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This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning…

Theoretical Economics · Economics 2026-02-10 Cheaheon Lim

We characterize a notion of confidence that arises in learning or updating beliefs: the amount of trust one has in incoming information and its impact on the belief state. This learner's confidence can be used alongside (and is easily…

Machine Learning · Computer Science 2025-08-18 Oliver Ethan Richardson

In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…

Artificial Intelligence · Computer Science 2019-07-01 Daniel Huang

We study conditioning on null events, or surprises, and behaviorally characterize the Ordered Surprises (OS) representation of beliefs. For feasible events, our Decision Maker (DM) is Bayesian. For null events, our DM considers a hierarchy…

Theoretical Economics · Economics 2022-08-09 Adam Dominiak , Matthew Kovach , Gerelt Tserenjigmid

An important use of machine learning is to learn what people value. What posts or photos should a user be shown? Which jobs or activities would a person find rewarding? In each case, observations of people's past choices can inform our…

Artificial Intelligence · Computer Science 2015-12-21 Owain Evans , Andreas Stuhlmueller , Noah D. Goodman

Although behavioral economics has demonstrated that there are many situations where rational choice is a poor empirical model, it has so far failed to provide quantitative models of economic problems such as price formation. We make a step…

Physics and Society · Physics 2008-12-02 Szabolcs Mike , J. Doyne Farmer

Randomized experiments have long been the gold standard for scientists seeking to learn about cause and effect. When randomized experiments are infeasible, scientists often resort to observational studies, which are widely available and…

Methodology · Statistics 2026-04-13 Bohan Wu , Sebastian Salazar , Donald P. Green , David M. Blei

Human cooperation depends on how accurately we infer others' motives--how much they value fairness, generosity, or self-interest from the choices they make. We model that process in binary dictator games, which isolate moral trade-offs…

Neurons and Cognition · Quantitative Biology 2025-11-12 Gregory Stanley , Jun Zhang , Rick Lewis

To estimate causal effects from observational data, an applied researcher must impose beliefs. The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of…

Econometrics · Economics 2020-11-17 Francis J. DiTraglia , Camilo Garcia-Jimeno

We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…

Theoretical Economics · Economics 2025-02-04 Adam Dominiak , Matthew Kovach , Gerelt Tserenjigmid

This paper characterizes the conditions under which the observed beliefs of a group of agents are consistent with Bayesian updating. Beliefs are consistent with Bayesianism if they arise from the application of Bayes' rule given some…

Theoretical Economics · Economics 2024-01-19 Pooya Molavi

This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a…

Computer Science and Game Theory · Computer Science 2019-10-02 Daewon Seo , Ravi Kiran Raman , Joong Bum Rhim , Vivek K Goyal , Lav R Varshney

This paper presents an experimental study to investigate the learning and decision making behavior of individuals in a human society. Social learning is used as the mathematical basis for modelling interaction of individuals that aim to…

Social and Information Networks · Computer Science 2014-08-25 Maziyar Hamdi , Grayden Solman , Alan Kingstone , Vikram Krishnamurthy

In this study, I present a theoretical social learning model to investigate how confirmation bias affects opinions when agents exchange information over a social network. Hence, besides exchanging opinions with friends, agents observe a…

Theoretical Economics · Economics 2023-02-27 Marcos R. Fernandes

We study a setting where a group of agents, each receiving partially informative private observations, seek to collaboratively learn the true state (among a set of hypotheses) that explains their joint observation profiles over time. To…

Systems and Control · Computer Science 2019-03-15 Aritra Mitra , John A. Richards , Shreyas Sundaram

Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds.…

Physics and Society · Physics 2015-04-15 Víctor M. Eguíluz , N. Masuda , J. Fernández-Gracia

Many multiagent applications require an agent to learn quickly how to interact with previously unknown other agents. To address this problem, researchers have studied learning algorithms which compute posterior beliefs over a hypothesised…

Artificial Intelligence · Computer Science 2019-07-12 Stefano V. Albrecht , Jacob W. Crandall , Subramanian Ramamoorthy

In the Bayesian persuasion model, a sender can convince a receiver to choose an alternative action to the one originally preferred by the receiver. A crucial assumption in this model is the sender's commitment to a predetermined information…

Computer Science and Game Theory · Computer Science 2024-12-04 Jiahao Zhang , Shuran Zheng , Renato Paes Leme , Zhiwei Steven Wu

External information borrowing is often considered in order to improve a clinical trial's efficiency. The Bayesian approach borrows such external information by specifying an informative prior distribution. A potential issue with this…

Methodology · Statistics 2025-08-25 Silvia Calderazzo , Manuel Wiesenfarth , Vivienn Weru , Annette Kopp-Schneider

This work investigates the case of a network of agents that attempt to learn some unknown state of the world amongst the finitely many possibilities. At each time step, agents all receive random, independently distributed private signals…

Applications · Statistics 2016-11-29 M. Amin Rahimian , Ali Jadbabaie