Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version

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. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs.Decision making, Bayesian, Behavioral Economics

Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version

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.Decision making, Bayesian, Behavioral Economics

Three analyses of sour grapes

The phenomenon of adaptive preferences – sometimes also known under the name of sour grapes – has long caused a stir in Social Theory. In this paper, the precise problem posed by adaptive preferences, as seen from the point of view of a theoretician who intends to model or understand the phenomenon, will be clarified, and three models of the phenomenon will be presented and compared. The general intention of the article is to sound out some of the wider consequences of the phenomenon for the project of modelling and understanding the relationship between decisions taken in different situations. Difficulties which arise when several decisions and several situations are involved shall be discussed, and an approach to these difficulties shall be suggested.Adaptive preferences; preference change; belief change; decision theory; belief and utility elicitation; representation theorems.

Decision-Making in the Context of Imprecise Probabilistic Beliefs

Coherent imprecise probabilistic beliefs are modelled as incomplete comparative likelihood relations admitting a multiple-prior representation. Under a structural assumption of Equidivisibility, we provide an axiomatization of such relations and show uniqueness of the representation. In the second part of the paper, we formulate a behaviorally general axiom relating preferences and probabilistic beliefs which implies that preferences over unambiguous acts are probabilistically sophisticated and which entails representability of preferences over Savage acts in an Anscombe-Aumann-style framework. The motivation for an explicit and separate axiomatization of beliefs for the study of decision-making under ambiguity is discussed in some detail.

Ambiguous correlation

Many decisions are made in environments where outcomes are determined by the realization of multiple random events. A decision maker may be uncertain how these events are related. We identify and experimentally substantiate behavior that intuitively reflects a lack of confidence in their joint distribution. Our findings suggest a dimension of ambiguity which is different from that in the classical distinction between risk and "Knightian uncertainty"

Ambiguity and Social Interaction

We present a non-technical account of ambiguity in strategic games and show how it may be applied to economics and social sciences. Optimistic and pessimistic responses to ambiguity are formally modelled. We show that pessimism has the effect of increasing (decreasing) equilibrium prices under Cournot (Bertrand) competition. In addition the effects of ambiguity on peace-making are examined. It is shown that ambiguity may select equilibria in coordination games with multiple equilibria. Some comparative statics results are derived for the impact of ambiguity in games with strategic complements