Large Language Models (LLMs) have rapidly transformed natural language processing, driving breakthroughs in text generation, translation, summarizing, and interactive artificial intelligence (AI) systems (Bommasani et al., 2021; Brown et al., 2020). Their integration into academic, professional, and public settings has fuelled both optimism and concern regarding their growing influence on cognitive work, decision-making, and epistemic reliance on automated systems (Bommasani et al., 2021; Weidinger et al., 2021). As LLMs increasingly function as partners in judgment and reasoning tasks, understanding their strengths and limitations in probabilistic inference becomes critical.

Recent model generations, including OpenAI’s GPT-5, are explicitly optimized for complex multi-step reasoning and knowledge-intensive decision support (OpenAI, 2025). Such systems may therefore be perceived as credible sources of consultation on probabilistic tasks, given (i) their access to large bodies of human-generated knowledge, (ii) their status as cutting-edge AI, and (iii) their frictionless accessibility without social scrutiny (of course, there are concerns regarding data privacy, though related issues are typically poorly understood at best). Real-world usage patterns already point to this shift: students seek help with academic reasoning, professionals turn to LLMs for second opinions on uncertain tasks, and some individuals consult them for personal guidance (Bright et al., 2024; Hou et al., 2024; Jung et al., 2024). Yet the quality of advice supplied by LLMs remains insufficiently examined. Their effectiveness and trustworthiness ultimately depends on two dimensions: (1) accuracy of domain-relevant knowledge and (2) adherence to normative standards of rational decision-making. The first dimension is highly contextual and task-specific, whereas the second relates to a broader debate in cognitive science: to what extent are probabilistic inferences normatively rational, and to what extent are they systematically biased (Kahneman and Tversky, 1979; Tversky and Kahneman, 1983)?

Normative probabilistic inference is grounded on the principles of Bayesian probability theory. Under this framework, probabilistic judgments are expected to satisfy fundamental constraints such as additivity, complementarity, and overall coherence. These requirements have played a central role in both cognitive science and formal probabilistic modelling (Griffiths et al., 2008; Oaksford and Chater, 2009; Tenenbaum et al., 2011). Decades of behavioural research reveal that human probabilistic reasoning is often consistent with Bayesian principles, but also invariably systematically deviates from these principles, giving rise to robust evidence for cognitive biases such as the conjunction and disjunction fallacies (Carlson and Yates, 1989; Kahneman and Tversky, 1979; Tversky and Kahneman, 1983).

A wide range of formal frameworks have been developed to account for systematic deviations from (baseline) classical probability theory in human judgment (Busemeyer and Bruza, 2012; Tversky and Kahneman, 1974, 1983; Zhu et al., 2020). Broadly, these approaches fall into three families: classical Bayesian models, which (in their baseline form) preserve the Kolmogorov axioms and attribute errors to cognitive limitations or noise, heuristic approaches, which explain fallacies with individual, often unconnected principles, and quantum probability models, which posit a fundamentally different geometric structure of mental representations that naturally gives rise to certain violations. In this work, we focus on Bayesian and quantum approaches, only because these approaches provide more constraints regarding what probabilistic inference should be like.

Classical Bayesian models treat probabilities as measures over subsets of a fixed sample space (Oaksford and Chater, 2007). Within this framework, conjunctions, disjunctions, and conditional probabilities must satisfy additivity and coherence constraints. To explain departures from these constraints, early classical accounts introduced stochastic mechanisms based on sampling and noise. In the probability-plus-noise model (Costello and Watts, 2016, 2014, 2018), individuals maintain internally coherent classical probabilities, but their expressed judgments are corrupted by “recording noise.” Increasing the noise for complex events allows the model to reproduce conjunction and disjunction fallacies. A related approach, the Bayesian sampler (Zhu et al., 2020), assumes that people generate probability estimates from finite memory samples governed by a symmetric beta prior. Smaller samples for conjunctions and disjunctions lead those judgments to be more heavily influenced by the prior, yielding systematic biases. Both models produce mostly similar predictions.

