Elicitation methods, such as asking people to produce the deciles of a distribution, are standard practices in policy or applied statistics. Similarly, much of cognitive science and psychology focuses on determining people's people's beliefs or latent traits through questionnaires or judgment tasks. However, these approaches often only capture a rough outline of what people know and are usually limited to point estimates of people's beliefs. Here, we present a novel experimental paradigm that allows us to access people's beliefs and how variable these beliefs are. Our task is based on an established random generation paradigm in which participants produce quantities from a particular domain as randomly as possible. We hypothesize that due to the minds' general-purpose mechanisms for probabilistic inferences, these random sequences represent the participants' underlying prior beliefs. We show that our method can infer participants' beliefs for a wide range of numeric quantities at comparable accuracy as an established elicitation method. Moreover, these inferred beliefs are consistent with individual participants' generalization and inference patterns in a subsequent conditional prediction task. We then extend our approach to non-numeric belief elicitation, highlighting how our method can go beyond numeric elicitation and provide insight into complex beliefs that are challenging to assess experimentally. Empirically, our results highlight that people know the rough shapes of environmental distributions, and these beliefs guide inference and generalization. Moreover, using our novel approach, we also show that people know the fine details of environmental distributions. Finally, our experimental results show that random generation paradigms can be a useful tool for cognitive scientists, psychologists, and applied statisticians.
Resource-rational belief revision can mitigate as well as amplify polarization
People's beliefs sometimes diverge after observing the same information, which has been interpreted as evidence of irrationality. This behaviour has been proposed to result from people's limited cognitive resources and motivated reasoning, but how belief revision differs across these explanations has not been formalized or compared to a rational norm. Further, while people may be biased relative to a normative ideal, they may still make optimal choices given their limited cognitive resources, or rationally balance the utility of holding accurate beliefs with the belief's intrinsic utility. Across two studies, we develop and test a unified computational account of belief polarization under these proposed mechanisms, showing that people's performance on a belief updating task best fits a limited-resource Bayesian model; external motivations may contribute to divergence (or convergence) by determining what pre-existing information people consider relevant to a situation, rather than by changing how people evaluate new information in isolation.
Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first comprehensive study of the reasoning capabilities of LLMs over explicit discrete probability distributions. Given observations from a probability distribution, we evaluate models on three carefully designed tasks, mode identification, maximum likelihood estimation, and sample generation, by prompting them to provide responses to queries about either the joint distribution or its conditionals. These tasks thus probe a range of probabilistic skills, including frequency analysis, marginalization, and generative behavior. Through comprehensive empirical evaluations, we demonstrate that there exists a clear performance gap between smaller and larger models, with the latter demonstrating stronger inference and surprising capabilities in sample generation. Furthermore, our investigations reveal notable limitations, including sensitivity to variations in the notation utilized to represent probabilistic outcomes and performance degradation of over 60% as context length increases. Together, our results provide a detailed understanding of the probabilistic reasoning abilities of LLMs and identify key directions for future improvement.
Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first comprehensive study of the reasoning capabilities of LLMs over explicit discrete probability distributions. Given observations from a probability distribution, we evaluate models on three carefully designed tasks, mode identification, maximum likelihood estimation, and sample generation, by prompting them to provide responses to queries about either the joint distribution or its conditionals. These tasks thus probe a range of probabilistic skills, including frequency analysis, marginalization, and generative behavior. Through comprehensive empirical evaluations, we demonstrate that there exists a clear performance gap between smaller and larger models, with the latter demonstrating stronger inference and surprising capabilities in sample generation. Furthermore, our investigations reveal notable limitations, including sensitivity to variations in the notation utilized to represent probabilistic outcomes and performance degradation of over 60% as context length increases. Together, our results provide a detailed understanding of the probabilistic reasoning abilities of LLMs and identify key directions for future improvement.
