Paper

SSRN Electronic Journal, 2000

Economic modeling assumes, for the most part, that agents are Bayesian, that is, that they entertain probabilistic beliefs, objective or subjective, regarding any event in question. We argue that the formation of such beliefs calls for a deeper examination and for explicit modeling. Models of belief formation may enhance our understanding of the probabilistic beliefs when these exist, and may also help up characterize situations in which entertaining such beliefs is neither realistic nor necessarily rational. * Our thinking on these issues was greatly influenced by discussions with many people. Gilboa and

Economic Theory, 1996

On the diversity of probability beliefs Sharp differences of opinions and probability beliefs among economic agents are very commonly observed phenomena. Both the Arrow-Debreu [1954] model as well as Savage's [1954] theory accommodate these empirical observations and permit agents to hold diverse probability belief about the exogenous states. However, within the Arrow-Debreu model this diversity has very limited implications. The diversity of probability beliefs becomes a very significant question in any model in

2004

Economic theory reduces the concept of rationality to internal consistency. The practice of economics, however, distinguishes between rational and irrational beliefs. There is therefore an interest in a theory of rational beliefs, and of the process by which beliefs are generated and justified. We argue that the Bayesian approach is unsatisfactory for this purpose, for several reasons. First, the Bayesian approach begins with a prior, and models only a very limited form of learning, namely, Bayesian updating. Thus, it is inherently incapable of describing the formation of prior beliefs. Second, there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. Third, this lack of information is even more acute when we address the beliefs that can be attributed to a society. We hold that one needs to explore other approaches to the representation of information and of beliefs, which may be helpful in describing the formation of Baye...

Economic Theory, 2010

Papers in this symposium were presented at a Stanford University conference on August 10-14, 2009 entitled "When Are Diverse Beliefs Central?" They reflect the rapidly growing literature on the impact of diverse beliefs. It may thus be helpful to the reader if I use this introduction to highlight some ideas of this literature as reflected in the papers of this volume. As the era of Rational Expectations (in short RE) comes to a close it is important to clarify two points. First, the success of RE in disciplining macroeconomic modeling should not obscure the fact that the term "rational" is merely a label. Rationality of actions and rationality of beliefs have little to do with each other and using the term "rational" in RE has tended to brand other beliefs as "irrational." Studying axioms of belief rationality is actually a fruitful area of research that can fill the wide open space between RE and true irrational beliefs. A second point relates to private information. Not wishing to contradict RE, many adopted the device of asymmetric private information as the "cause" of diverse beliefs. Indeed, some view diverse beliefs as equivalent to asymmetric information. This is theoretically and empirically the wrong solution and in Kurz (2008, 2009) I explain why. It suffices to say that in large markets behavior under private information is different from behavior under diverse beliefs with common information. Also, all empirical evidence associates diverse forecasts with diverse modeling or diverse interpretation of public information. Finally, due to stochastic independence of private information over agents and time, RE models with asymmetric private information fail to deliver the key dynamic properties that are the central implications of I thank George Evans, Carsten Nielsen, Volker Wieland and Mike Wolters for constructive comments on earlier drafts of this Introduction.

2000

Many applications of intelligent systems require reasoning about the mental states of agents in the domain. We may want to reason about an agent's beliefs, including beliefs about other agents; we may also want to reason about an agent's preferences, and how his beliefs and preferences relate to his behavior. We define a probabilistic epistemic logic (PEL) in which belief statements are given a formal semantics, and provide an algorithm for asserting and querying PEL formulas in Bayesian networks. We then show how to reason about an agent's behavior by modeling his decision process as an influence diagram and assuming that he behaves rationally. PEL can then be used for reasoning from an agent's observed actions to conclusions about other aspects of the domain, including unobserved domain variables and the agent's mental states.

Economics and Philosophy, 2018

The standard, Bayesian account of rational belief and decision is often argued to be unable to cope properly with severe uncertainty, of the sort ubiquitous in some areas of policy making. This paper tackles the question of what should replace it as a guide for rational decision making. It defends a recent proposal, which reserves a role for the decision maker's confidence in beliefs. Beyond being able to cope with severe uncertainty, the account has strong normative credentials on the main fronts typically evoked as relevant for rational belief and decision. It fares particularly well, we argue, in comparison to other prominent non-Bayesian models in the literature.

2011

Abstract. We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task, and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other, and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions w...

2000

Many economic decisions involve a substantial amount of uncertainty. Therefore it is crucial for economists to understand how people process probabilistic information. In this paper, we measure the capability for probability judgment in a representative sample of the German population. Our results show that almost a third of the respondents exhibits biased probability judgment. Moreover, the distribution of judgment biases

Belief Change in Rational …, 2005

1 Motivation

Economic Theory, 1994

The paper proposes that the theory of expectations be reformulated under the assumption that agents do not know the structural relations (such as equilibrium prices) of the economy. Instead, we postulate that they can observe past data of the economy and form probability beliefs based on the data generated by the economy. Using past data agents can compute relative frequencies and the basic assumption of the theory is that the system which generates the data is stable in the sense that the empirically computed relative frequencies converge. It is then shown that the limit of these relative frequencies induce a probability on the space of infinite sequences of the observables in the economy. This probability is stationary. A belief of an agent is a probability on the space of infinite sequences of the observable variables in the economy. Such a probability represents the "theory" or "hypothesis" of the agent about the mechanism which generates the data. A belief is said to be compatible with the data if under the proposed probability belief the economy would generate the same limit of the relative frequencies as computed from the real data. A theory which is "compatible with the data" is a theory which cannot be rejected by the data. A belief is said to be a Rational Belief if it is (i) compatible with the data and (ii) satisfies a certain technical condition. The Main Theorem provides a characterization of all Rational Beliefs.