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Decision theory can be used to test the logic of decision making—one may ask whether a given set of decisions can be justified by a decision‐theoretic model. Indeed, in principal–agent settings, such justifications may be required—a manager of an investment fund may be asked what beliefs she used when valuing assets and a government may be asked whether a portfolio of rules and regulations is coherent. In this paper we ask which collections of uncertain‐act evaluations can be simultaneously justified under the maxmin expected utility criterion by a single set of probabilities. We draw connections to the fundamental theorem of finance (for the special case of a Bayesian agent) and revealed‐preference results.

It has been argued that Pareto-improving trade is not as compelling under uncertainty as it is under certainty. The former may involve agents with different beliefs, who might wish to execute trades that are no more than betting. In response, the concept of no-betting Pareto dominance was introduced, requiring that putative Pareto improvements must be rationalizable by some common probabilities, even though the participants’ beliefs may differ. In this paper, we argue that this definition might be too narrow for use when agents are not Bayesian. Agents who face ambiguity might wish to trade in ways that can be justified by common ambiguity, though not necessarily by common probabilities. We accordingly extend the notion of no-betting Pareto dominance to characterize trades than are “no-betting Pareto” ranked according to the maxmin expected utility model.

A literal interpretation of neo-classical consumer theory suggests that the consumer solves a very complex problem. In the presence of indivisible goods, the consumer problem is NP-Hard, and it appears unlikely that it can be optimally solved by a human. Two implications of this observation are that (i) households may imitate each other’s choices; (ii) households may adopt heuristics that give rise to the phenomenon of mental accounting.

We present and axiomatize a model combining and generalizing theory-based and analogy-based reasoning in decision under uncertainty. An agent has beliefs over a set of theories describing the data generating process, given by decision weights. She also puts weight on similarity to past cases. When a case is added to her memory and a new problem is encountered, two types of learning take place. First, the decision weight assigned to each theory is multiplied by its conditional probability. Second, subsequent problems are assessed for their similarity to past cases, including the newly-added case. If no weight is put on past cases, the model is equivalent to Bayesian reasoning over the theories. However, when this weight is positive, the learning process continually adjusts the balance between case-based and theory-based reasoning. In particular, a “black swan” which is considered a surprise by all theories would shift the weight to case-based reasoning.

Ivan Moscati’s new book is a wonderful addition to the history of economic thought, dealing with the question of utility measurement since 1870 to 1985. It is fantastically insightful and extremely...

Decision makers often stick to a status quo without explicitly reconsidering it. Yet, their observed choices might be compatible with a fully rational model. We ask when such a rationalization is possible. We assume as observable only the choice of sticking to the status quo vs. changing it, as a function of a database of cases. We state conditions on the set of databases that would make the decision maker change the status quo, which are equivalent to the following representation: the decision maker entertains a set of theories, of which one is that her current choice is the best; she is inert as long as that theory beats any alternative theory according to a maximum likelihood criterion.

Do axiomatic derivations advance positive economics? If economists are interested in predicting how people behave, without a pretense to change individual decision making, how can they benefit from representation theorems, which are no more than equivalence results? We address these questions. We propose several ways in which representation results can be useful and discuss their implications for axiomatic decision theory.

International audience; Policymaking during a pandemic can be extremely challenging. As COVID-19 is a new disease and its global impacts are unprecedented, decisions are taken in a highly uncertain, complex, and rapidly changing environment. In such a context, in which human lives and the economy are at stake, we argue that using ideas and constructs from modern decision theory, even informally, will make policymaking a more responsible and transparent process.

Trust is a fundamental concept in relationships, between humans and organizations alike. It has been noted that trust is essential to almost all business transactions (B2B or B2C); moreover, trust is essential to internal organizational aspects as well. Management scholars define trust as the willingness to be vulnerable to the actions of another party based on the expectation that the other will perform a particular action important to the trustor. This definition, although consistent with the Trust Game in experimental economics, accounts for reciprocity; yet, it fails to account for high risk or uncertainty. For instance, there are cases where the trustor trusts the trustee in a generalized sense without anticipating concrete actions from the trustee.