Guessing reveals internal models of perceptual precision
When observers lack sufficient information to support a confident response, they often guess. Guessing plays a pervasive role in visual cognition and working memory, yet the mechanisms that govern how observers generate guesses remain poorly understood. Standard models traditionally assume that responses produced in the absence of information are either uniformly distributed over feature space or are perhaps weighted towards prevailing environmental statistics. In contrast, here we consider an intriguing alternative: that guesses incorporate observers’ knowledge of their own perceptual capacities. We empirically measured guessing by eliciting responses under extreme target uncertainty (Experiment 1) as well as a novel “0ms presentation” approach in which no stimulus appeared but subjects believed one had (Experiment 2). We evaluated three accounts of guesses under these conditions: unsystematic (lapse) responding, biases toward environmental statistics, and a self-representational account in which guesses reflect observers’ knowledge of their own feature-dependent precision (e.g., preferring to guess feature values they believe they would be likely to miss). Guess responses were non-uniform and systematically biased toward feature values typically encoded with the least precision (e.g., oblique orientations) — a counterintuitive bias away from high-frequency, high-fidelity feature values (e.g., cardinal orientations). This complementary relationship between guessing and perceptual fidelity held within individuals and across paradigms, and was recoverable via an empirical-guess mixture model that replaced the standard uniform assumption with empirically measured guess distributions. Our findings challenge prevailing views that guesses reflect random noise, and suggest instead that guessing behavior reflects metacognitive knowledge of internal precision. Rather than defaulting to environmental priors, observers appear to model their own sensory limitations and leverage these representations to inform decisions in the absence of evidence. These results reframe guessing as a theoretically informative behavior that expresses observers’ own beliefs about their perceptual capacities. Significance Guessing is commonly treated as random noise in models of perception and memory, assumed to reflect lapses or uninformed responses. Instead, we show that human guesses are systematically structured across feature space: observers preferentially guess values they typically encode with the least precision, revealing a consistent, strategic bias away from high-fidelity representations. By directly measuring guess behavior on stimulus-absent trials and integrating these empirical distributions into a mixture model, we find that guesses on stimulus-present trials can be systematically recovered, and that they too form the complement of perceptual precision. These findings challenge foundational psychophysical modeling assumptions and position guessing as a strategic, informative behavior that engages self-representation.
From Predictive Algorithms to Automatic Generation of Anomalies
Machine learning algorithms can find predictive signals that researchers fail to notice; yet they are notoriously hard-to-interpret. How can we extract theoretical insights from these black boxes? History provides a clue. Facing a similar problem – how to extract theoretical insights from their intuitions – researchers often turned to “anomalies:” constructed examples that highlight flaws in an existing theory and spur the development of new ones. Canonical examples include the Allais paradox and the Kahneman-Tversky choice experiments for expected utility theory. We suggest anomalies can extract theoretical insights from black box predictive algorithms. We develop procedures to automatically generate anomalies for an existing theory when given a predictive algorithm. We cast anomaly generation as an adversarial game between a theory and a falsifier, the solutions to which are anomalies: instances where the black box algorithm predicts - were we to collect data - we would likely observe violations of the theory. As an illustration, we generate anomalies for expected utility theory using a large, publicly available dataset on real lottery choices. Based on an estimated neural network that predicts lottery choices, our procedures recover known anomalies and discover new ones for expected utility theory. In incentivized experiments, subjects violate expected utility theory on these algorithmically generated anomalies; moreover, the violation rates are similar to observed rates for the Allais paradox and Common ratio effect.
Relevant answers to polar questions
People often provide answers that go beyond what a question literally asks, but it has been difficult to pin down what makes some answers more relevant than others. Here, we introduce Pragmatic Reasoning In Overinformative Responses to Polar Questions (PRIOR-PQ), a probabilistic cognitive model formalizing how people use theory of mind (ToM) to produce and interpret relevantly overinformative answers to yes–no questions. Specifically, PRIOR-PQ grounds the pragmatics of question answering in inferences about the underlying goal that motivated the questioner to ask the given question as opposed to a different question. We evaluate our probabilistic model against human answering behaviour elicited in three case studies of increasing complexity, demonstrating its ability to predict nuanced patterns of relevance better than existing models, including state-of-the-art large language models. We also show how the goal-sensitive reasoning instantiated in our probabilistic model motivates a novel chain-of-thought prompting method allowing language models to approach more human-like performance. This work illuminates the mechanistic role of ToM in the pragmatics of question–answer exchanges, bridging formal semantics, cognitive science and artificial intelligence. Our findings have implications for developing more socially grounded dialogue systems and highlight the importance of integrating explanatory cognitive models with machine learning approaches. This article is part of the theme issue ‘At the heart of human communication: new views on the complex relationship between pragmatics and Theory of Mind’.