Quantum probability models offer a contrasting theoretical foundation for probabilistic inference, by representing probabilities as geometric projections of a cognitive state vector in a Hilbert space (Busemeyer and Bruza, 2012). A central insight of this framework is that certain cognitive questions are incompatible: forming a judgment about one event changes the internal state relevant for judging another (Busemeyer and Bruza, 2012, 2024; Pothos and Busemeyer, 2013, 2022). When events are incompatible, quantum theory requires conjunctions and disjunctions to be computed sequentially, rather than through classical set-theoretic rules. Busemeyer et al. (2011) applied this principle by proposing a “more-likely-first” rule: people evaluate the event they judge more probable first and then the one considered less likely. Under this assumption, the quantum model predicts directional fallacies—conjunction errors involving the less probable event and disjunction errors involving the more probable event—while strictly prohibiting double fallacies. For example, if P ( A ) > P ( B ) , the sequential rule requires P ( A and then B ) ≤ P ( A ) , making it impossible for the conjunction to exceed both constituents. Equivalent constraints govern disjunctions. Thus, quantum models explain certain systematic patterns in human judgments, while sharply restricting others.

Early quantum models left open how internal quantum probabilities translate into the noisy numerical ratings that participants report. Huang et al. (2025) addressed this limitation by introducing the quantum sequential sampler, a hybrid model that merges quantum state dynamics with sampling mechanisms inspired by classical memory-based accounts. The quantum sampler assumes that people draw sequential samples from a quantum cognitive state and convert these samples into explicit numerical judgments subject to estimation noise.

An innovation of the quantum sampler is its use of POVMs (positive operator-valued measures) to compute probabilities, instead of the ideal projective measurements assumed in earlier work (Busemeyer et al., 2011). POVMs allow a controlled mismatch between the underlying cognitive state and the observed response, providing a principled noise model that generalizes classical “recording noise” into the quantum framework. This increased flexibility enables the model to capture a broader spectrum of empirical phenomena, including systematic violations of binary complementarity and the presence of both double conjunction and double disjunction fallacies—patterns the earlier quantum models could not accommodate.

To evaluate the quantum sequential sampler against the predominant Bayesian model (the Bayesian sampler), Huang et al. (2025) conducted a large-scale study with 1,451 U. S. participants shortly before the 2020 US presidential election. Each participant provided 78 judgments, including marginal, conditional, conjunctive, disjunctive, and negation probabilities across three event pairs. Across multiple generalization tests, the quantum sampler consistently outperformed the Bayesian sampler, offering the best available joint explanation of the full pattern of human probabilistic judgments.

Briefly, the main aim of this study is to examine whether GPT-5, a state-of-the-art LLM, exhibits human-like patterns of probabilistic bias when confronted with the same tasks used in recent behavioural studies, specifically Huang et al. (2025). This study asked U.S. participants to judge the likelihood that the 2020 presidential candidates—Joe Biden and Donald Trump—would win various combinations of states. Human responses reliably violated classical axioms, including complementarity, conjunction, and disjunction constraints.

Our central objective is to assess whether GPT-5, when instructed through persona-based prompts mirroring the demographic profiles of Huang et al.’s participants (age, gender, educational attainment, and geographic region), reproduces these non-normative patterns. The persona strategy enables a one-to-one mapping between individual human participants and corresponding model simulations, thereby allowing a fine-grained comparison of response distributions.

The present findings reveal a clear and systematic divergence between human and GPT-5 probabilistic reasoning. Human participants displayed the well-documented pattern of conjunction and disjunction fallacies, including a substantial number of double violations (Crupi et al., 2018; Tversky and Kahneman, 1983; Wojciechowski and Pothos, 2018). These errors were accompanied by large and heterogeneous violations of both marginal and joint complementarity (Huang et al., 2025). In some cases, such errors exceeded theoretical limits by wide margins. This broad variability is consistent across behavioural studies and indicates a plurality of generative mechanisms for probability judgments. Possible mechanisms include Bayesian and quantum processes, but perhaps heuristics too, which are outside formal probabilistic models (Huang et al., 2025).

GPT-5, by contrast, showed a markedly different profile. The model produced fewer single fallacies and almost no double fallacies; its complementarity deviations were extremely small—near the level of numerical noise. This narrow spread of GPT-5 results indicates that the model’s rare departures from coherence do not arise from noisy representations or fluctuating uncertainty. Instead, they reflect a highly stable and internally constrained inferential process.

The correlation analysis further highlights this structural distinction. Among human participants, conjunction and disjunction fallacies were essentially uncorrelated, this suggests that these violations originate from processes which are not restricted to the ones assumed in formal probabilistic models (as noted, noise-less quantum theory predicts a correlation between CFs and DFs). GPT-5 displayed the opposite pattern: when errors occurred, they were strongly correlated across CFs and DFs. This tight coupling implies a common mechanism in the workings of the model, which is the cause of both kinds of fallacies.

