalitions (Schofield and Laver, <xref ref-type="bibr" rid="B95">1985</xref>), coalition governments based on pre-election pacts (Carroll and Cox, <xref ref-type="bibr" rid="B26">2007</xref>), or when using methods that estimate time-varying measures of ministerial portfolio importance (Bucur, <xref ref-type="bibr" rid="B21">2016</xref>).</p></fn>
<fn id="fn0005"><p><sup>5</sup>It is worth noting that, similar to the quantitative theory (see also text footnote 2), the predictive power of the qualitative theory also varies across countries&#x02014;ranging from below 44% in Belgium to above 70% in Germany. Two main factors are thought to influence this variation: the number of cabinet parties that typically form coalition governments in a given country, and the distinctive national experiences of parties in forming and cooperating within such governments (B&#x000E4;ck et al., <xref ref-type="bibr" rid="B7">2011</xref>, p. 465).</p></fn>
<fn id="fn0006"><p><sup>6</sup>Mirko Crulli and Daniele Albertazzi&#x00027;s recent research argues that the increasing frequency with which RRPs enter coalition governments only fulfills a functional interpretation of being mainstream. To determine whether RRPs are fully mainstream, one must also consider whether their attitudes are widely shared by the majority of the public, without any statistically or substantively significant differences in endorsement across political groups. From this attitudinal perspective, RRPs clearly do not qualify as fully mainstream. Therefore, the authors suggest that RRPs would be more accurately defined as &#x0201C;&#x02018;established but not mainstream&#x00027; in contemporary European politics&#x0201D; (Crulli and Albertazzi, <xref ref-type="bibr" rid="B29">2024</xref>, p. 23). We agree with this perspective. However, to avoid conceptual disputes, we have decided to use the prefix &#x0201C;traditional&#x0201D; when referring to parties generally accepted as fully mainstream, such as liberal or social democratic parties, to differentiate them from RRPs, which are also sometimes referred to as the &#x0201C;new&#x0201D; mainstream (Vampa and Albertazzi, <xref ref-type="bibr" rid="B107">2021</xref>, p. 283&#x02013;284).</p></fn>
<fn id="fn0007"><p><sup>7</sup>Except for the single-party governments led by Hungary&#x00027;s Fidesz and Poland&#x00027;s Law and Justice Party.</p></fn>
<fn id="fn0008"><p><sup>8</sup>Western Europe: (1) Austria, (2) Netherlands, (3) Switzerland; Northern Europe: (4) Finland, (5) Norway; Eastern Europe: (6) Bulgaria, (7) Estonia, (8) Latvia, (9) Poland, (10) Slovakia; Southern Europe: (11) Cyprus, (12) Greece, (13) Italy. In subsequent analyses, due to the limitation of sample size, these 13 countries are grouped into two regions: Western Europe (including Northern and Southern Europe) and Eastern Europe.</p></fn>
<fn id="fn0009"><p><sup>9</sup>When testing the hypothesis of whether RRPs conform to the proportionality principle using H0: &#x003B2; = 0 as the null hypothesis, if &#x003B2; is assumed to be 0.5 and the standard error is small, it is still statistically significant to reject H0: &#x003B2; = 0, indicating that RRPs follow the proportionality principle. However, since &#x003B2; = 0.5 is less than &#x003B2; = 1, it does not indicate a strict proportional relationship. Therefore, setting the null hypothesis as H0: &#x003B2; = 1 might be more appropriate, as it directly tests whether RRPs strictly follow the proportionality principle. We are grateful to Takeshi Hieda (Osaka Metropolitan University) for providing this valuable suggestion. However, we did not adopt this approach because, as noted in text footnote 2, the proportionality principle is often not strictly followed in the actual process of ministerial portfolio allocation, which becomes even more evident when examining this principle by country. An analysis of ministerial portfolio allocation in 14 Western European countries found that although parties&#x00027; ministerial portfolio payoffs are generally determined by their contribution of seats to coalition governments (&#x003B2; = 0.782), the &#x003B2; values across countries fluctuate between 0.52 (Iceland) and 0.938 (France). Thus, the ministerial portfolio allocations in most countries do not adhere strictly to the proportionality principle (B&#x000E4;ck et al., <xref ref-type="bibr" rid="B9">2009</xref>, p. 17; see also Schofield and Laver, <xref ref-type="bibr" rid="B95">1985</xref>, p. 160, and Indridason, <xref ref-type="bibr" rid="B56">2015</xref>, p. 12). As a result, setting the null hypothesis as H0: &#x003B2; = 1 would lead to the conclusion that most cases do not conform to the proportionality principle, even though we know this is not entirely accurate. Therefore, this paper continues to use H0: &#x003B2; = 0 as the null hypothesis.</p></fn>
<fn id="fn0010"><p><sup>10</sup>These seven ministerial portfolios are: (1) Agriculture; (2) Defense; (3) Education; (4) Finance; (5) Foreign Affairs; (6) Interior; and (7) Justice.</p></fn>
<fn id="fn0011"><p><sup>11</sup>It is important to note that the names and responsibilities of ministerial portfolios vary between countries. Therefore, to better illustrate the characteristics of the ministerial portfolios held by RRPs, the ministerial portfolio shares displayed in this figure do not represent the actual numerical shares. Instead, they show the share of each policy domain managed by RRPs relative to all the policy domains they oversee. For example, from 2004 to 2007, the Swiss People&#x00027;s Party held a ministerial portfolio titled Minister of Defence, Civil Protection, and Sport. To more intuitively convey the characteristics of this ministerial portfolio and facilitate comparisons with cases from other countries, I divided it into three separate ministerial portfolios: (1) Defence; (2) Interior; and (3) Culture, Public Services, Sports, Tourism. However, in subsequent regression analyses, when we examine the quantitative allocation of ministerial portfolios to RRPs, we use the actual number of ministerial portfolios. When we examine the qualitative allocation of ministerial portfolios to RRPs, we use the adjusted number of ministerial portfolios. The actual and [adjusted] numbers of ministerial portfolios held by RRPs in different regions are as follows: All Europe (283 [348]), Western Europe (32 [54]), Northern Europe (40 [44]), Eastern Europe (124 [146]), and Southern Europe (87 [104]) (see also <xref ref-type="supplementary-material" rid="SM1">Appendix 1</xref>).</p></fn>
<fn id="fn0012"><p><sup>12</sup><ext-link ext-link-type="uri" xlink:href="https://ejpr.onlinelibrary.wiley.com/journal/20478852">https://ejpr.onlinelibrary.wiley.com/journal/20478852</ext-link></p></fn>
<fn id="fn0013"><p><sup>13</sup>In calculating the power index/vote weight, we utilized an online algorithm program based on the fundamental definition by Shapley and Shubik (<xref ref-type="bibr" rid="B97">1954</xref>) (<ext-link ext-link-type="uri" xlink:href="https://homepages.warwick.ac.uk/&#x0007E;ecaae/ssdirect.html">https://homepages.warwick.ac.uk/&#x0007E;ecaae/ssdirect.html</ext-link>). This algorithm has the advantages of being simple and providing exact values for the power index/vote weight. The correlation coefficients between the seat share of RRPs in coalition governments and their power index/vote weight for All Europe, Western Europe, and Eastern Europe are 0.873, 0.863, and 0.805, respectively.</p></fn>
<fn id="fn0014"><p><sup>14</sup><ext-link ext-link-type="uri" xlink:href="https://whogoverns.eu/cabinets/">https://whogoverns.eu/cabinets/</ext-link></p></fn>
<fn id="fn0015"><p><sup>15</sup>The database records changes in the cabinet when: (1) there is a change in the partisan composition of the government coalition; (2) the Prime Minister leaves office; and (3) parliamentary elections are held, even if there is no resulting change in the partisan composition of the cabinet. As one reviewer insightfully pointed out, the integration of RRPs into coalition governments cannot be divorced from regime type. Fortunately, this factor does not substantially affect the analysis presented in this paper, for several reasons. First, the focus here is not on why traditional mainstream parties accept RRPs, but rather on how many and what kinds of ministerial