The Wisdom of Individuals: Exploring People's Knowledge About Everyday Events Using Iterated Learning
Abstract Determining the knowledge that guides human judgments is fundamental to understanding how people reason, make decisions, and form predictions. We use an experimental procedure called ‘‘iterated learning,’’ in which the responses that people give on one trial are used to generate the data they see on the next, to pinpoint the knowledge that informs people's predictions about everyday events (e.g., predicting the total box office gross of a movie from its current take). In particular, we use this method to discriminate between two models of human judgments: a simple Bayesian model ( Griffiths & Tenenbaum, 2006 ) and a recently proposed alternative model that assumes people store only a few instances of each type of event in memory (Min K ; Mozer, Pashler, & Homaei, 2008 ). Although testing these models using standard experimental procedures is difficult due to differences in the number of free parameters and the need to make assumptions about the knowledge of individual learners, we show that the two models make very different predictions about the outcome of iterated learning. The results of an experiment using this methodology provide a rich picture of how much people know about the distributions of everyday quantities, and they are inconsistent with the predictions of the Min K model. The results suggest that accurate predictions about everyday events reflect relatively sophisticated knowledge on the part of individuals.
Can Revealed Preferences Clarify LLM Alignment and Steering?
LLMs are increasingly used to make or support high-stakes decisions under uncertainty, where alignment depends not only on factual accuracy but on how models weigh tradeoffs between different outcomes. We present an empirical pipeline for estimating the implied preferences that an LLM's observed choices optimize: we elicit the model's probability distribution over unknowns along with the choice it would make for the decision task and then fit a discrete choice model to recover the cost function that best rationalizes the model's decisions. We show how this revealed-preference description allows rigorous evaluation of whether models behave in a consistently goal-directed way, whether they can verbalize a description of their objectives which matches their revealed decision policy, and whether prompting can reliably steer those policies to implement a user-specified cost function. We apply this evaluation across four medical diagnosis domains and multiple frontier and open-source models. We find that while many models have a nontrivial degree of internal coherence, they also have significant weaknesses in faithfully reporting or adopting preferences in response to user direction.
Against theory-motivated experimentation: Can random experimental choice lead to better theories?
Scientists must choose which among many experiments to perform. We study the epistemic success of experimental choice strategies proposed by philosophers of science or executed by scientists themselves. We develop a multi-agent model of the scientific process that jointly formalizes its core aspects: active experimentation, theorizing, and social learning. We find that agents who choose new experiments at random develop the most informative and predictive theories of the world. The agents aiming to confirm, falsify theories, or resolve theoretical disagreements end up with an illusion of epistemic success: they develop promising accounts for the data they collected, while misrepresenting the ground truth that they intended to learn about. Agents experimenting in these theory-motivated ways acquire less diverse or less representative samples from the ground truth that also turn out to be easier to account for. Random data collection, on the other hand, combines virtues of diverse and representative sampling from a target scientific domain which enables cumulative development of the successful theoretical accounts of it. We suggest that randomization, already a gold standard within experiments, is also beneficial at the level of experiments themselves.
