As scholars in the field of social science, we find Soumyanetra Munshi's article, titled “Clientelism or Public Goods: Dilemma in a Divided Democracy,” to be both captivating and thought-provoking. However, we wish to address two issues we have identified within her theoretical framework. Our discussion adheres to the framework articulated by Rubinstein (2006), where one of the paramount functions of a formal model lies in generating conclusions. It is noteworthy that some of these conclusions may appear absurd, despite being derived from sound assumptions. The recognition of an absurd conclusion carries as much significance as identifying a contradiction within a mathematical model itself. In this concise paper, we engage with Munshi's work by initially examining an absurd conclusion and subsequently delving into a logical contradiction.

The paper is organized as follows. In Section 2, we present the theoretical model setup of Munshi (2022). Section 3 introduces an absurd conclusion inferred from Munshi's (2022) model. In Section 4, we present a logical inconsistency identified in the structure of Munshi's (2022) model. Finally, Section 5 presents the conclusion.

In many contemporary societies, according to Munshi (2022), the relevance of the distinction between left- and right-wing parties is diminishing compared to the distinction between elite and non-elite parties. Elite parties primarily cater to the preferences and needs of higher and middle-income groups, with a particular focus on not providing mass public goods. Non-elite individuals, who predominantly require these public goods, rely on them as high-income individuals can acquire them through market mechanisms.

Elite parties generally face a numerical disadvantage. Consequently, in order to succeed in electoral contests, elite parties can adopt one of two strategies: (1) providing the public goods demanded by non-elite individuals, even at the risk of alienating their elite support base; or (2) offering clientelistic bribes, whether in monetary form or in the form of favors and employment opportunities to a sufficient number of non-elite individuals.

In a first possible world, Munshi (2022) assumes that the elite party does not produce public goods for non-elite voters, i.e., g_A = 0. Although Munshi (2022) does not explicitly state the scarcity assumption, it holds that u_i(g_B)−u_i(0)>0 if g_B>0. Therefore, the expression (Equation 2.6) is as follows:

such that viAN-viBN=viN and ui(gB)-ui(0)=2gB·gi-gB2. Hence,

is the probability that the non-elite voter i∈N votes for party A. The number of non-elite votes that party A expects is as follows:

Munshi (2022, p. 491) shows that to maximize the number of votes, party B announces a policy gB*=g¯ such that g¯=(g1+g2+...+gnN)/nN is the average demand of these non-elite voters for public goods, measured in physical units. Replacing gB*=g¯ in Equation 3.2, the expression is as follows:

Therefore, the number of non-elite voters VBN=nN-VAN who vote for party B is

Why does the above lead to an absurd conclusion?

Munshi (2022) never makes clear and explicit assumptions about the behavior of voters' partisan biases, which is a serious methodological error. Indeed, Munshi (2022) does not make any assumptions about the parameters of the distribution functions (Equations 2.1, 2.4), which are behavioral parameters. When Munshi (2022) does not make explicit assumptions about behavioral variables, the reasoning remains open: anything can be said. The following corollary draws an absurd conclusion using the Munshi (2022) model set-up when parameters are added, which builds upon well-established statements of political theory and electoral behavior.

Corollary 1. An Absurd Conclusion—In a liberal democracy without clientelism and without constraints on the decision to vote, the median voter votes for the elite party if

In a uniform distribution, the mean is equal to its median, and consequently, the median voter is located in the median of the voter distribution, that is, at the point b_N/f_N. If f_N>0 and b_N>0, it holds that the median of non-elite voters ideologically prefer party A to party B. From the above, we have that the inequality

geometrically corresponds to the case illustrated by Figure 1.

The square of the average demand for public goods by non-elite voters is inevitably less than the maximum value of the distribution. This holds true under the condition that f_N → 0, indicating a high variance in partisan biases among non-elite voters, and reflecting the fragmented nature of the non-elite social group in terms of ideology. In contrast, the elite constitutes a small, exclusive, and cohesive group wielding significant political, social, and economic influence. In stark contrast, the non-elite voters exhibit heterogeneity, low social integration, and limited access to centers of power. With minimal political autonomy, the median voter among the non-elite is highly susceptible to the influence of the ruling class (Stokes et al., 2013; Holcombe, 2021). Although the elite itself is not a homogeneous social group in terms of identities and interests, its cooperative processes revolve around a clear and defined axis: the preservation of privilege.