Policymaking during a pandemic can be extremely challenging. As COVID-19 is a new disease and its global impacts are unprecedented, decisions need to be made in a highly uncertain, complex and rapidly changing environment. In such a context, in which human lives and the economy are at stake, we argue that using ideas and constructs from modern decision theory, even informally, will make policymaking more a responsible and transparent process.

Beginning with Robert Aumann's 1976 “Agreeing to Disagree” result, a collection of papers have established conditions under which it is impossible for rational agents to disagree, or bet against each other, or speculate in markets. The subsequent literature has provided many explanations for disagreement and trade, typically exploiting differences in prior beliefs or information processing. We view such differences as arising most naturally in a “large worlds” setting, where there is no commonly-accepted understanding of the underlying uncertainty. This paper develops a large-worlds model of reasoning and examines how agents learn in such a setting, with particular interest in whether accumulated experience will lead them to common beliefs (and hence to agree, and to cease trading). No learning rule invariably ensures learning, leaving ample room for persistent disagreement and trade. However, there are intuitive learning rules that lead people with different models of the underlying uncertainty to a common view of the world if the data generating process is sufficiently structured.

Decision theory offers a formal approach to decision making, which is often viewed and taught as the rational way to approach managerial decisions. Half a century ago it generated high hopes of capturing and perhaps replacing intuition, and providing the “right” answer in practically all managerial situations. Today it seems fair to say that decision theory has not lived up to these expectations. Behavioral science provides ample evidence that managers fail to follow the dicta of decision theory, even when these are explained to them. As a result, executives often find decision theory frustrating and useless and prefer to rely on their intuition. This paper suggests that this extreme conclusion is unwarranted and calls for a re-appraisal of decision theory. We propose that it should not always be regarded as a mathematical tool that produces the answer; rather, it can be viewed as a framework for a dialog between the decision maker and the decision theorist. In one extreme, the decision theorist studies the problem and provides the “correct’’ answer. But in another, the decision theorist only challenges the decision maker's intuition and logic. In between, a whole gamut of possible dialogs exists, in which decision theory doesn't replace intuition, but supports and refines it.

We suggest that one way in which economic analysis is useful is by offering a critique of reasoning. According to this view, economic theory may be useful not only by providing predictions, but also by pointing out weaknesses of arguments. It is argued that, when a theory requires a non-trivial act of interpretation, it's roles in producing predictions and offering critiques vary in a substantial way. We offer a formal model i which these different roles can be captured.

Significance How do people generate beliefs about economic, political, and social events? A natural formula for the predicted value of a variable is its weighted average value in the past, where past values are given a higher weight if they were observed in circumstances more similar to the current ones. Agents learn from the data the best way to assess the similarity of past cases to the present one. The basic formula and this learning process appeared both in statistics and in psychology and they thus make sense for modeling economic agents. We study this process and identify circumstances under which agents are likely to agree on predictions and conditions under which disagreement over predictions may be reasonably expected.

Relying on a literal interpretation of Weber’s law in psychophysics, we show that a simple condition of independence across good categories implies the Cobb–Douglas preferences.

We argue that a precedent is important not only because it changes the relative frequency of a certain event, making it positive rather than zero, but also because it changes the way that relative frequencies are weighed. Specifically, agents assess probabilities of future events based on past occurrences, where not all of these occurrences are deemed equally relevant. More similar cases are weighed more heavily than less similar ones. Importantly, the similarity function is also learnt from experience by "second-order induction". The model can explain why a single precedent affects beliefs above and beyond its effect on relative frequencies, as well as why it is easier to establish reputation at the outset than to re-establish it after having lost it. We also apply the model to equilibrium selection in a class of games dubbed "Statis- tical Games", suggesting the notion of Similarity-Nash equilibria, and illustrate the impact of precedents on the play of coordination games.

Relying on a literal interpretation of Weber's law in psychophysics, we show that a simple condition of independence across good categories implies the Cobb-Douglas preferences.