portfolios RRPs receive after successfully entering coalition governments. Second, of the 13 countries examined, all except Cyprus, Poland, and Switzerland are republics with a multi-party parliamentary cabinet system. Third, due to data limitations, Cyprus is not included in the analysis of the qualitative allocation of ministerial portfolios (see also text footnote 19). Fourth, Poland is commonly classified as a semi-presidential regime with a strong parliamentary character&#x02014;specifically, a form of &#x0201C;premier-presidentialism&#x0201D; (Elgie, <xref ref-type="bibr" rid="B42">2011</xref>, p. 27&#x02013;29)&#x02014;and Switzerland&#x00027;s collegial executive system, often referred to as the &#x0201C;magic formula&#x0201D;, also operates within a strong parliamentary framework (Cruz et al., <xref ref-type="bibr" rid="B30">2021</xref>).</p></fn>
<fn id="fn0016"><p><sup>16</sup>The 22 RRPs from the 13 countries are as follows: Austria (1. Alliance for the Future of Austria; 2. Freedom Party of Austria), Bulgaria (3. Bulgarian National Movement; 4. Conservative Bulgaria), Cyprus (5. European Party), Estonia (6. Conservative People&#x00027;s Party of Estonia), Finland (7. Finns Party), Greece (8. Independent Greeks; 9. Popular Orthodox Rally), Italy (10. National Alliance; 11. Brothers of Italy; 12. Lega Nord), Latvia (13. For a Humane Latvia; 14. For Fatherland and Freedom/LNNK; 15. National Alliance), Netherlands (16. Pim Fortuyn List), Norway (17. Progress Party), Poland (18. League of Polish Families; 19. Self-Defence of the Republic of Poland), Slovakia (20. Slovak National Party; 21. We Are Family), Switzerland (22. Swiss People&#x00027;s Party). We acknowledge that the policy positions of RRPs are not static and that different RRPs may exhibit distinct characteristics depending on their region or country. Moreover, even within the same country, different RRPs can display unique traits. However, according to the latest and most comprehensive &#x0201C;PopuList&#x0201D; dataset (Rooduijn et al., <xref ref-type="bibr" rid="B90">2023</xref>), which provides academics and journalists with an overview of populist, far-left, and far-right parties in Europe from 1989 to 2022, the vast majority of the 22 RRPs listed above possess populist, nativist, and authoritarian characteristics (the so-called populist far-right in the dataset). Italy&#x00027;s National Alliance and Latvia&#x00027;s National Alliance are considered non-populist far-right; While Alliance for the Future of Austria, For Humane Latvia, the Netherlands&#x00027; Pim Fortuyn List, and Self-Defence of the Republic of Poland are classified as Eurosceptic, populist right-wing. Despite these (minor) differences among them, according to the definition used in this paper (see also text footnote 1), they all fall under the category of RRPs.</p></fn>
<fn id="fn0017"><p><sup>17</sup>The data for Cyprus, Greece, Latvia, and Switzerland are missing.</p></fn>
<fn id="fn0018"><p><sup>18</sup>It must be acknowledged that the expert surveys conducted by these two databases are now nearly 20 years old. As Martin (<xref ref-type="bibr" rid="B69">2016</xref>, p. 10, n. 8) noted, it is potentially problematic to apply this data since the importance of ministerial portfolios has likely not remained constant over the entire post-war period. Additionally, except for ministerial portfolios like the Prime Minister, the importance of other ministerial portfolios may not be consistent across parties. Furthermore, it is unclear from the survey questionnaire which specific criteria experts used to assess objective importance. Moreover, the data for Cyprus, Greece, Latvia, and Switzerland&#x02014;countries with histories of RRPs entering coalition governments&#x02014;are missing. While the validity of expert judgments has been criticized for being static, descriptive, and susceptible to endogeneity problems, a recent study deriving estimates of ministerial portfolio importance from context-sensitive sources, capturing changes in the value of ministries from one cabinet to another from 1959 to 2014 in the Fifth French Republic, found results with high correlations to Druckman and Warwick (<xref ref-type="bibr" rid="B40">2005</xref>) and Druckman and Roberts (<xref ref-type="bibr" rid="B39">2008</xref>), demonstrating the continued high accuracy of these nearly 20-year-old studies (Bucur, <xref ref-type="bibr" rid="B21">2016</xref>, p. 7, p. 10). Moreover, Druckman and Warwick (<xref ref-type="bibr" rid="B40">2005</xref>) and Druckman and Roberts (<xref ref-type="bibr" rid="B39">2008</xref>) remain the most comprehensive and up-to-date datasets available for Portfolio Importance Scores. Therefore, this paper continues to use them to test its hypotheses.</p></fn>