Language and Experience: A Computational Model of Social Learning in Complex Tasks
The ability to combine linguistic guidance from others with direct experience is central to human development, enabling safe and rapid learning in new environments. How do people integrate these two sources of knowledge, and how might AI systems? We present a computational framework that models social learning as joint probabilistic inference over structured, executable world models given sensorimotor and linguistic data. We make this possible by turning a pretrained language model into a probabilistic model of how humans share advice conditioned on their beliefs, allowing our agents both to generate advice for others and to interpret linguistic input as evidence during Bayesian inference. Using behavioral experiments and simulations across 10 video games, we show how linguistic guidance can shape exploration and accelerate learning by reducing risky interactions and speeding up key discoveries in both humans and models. We further explore how knowledge can accumulate across generations through iterated learning experiments and demonstrate successful knowledge transfer between humans and models -- revealing how structured, language-compatible representations might enable human-machine collaborative learning.
The Inversion Problem: Why Algorithms Should Infer Mental State and Not Just Predict Behavior
More and more machine learning is applied to human behavior. Increasingly these algorithms suffer from a hidden—but serious—problem. It arises because they often predict one thing while hoping for another. Take a recommender system: It predicts clicks but hopes to identify preferences. Or take an algorithm that automates a radiologist: It predicts in-the-moment diagnoses while hoping to identify their reflective judgments. Psychology shows us the gaps between the objectives of such prediction tasks and the goals we hope to achieve: People can click mindlessly; experts can get tired and make systematic errors. We argue such situations are ubiquitous and call them “inversion problems”: The real goal requires understanding a mental state that is not directly measured in behavioral data but must instead be inverted from the behavior. Identifying and solving these problems require new tools that draw on both behavioral and computational science.
Thinking—Fast, Slow, and Artificial: How AI is Reshaping Human Reasoning and the Rise of Cognitive Surrender
People increasingly consult generative artificial intelligence (AI) while reasoning. As AI becomes embedded in daily thought, what becomes of human judgment? We introduce Tri-System Theory, extending dual-process accounts of reasoning by positing System 3: artificial cognition that operates outside the brain. System 3 can supplement or supplant internal processes, introducing novel cognitive pathways. A key prediction of the theory is “cognitive surrender”—adopting AI outputs with minimal scrutiny, overriding intuition (System 1) and deliberation (System 2). Across three preregistered experiments using an adapted Cognitive Reflection Test (N = 1,372; 9,593 trials), we randomized AI accuracy via hidden seed prompts. Participants chose to consult an AI assistant on a majority of trials (>50%). Relative to baseline (no System 3 access), accuracy significantly rose when AI was accurate and fell when it erred (+25/-15 percentage points; Study 1), the behavioral signature of cognitive surrender (AI-Accurate vs. AI-Faulty contrast; Cohen’s h = 0.81). Engaging System 3 also increased confidence, even following errors. Time pressure (Study 2) and per-item incentives and feedback (Study 3) shifted baseline performance but did not eliminate this pattern: when accurate, AI buffered time-pressure costs and amplified incentive gains; when faulty, it consistently reduced accuracy regardless of situational moderators. Across studies, participants with higher trust in AI and lower need for cognition and fluid intelligence showed greater surrender to System 3. Tri-System Theory thus characterizes a triadic cognitive ecology, revealing how System 3 reframes human reasoning and may reshape autonomy and accountability in the age of AI.
Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting
Large Language Models (LLMs) can achieve strong performance on many tasks by producing step-by-step reasoning before giving a final output, often referred to as chain-of-thought reasoning (CoT). It is tempting to interpret these CoT explanations as the LLM's process for solving a task. This level of transparency into LLMs' predictions would yield significant safety benefits. However, we find that CoT explanations can systematically misrepresent the true reason for a model's prediction. We demonstrate that CoT explanations can be heavily influenced by adding biasing features to model inputs--e.g., by reordering the multiple-choice options in a few-shot prompt to make the answer always "(A)"--which models systematically fail to mention in their explanations. When we bias models toward incorrect answers, they frequently generate CoT explanations rationalizing those answers. This causes accuracy to drop by as much as 36% on a suite of 13 tasks from BIG-Bench Hard, when testing with GPT-3.5 from OpenAI and Claude 1.0 from Anthropic. On a social-bias task, model explanations justify giving answers in line with stereotypes without mentioning the influence of these social biases. Our findings indicate that CoT explanations can be plausible yet misleading, which risks increasing our trust in LLMs without guaranteeing their safety. Building more transparent and explainable systems will require either improving CoT faithfulness through targeted efforts or abandoning CoT in favor of alternative methods.
Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting
Large Language Models (LLMs) can achieve strong performance on many tasks by producing step-by-step reasoning before giving a final output, often referred to as chain-of-thought reasoning (CoT). It is tempting to interpret these CoT explanations as the LLM's process for solving a task. This level of transparency into LLMs' predictions would yield significant safety benefits. However, we find that CoT explanations can systematically misrepresent the true reason for a model's prediction. We demonstrate that CoT explanations can be heavily influenced by adding biasing features to model inputs--e.g., by reordering the multiple-choice options in a few-shot prompt to make the answer always "(A)"--which models systematically fail to mention in their explanations. When we bias models toward incorrect answers, they frequently generate CoT explanations rationalizing those answers. This causes accuracy to drop by as much as 36% on a suite of 13 tasks from BIG-Bench Hard, when testing with GPT-3.5 from OpenAI and Claude 1.0 from Anthropic. On a social-bias task, model explanations justify giving answers in line with stereotypes without mentioning the influence of these social biases. Our findings indicate that CoT explanations can be plausible yet misleading, which risks increasing our trust in LLMs without guaranteeing their safety. Building more transparent and explainable systems will require either improving CoT faithfulness through targeted efforts or abandoning CoT in favor of alternative methods.
Thinking—Fast, Slow, and Artificial: How AI is Reshaping Human Reasoning and the Rise of Cognitive Surrender
People increasingly consult generative artificial intelligence (AI) while reasoning. As AI becomes embedded in daily thought, what becomes of human judgment? We introduce Tri-System Theory, extending dual-process accounts of reasoning by positing System 3: artificial cognition that operates outside the brain. System 3 can supplement or supplant internal processes, introducing novel cognitive pathways. A key prediction of the theory is "cognitive surrender"-adopting AI outputs with minimal scrutiny, overriding intuition (System 1) and deliberation (System 2). Across three preregistered experiments using an adapted Cognitive Reflection Test (N = 1,372; 9,593 trials), we randomized AI accuracy via hidden seed prompts. Participants chose to consult an AI assistant on a majority of trials (>50%). Relative to baseline (no System 3 access), accuracy significantly rose when AI was accurate and fell when it erred (+25/-15 percentage points; Study 1), the behavioral signature of cognitive surrender (AI-Accurate vs. AI-Faulty contrast; Cohen's h = 0.81). Engaging System 3 also increased confidence, even following errors. Time pressure (Study 2) and per-item incentives and feedback (Study 3) shifted baseline performance but did not eliminate this pattern: when accurate, AI buffered time-pressure costs and amplified incentive gains; when faulty, it consistently reduced accuracy regardless of situational moderators. Across studies, participants with higher trust in AI and lower need for cognition and fluid intelligence showed greater surrender to System 3. Tri-System Theory thus characterizes a triadic cognitive ecology, revealing how System 3 reframes human reasoning and may reshape autonomy and accountability in the age of AI.
A Theory of Response Sampling in LLMs: Part Descriptive and Part Prescriptive
Large Language Models (LLMs) are increasingly utilized in autonomous decision-making, where they sample options from vast action spaces. However, the heuristics that guide this sampling process remain under-explored. We study this sampling behavior and show that this underlying heuristics resembles that of human decision-making: comprising a descriptive component (reflecting statistical norm) and a prescriptive component (implicit ideal encoded in the LLM) of a concept. We show that this deviation of a sample from the statistical norm towards a prescriptive component consistently appears in concepts across diverse real-world domains like public health, and economic trends. To further illustrate the theory, we demonstrate that concept prototypes in LLMs are affected by prescriptive norms, similar to the concept of normality in humans. Through case studies and comparison with human studies, we illustrate that in real-world applications, the shift of samples toward an ideal value in LLMs' outputs can result in significantly biased decision-making, raising ethical concerns.