Due to their lack of privileges and the broad diversity within the social group, non-elite voters often lack awareness regarding the benefits of social cooperation, resulting in a fragmented scenario (Schwander, 2019; Wren and McElwain, 2011; Inglehart, 1997). Consequently, the formation of cohesive political networks becomes challenging within this context (Daby, 2021; Graziano, 1976).

The crux of the matter lies in the presence of effective class cohesion, where each individual within the social group enjoys equitable access to scarce resources, both political and economic. This equitable access ensures the stability of the social group. However, given the lack of symmetrical access to resources among the general public, achieving effective cohesion becomes challenging, leading to persistent social disarticulation (Stokes, 2007; Häusermann and Schwander, 2012; Hicken, 2007; Robinson and Verdier, 2003). Consequently, the expression (Equation 3.5) holds true. Furthermore, comparing the expressions (Equations 3.3, 3.4) if f_N → 0 we have that

This situation arises when the median voter, paradoxically, not only votes for their own oppressor but also strictly prefers them over the political party that represents their interests more effectively. While such scenarios may be conceivable in non-liberal political regimes characterized by high levels of citizen alienation, they are highly implausible within a liberal and democratic institutional framework. Unless explicit institutional constraints are in place that compel such behavior, which is not the case, such outcomes are unlikely to occur.

The non-elite political party (B) is assumed to have broad ideological and identity connections with the majority of non-elite voters; consequently, if political party B provides public goods to non-elite voters, the electoral support of non-elite voters for party B should be expected to be in the majority. On the other hand, although non-elite voters can vote for elite parties, it is not feasible for the elite party to obtain the majority support of non-elite voters in elections without the supply of public goods or payment for votes. Without the supply of public goods or monetary payments, the majority support of the non-elite voters for the elite party is unfeasible and, therefore, rationally absurd. A scenario of the majority support of non-elite voters for an elite party will necessarily be mediated by a strategy of rapprochement through the provision of goods and services (Thachil, 2014a,b).

In Propositions 1 and 2 of Munshi's paper we have detected not only a methodological problem in terms of units of measure, but also in the use of ex-post parameters not defined in the model assumptions. Both the problem of units of measurement and the introduction of ex-post variables lead the reasoning toward a logical contradiction. In subsections 1 and 2 we reconstruct the reasoning based on the variables used to formulate propositions 1 and 2 of Munshi (2022). In subsection 4.3, the logical inconsistency that is logically inferred from the propositions of Munshi (2022) is presented.

We welcome the addition of Munshi (2022) to the scholarship on clientelism in elections and the lack of public goods provision by parties that win following that strategy. Such a topic and approach are of fundamental importance of understanding the problems of democracies in different countries and cultures. However, we have detected two problems in this article, first, we have revealed a problem of tautological reasoning, the non-elite voters of this model already have a partisan affiliation to the Elite party. Therefore, they do not need to be swayed to it by either expenses in public goods or clientelistic payments by the Elite party, an absurd conclusion; and second, we have demonstrated the incomparability of the units of measurement in clientelism versus public goods and in their corresponding cost valuation. These two features are at the core of Munshi's argument and the narratives of selected cases.

In the first feature discussed, we highlighted that in the expression for the number of non-elite individuals who vote for the Elite party, there is a generalizability problem. The parameters can be chosen in such a way that a higher number of non-elite voters simply prefer the Elite party. Public goods expenses or clientelistic payments are not needed to sway these voters; they were already “affiliated” with the Elite party. In the second, we detected that the expressions requires the impossibility of comparing physical units of public goods against monetary amounts of clientelistic expenses. Furthermore, the definition of the monetary cost of producing public goods is not clear, we do not know if these public goods are purchased from a private provider or produced by the government, in which case we would need to know if the marginal costs are increasing or constant (Rubinstein, 2006; Friedman, 1966). We prove that both a marginal and an average cost interpretations contradict themselves, invalidating the important inference in Munshi's paper that public goods provision is more costly than clientelism.

We do not intend to imply that we do not highly value Munshi's work; on the contrary, we build upon it as a framework for developing new applied theory and informing an empirical research agenda. The article addresses a topic of fundamental importance, and the structure of the model merits further exploration and improvement. Our aim is simply to highlight certain analytical features that, in our view, require deeper analysis to ensure conceptual soundness.