Specifically, when GPT-5 does produce fallacies, results show that its behaviour is consistent with early quantum-probabilistic models, for example, the original model for CFs and DFs proposed by Busemeyer et al. (2011). This model allows single conjunction or disjunction fallacies, while strictly prohibiting double fallacies and enforcing complementarity. Moreover, in this model CFs and DFs are correlated with each other. In contrast, the quantum model proposed by Huang et al. (2025) could generate a broad range of violations—including frequent double fallacies and complementarity failures. The greater expressivity in Huang et al.’s (2025) models was due to the introduction of noise through POVMs and sample-based estimation. This additional flexibility does not match GPT-5’s profile. Overall, the results indicate that GPT-5 is not simply “less noisy” than humans. Its pattern of errors is qualitatively different. The model maintains a high degree of probabilistic coherence and, when it fails, it does so in a structured and internally consistent manner.

These differences suggest that GPT-5 relies on a computational mechanism for probabilistic assessment that is not isomorphic to the one employed in human cognition, even under task conditions designed to approximate human working-memory constraints. It is possible that such a mechanism is just closer to normative requirement. A noteworthy alternative possibility is that GPT-5 attains better normative behaviour because, across iterations, it avoids inconsistencies due to random variation (e.g., compare with a human judge, who might be more lenient on some days because they are in a good mood, cf. Kahneman et al., 2021). Yet another possibility is that the high correlation between the CF and DF rates which is the main source of evidence for concluding that GPT-5 behaves more like the simple quantum model of Busemeyer et al. (2011) is due to the floor effects fallacies in GPT-5. Unfortunately, without identifying some situation for which GPT-5 does have high CF and DF rates, we cannot further examine this interesting issue. Finally, our analysis of political-content prompts indicates that GPT-5’s probability assignments are informed by a reasonable degree of political sensitivity. The model’s forecasts diverge systematically across states and candidates in election scenarios. This demonstrates that its probabilistic behaviour is not uniform across structurally similar prompts.

Having said all the above, there are several limitations. The most important one concerns the research question: our objective was to capture performance of GPT-5 “by default.” The rationale is that typical GPT-5 users would be interested in whether GPT-5 conducts probabilistic inference in a way analogous to that of humans or not, in typical use. The difficulty lies in that by default for humans often implies a particular context, including a mindset, information, processing constraints etc. We contend that the suitable sense of by default in GPT-5 has to include similar characteristics, that is, characteristics which would plausibly get GPT-5 to approach these probabilistic questions in a way similar to that of humans—the persona and memory manipulations were intended to capture some aspects of this.

How much did these manipulations affect results? It is difficult to have confidence of their validity. In the case of the persona matching, it has to be noted that, without this manipulation, the GPT-5 simulations would have been simpler–this is because, simply, persona matching required unique GPT-5 runs matched to individual participants. We investigated the rate of conjunction and disjunction fallacies separately, with an ANCOVA model with state triplet (there were two state triplets), gender, and education level (four levels: high school or less, some college, bachelor’s degree, postgraduate education) as between-participants independent variables and age as a covariate. State Triplet exerted a strong effect on both disjunction and conjunction fallacy rates (both p < 0.001). In contrast, no robust main effects of demographic persona variables were observed for either fallacy type (all p > 0.13, this includes the covariate, age). A modest interaction between gender and education emerged for disjunction fallacies (p = 0.041) and marginally for conjunction fallacies (p = 0.091). Overall, the evidence that persona matching had a measurable impact on GPT-5 behaviour is weak at best, though not completely negligible.

Regarding the memory window, our motivation for the particular length we used was that humans going through a similar task would be making their judgments in the context of other temporally proximal responses. For GPT-5, a choice has to be made regarding the extent of context of previous responses, given that the default setting of having each response given as if the GPT-5 mental state is ‘tabula rasa’ seems unrealistic. This was our thinking for setting a memory window of a particular size (cf. Hagendorff et al., 2023; Liu et al., 2025). Note, one way in which memory window might affect probabilistic coherence is if memory of earlier responses helps ensure consistency with later ones. Indeed, in early experimental work on probabilistic fallacies, the relevant questions would be typically presented together or in successive trials (e.g., Tversky and Kahneman, 1983). However, in more recent investigations (such as Huang et al., 2025), it cannot be assumed that relevant probability responses would be judged together, even with a lengthy working memory window. In general, we would argue that the claim of probabilistic coherence is independent of memory processes and rather about whether probabilities are generated in a coherent way. From this perspective, manipulations of memory window would be expected to just have minor contextual influences on responses (for human or artificial agents). While we think this approach is plausible given what we know, we did not systematically evaluate the importance of the memory window length and any conclusions here are conditional on this methodological choice.