<fn id="fn0019"><p><sup>19</sup>Data is missing for Cyprus (European Party) from the Anastasiades I cabinet (01/03/2013 to 28/02/2014) and the Anastasiades II cabinet (14/03/2014 to 29/02/2016). Ministers without portfolio are not included in this analysis.</p></fn>
<fn id="fn0020"><p><sup>20</sup>The 13 categories of ministerial portfolios are: (1) Foreign Affairs; (2) Interior; (3) Justice; (4) Finance; (5) Economic Affairs; (6) Defence; (7) Labor; (8) Education; (9) Health; (10) Agriculture; (11) Industry; (12) Environment; and (13) Social Affairs.</p></fn>
<fn id="fn0021"><p><sup>21</sup>From Model 1 to Model 12, the correlation coefficients between the independent and dependent variables are as follows: (1) 0.702, (2) 0.647, (3) 0.683, (4) 0.620, (5) 0.814, (6) 0.748, (7) 0.691, (8) 0.743, (9) 0.550, (10) 0.662, (11) 0.690, and (12) 0.648. Except for Model (9), the correlation coefficients in the other five models all exceed 0.683, indicating a strong correlation between the seat share of RRPs and their ministerial portfolio share. This pattern aligns with the characteristics observed among traditional mainstream parties (Browne and Franklin, <xref ref-type="bibr" rid="B19">1973</xref>, p. 460).</p></fn>
<fn id="fn0022"><p><sup>22</sup>From the bar chart distribution in <xref ref-type="fig" rid="F1">Figure 1</xref>, it is clear that Northern European RRPs have a closer one-to-one proportional relationship between their average seat share and average ministerial portfolio share compared to other regions. The average seat share and weighted average ministerial portfolio share for RRPs in each region are as follows: All Europe = 0.247:0.179; Western Europe = 0.317:0.354; Northern Europe = 0.360:0.355; Eastern Europe = 0.118:0.174; Southern Europe = 0.160:0.291. Northern European RRPs continue to display the best proportional relationship, with Western European RRPs performing slightly better in this respect than their Eastern European counterparts. However, due to the relatively small overall sample size and the significant differences in sample sizes between regions, our analyses and calculations focus solely on the broader divisions of Western and Eastern Europe (see also text footnote 8).</p></fn>
<fn id="fn0023"><p><sup>23</sup>As shown in text footnote 13, seat share and bargaining power are closely related. The link between these two factors lies in the level of electoral system&#x00027;s disproportionality: in electoral systems with lower disproportionality, the relationship between a party&#x00027;s seat share and bargaining power becomes stronger. Therefore, when comparing and interpreting the impact of these two factors, it is crucial to control for the type of electoral system. To address this, we conducted additional analyses using the &#x0201C;Gallagher Index&#x0201D; (Gallagher, <xref ref-type="bibr" rid="B48">1991</xref>; data extracted from &#x0201C;WHO Governs in Europe and Beyond&#x0201D; and based on the authors&#x00027; own calculations) as a control variable. The results indicate that, after controlling for disproportionality, the analysis results in this paper remain largely unchanged. We appreciate the reviewer for highlighting this important issue, and the data is available upon request.</p></fn>
<fn id="fn0024"><p><sup>24</sup>However, it should be noted, as acknowledged by the author, that due to the limited sample size, this result is not statistically significant (Twist, <xref ref-type="bibr" rid="B106">2019</xref>, p. 26).</p></fn>
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