We consider a decision maker who follows a status quo without reconsidering her implicit decision at every period. Only as a result of certain events will she ask herself whether she would like to change her choice. We ask when this mode of decision making is compatible with optimality. We state conditions on the set of databases that would make the decision maker take an explicit decision, which are equivalent to the following representation: the decision maker entertains a set of theories, of which one is that her current choice is the best; she is inert as long as that theory beats any alternative theory according to a maximum likelihood criterion.

Agents make predictions based on similar past cases, while also learning the relative importance of various attributes in judging similarity. We ask whether the resulting "empirical similarity" is unique, and how easy it is to find it. We show that with many observations and few relevant variables, uniqueness holds. By contrast, when there are many variables relative to observations, non-uniqueness is the rule, and finding the best similarity function is computationally hard. The results are interpreted as providing conditions under which rational agents who have access to the same observations are likely to converge on the same predictions, and conditions under which they may entertain different probabilistic beliefs.

We discuss the notion of a state of the world in axiomatic decision theory, and argue that it should be viewed as an "eventuality" that is implicitly assumed to be independent of the process by which prefer- ences are observed. The distinction between states, which are assumed to resolve all uncertainty, and eventualities suggests certain limitations on the axiomatic approach for defining and measuring mental concepts (such as belief ) by observed choices

It is argued that, contrary to a rather prevalent view within economic theory, rationality does not imply Bayesianism. The note begins by defining these terms and justifying the choice of these definitions, proceeds to survey the main justification for this prevalent view, and concludes by highlighting its weaknesses.

People often wonder why economists analyse models whose assumptions are known to be false, while economists feel that they learn a lot from such exercises. We suggest that part of the knowledge generated by academic economists is case-based rather than rule-based. That is, instead of offering general rules or theories that should be contrasted with data, economists often analyse models that are ‘theoretical cases’, which help understand economic problems by drawing analogies between the model and the problem. Thus, economic models, empirical data, experimental results and other sources of knowledge are all on equal footing, that is, they all provide cases to which a given problem can be compared. We offer complexity arguments that explain why case-based reasoning may sometimes be the method of choice and why economists prefer simple cases. Many economists think of their discipline as a successful social science. Economics relies on rigorous and non-trivial mathematical and statistical analyses. The paradigm of microeconomics is viewed as a unified approach that can deal with all problems of social interaction and it is indeed adopted by other disciplines. Economics is popular with students and economics professors are in high demand within the academic world and outside it. 1 However, the basic assumptions of economic theories have been harshly criticised by psychologists, presumably showing in laboratory experiments that these assumptions frequently do not hold. If the assumptions of economics are all wrong, why do economists keep using them? Why do they develop sophisticated mathematical models based on such flimsy foundations? This question is our starting point. We elaborate on it and discuss two additional puzzles in Section 1. We then offer a possible resolution to these puzzles in Section 2, namely, that some of the reasoning in economics is casebased rather than rule-based and that economists view themselves as generating the ‘cases’ to which real problems might be analogous. True to the method of our discipline, we construct a model (in Section 4) that illustrates the advantages of this mode of research. In Section 5, we discuss the virtues of a general paradigm, or, to be precise, of the standard language that such a paradigm employs. Section 6 concludes.

We provide a microfoundation for a weighted utilitarian social welfare function that reflects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are sufficient. As suggested by Edgeworth (1881), just noticeable differences provide a common unit of measure for interpersonal comparisons of utility differences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's.

We argue that a precedent is important not only because it changes the relative frequency of a certain event, making it positive rather than zero, but also because it changes the way that relative frequencies are weighed. Specifically, agents assess probabilities of future events based on past occurrences, where not all of these occurrences are deemed equally relevant. More similar cases are weighed more heavily than less similar ones. Importantly, the similarity function is also learnt from experience by "second-order induction". The model can explain why a single precedent affects beliefs above and beyond its effect on relative frequencies, as well as why it is easier to establish reputation at the outset than to re-establish it after having lost it. Finally, we discuss more sophisticated forms of learning, by which similarity is defined not only on cases but also on attributes, and the importance of some attributes, learnt from the data by second-order induction, can also affect the perceived importance of other attributes.