Another potential limitation is that the study was carried out well after the 2020 US Presidential election. Therefore, the outcome of the election (including performance of the two candidates in different primaries) has been public knowledge that would be, presumably, accessible to GPT-5. With human participants, there is some evidence that, for fact-based propositions, probabilistic inference avoids common probabilistic fallacies (Collins et al., 2024; Karvetski et al., 2013). Whether this effect might have an analogue in GPT-5 is hard to assess. Nevertheless, empirically, there is a straightforward way to address this possibility. We ran a control whereby the task was framed as a hypothetical future election (the 2028 US Presidential election, which is the next scheduled such election), with as-yet to be identified candidates (instead of Biden and Trump in the original study, the probability questions were framed in terms of the Democratic and Republican candidates). For the purposes of this simulation, we randomly sampled 100 personas from the original set (50 for each triplet of states).

Contrary to expectation, there was an even lower rate for both CFs and DFs in the 2028 task vs. the 2020 one (respectively, Welch’s t(134.24) = 4.16, p < 0.001and t(160.26) = 4.74, p < 0.001). There were only 12.9% CFs and 14.7%DFs in the 2028 task. There were no differences between the two tasks regarding double CFs, double DF, and violations of binary complementarity (all p’s > 0.16). Therefore, we can certainly dismiss the possibility that low fallacy rates in 2020 version of the task were driven by post-election factual knowledge. There are many possible reasons for the difference in GPT-5 performance between the 2020 and 2028 task versions, including the fact that in the 2020 version the candidates were specific individuals. Rather than speculate on these differences, we highlight the main conclusion, which is that when testing GPT-5 with the version of the task best aligned with what human participants received, GPT-5 behaviour was closer to normative expectation.

More generally, it is unclear how impactful instructional and procedural manipulations are for GPT-5. In other work of ours, systematically exploring prompt engineering manipulations has had little effect. Likewise, in this case, we think it is likely that the impact of the instructional manipulations we adopted is, at best, minor. While it is tempting to systematically evaluate different variants regarding instructions and procedure, it is impractical to do so and, arguably, of less interest. These considerations are analogous to human experimental work: experimenters often devote considerable effort to fine-tuning instructions and procedures (e.g., randomisation protocols) to very exacting specifications. However, invariably, minor methods differences do not impact behaviour.

Regarding the present results, we believe the above issues are somewhat moot. The logic is this: by getting GPT-5 to behave more like humans (by simulating some characteristics of the participants, having memory limitations etc.), one could argue that we are making it more likely to observe fallacies in GPT-5 (since fallacies are an aspect of human behaviour). However, GPT-5 uniformly produced fewer probabilistic fallacies, compared to humans. That is, we can say that, conservatively, GPT-5 conducts probabilistic inference in a way more rational compared to humans.

This study sought to determine whether GPT-5’s violations of probabilistic axioms resemble those exhibited by human reasoners or whether they follow a distinct structural pattern. Despite efforts to place GPT-5 in conditions approximating human constraints, the model’s behaviour diverged sharply from human patterns. The findings therefore do not support the view that GPT-5 simply approximates “more accurate humans.” Instead, GPT-5 appears to instantiate a coherent form of probabilistic inference, that resembles a noise-free quantum model rather than the psychologically noisier mechanisms underlying human probability judgments. This distinction is important for interpreting LLM outputs. GPT-5 can provide probability assessments that are, in general, internally consistent and formally well-structured, as far as we can tell from this study.

These differences carry practical implications. As LLMs increasingly serve in advisory roles—educational, professional, and personal—results regarding their consistently coherent but cognitively non-human probabilistic guidance may influence when users are likely to resort to LLMs (and for what kind of judgments) and the trust they place in LLM output.

Future work should examine whether GPT-5’s coherence extends to more complex probabilistic domains, including conditional inference, belief updating, and sequential decision processes. An open question is whether aligning LLM behaviour with human fallacy patterns is desirable—or whether the value of such models lies precisely in their departure from human probabilistic limitations. The present study provides an initial foundation of results, showing that GPT-5 represents a distinct and unusually normative mode of probabilistic reasoning that stands apart from both classical human errors and models designed to explain them.