In light of the interest in axiomatic models of decision making in recent years, one is led to ask, in what ways do axiomatic derivations advance positive economics? If economists are interested in predicting how people behave, without a pretense to change individual decision making, how can they bene fit from representation theorems, which are no more than equivalence results? We address these questions. We propose several ways in which representation results can be useful and discuss their potential implications for axiomatic decision theory.

Agents make predictions based on similar past cases. The notion of similarity is itself learnt from experience by "second-order induction": past cases inform agents also about the relative importance of various attributes in judging similarity. However, there may be multiple "optimal" similarity functions for explaining past data. Moreover, the computation of the optimal similarity function is NP-Hard. We offer conditions under which rational agents who have access to the same observations are likely to converge on the same predictions, and conditions under which they may entertain different probabilistic beliefs.

We offer a model that combines and generalizes case-based decision theory and expected utility maximization. It is based on the premise that an agent looks ahead and assesses possible future scenarios, but may not know how to evaluate their likelihood and may not be sure that the set of scenarios is exhaustive. Consequently, she also looks back at her memory for past cases, and makes decisions so as to maximize a combined function, taking into account both scenarios and cases. We allow for non-additive set functions, both over future scenarios and over past cases, to capture (i) incompletely specified or unforeseen scenarios, (ii) ambiguity, (iii) the absence of information about counterfactuals, and (iv) some forms of case-to-rule induction ("abduction") and statistical inference. We axiomatize this model. Learning in this model takes several forms, and, in particular, changes the relative weights of the two forms of reasoning.

Pareto efficiency is not as compelling when people hold different beliefs as it is under common beliefs or certainty. In the present paper we propose to restrict the standard Pareto relation by imposing the following constraint: in order for one allocation to dominate another, all agents must prefer the former to the latter according to each agent’s belief. In contrast to this unanimity Pareto criterion, the no-betting Pareto concept suggested elsewhere by Gilboa, Samuelson, and Schmeidler supplements the standard Pareto relation with the requirement that there should exist a single hypothetical belief under which all agents prefer the former to the latter. This paper analyzes and compares these and other definitions.

We suggest that one way in which economic analysis is useful is by offering a critique of reasoning. According to this view, economic theory may be useful not only by providing predictions, but also by pointing out weaknesses of arguments. It is argued that, when a theory requires a non-trivial act of interpretation, its roles in producing predictions and offering critiques vary in a substantial way. We offer a formal model in which these different roles can be captured.

Economic theory reduces the concept of rationality to internal consistency. As far as beliefs are concerned, rationality is equated with having a prior belief over a “Grand State Space”, describing all possible sources of uncertainties. We argue that this notion is too weak in some senses and too strong in others. It is too weak because it does not distinguish between rational and irrational beliefs. Relatedly, the Bayesian approach, when applied to the Grand State Space, is inherently incapable of describing the formation of prior beliefs. On the other hand, this notion of rationality is too strong because there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs. 1. Rationality of Belief and Belief Formation Economic theory is both the birthplace and the prime application of the rational choice paradigm. Throughout the 20 th century, economics has relied on rationality, and refined the definition of rational choice, offering concepts such as subjective expected utility maximization and Nash equilibrium, which have proved useful in several other disciplines.

International audience; This note argues that, under some circumstances, it is more rational not to behave in accordance with a Bayesian prior than to do so. The starting point is that in the absence of information, choosing a prior is arbitrary. If the prior is to have meaningful implications, it is more rational to admit that one does not have sufficient information to generate a prior than to pretend that one does. This suggests a view of rationality that requires a compromise between internal coherence and justification, similarly to compromises that appear in moral dilemmas. Finally, it is argued that Savage's axioms are more compelling when applied to a naturally given state space than to an analytically constructed one, in the latter case, it may be more rational to violate the axioms than to be Bayesian.