Classical subjective expected utility

2016

Rabin and Thaler (2001) declared Expected Utility an ex-hypothesis or a dead parrot alluding to the famous sketch from Monthy Pythons Flying Circus. Following Cox and Sadiraj (2006) and others, one should distinguish between Expected Utility (EU) theory (a purely mathematical theory based on axioms) and Expected Utility models (EU theory plus a given economic interpretation). The most prevalent EU model is one that assumes consequentialism (Rubinstein, 2012). Consequentialism states that the decision maker has a single binary preference relation comparing probability distributions over final wealth levels. Preference relations over wealth changes for different levels of wealth are derived from this single preference relation. EU theory plus consequentialism is referred to as the standard EU model. It is argued that most of the critique against EU is against the standard EU model, or against consequentialism. We replace consequentialism with reference-dependence, retaining the EU hyp...

Theory and Decision, 2010

In this paper Savage's theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.

2003

Abstract Intelligent agents often need to assess user utility functions in order to make decisions on their behalf, or predict their behavior. When uncertainty exists over the precise nature of this utility function, one can model this uncertainty using a distribution over utility functions. This view lies at the core of games with incomplete information and, more recently, several proposals for incremental preference elicitation.

2010

This paper shows that subjective expected utility can be obtained using primitives that are much poorer than a preference relation on the set of acts. Our primitives only involve the fact that an act can be judged either “attractive”, “neutral” or “unattractive”. These categories may be interpreted as denoting the position of an act vis-à-vis a status quo. We give conditions implying that there are a utility function on the set of consequences and a probability distribution on the set of states such that attractive (resp. unattractive) acts have a subjective expected utility that is above (resp. below) some threshold. The numerical representation that is obtained has strong uniqueness properties. Our derivation uses results in conjoint measurement with ordered categories and, hence, we adopt a framework involving a finite set of states.

Erkenntnis, 1975

The Review of Economic Studies, 1991

Decision-making Process, 2009

2006

In this paper we extend Savage's theory of decision-making under uncertainty from a classical environment into a non-classical one. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility.

Journal of Mathematical Economics, 1987

Economic Theory, 2000

We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences in Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) settings, while it does not hold for subjective expected utility preferences in settings without rich state spaces. Indeed, when it holds the uniqueness property is even stronger than described above, as it needs only agreement on binary acts. The extension of the uniqueness property to the subjective case is possible because beliefs in the mentioned settings are shown to satisfy an analogous property: If two decision makers agree on a likelihood indifference class, they must have identical beliefs.

2007

In this paper we extend Savage's theory of decision-making under uncertainty from a classical environment into a non-classical one. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. We also propose an application in simple game context in the spirit of Harsanyi.

Social Choice and Welfare, 1984

Using axioms no stronger than those for the Neumann-Morgenstern expected utility hypothesis, with the recognition of finite sensibility, it is shown that the utility function derived by the N-M method is a neoclassical subjective utility function, contrary to the belief otherwise by prominent economists. This result is relevant for issues of utility measurability, social choice, etc. since it is subjective utility that is relevant for social choice. The relevance of individual risk aversion to the form of social welfare functions and the rationality of "pure" risk aversion are also discussed.

1997

If an agent (wealkly) prefers early resolution of uncertainty then the recursive forms of both the most commonly used non-expected utility models, betweenness and rank dependence, almost reduce to Kreps & Porteus's (1978) recurvise expected utility.

.In this paper, we present a brief version of de Finetti-Ramsey’s subjective probability theory and provide a rigorous yet intuitively plausible explanation of expected utility using elementary mathematics. In a final section, we take up the case of some “Paradoxes in Expected Utility Theory” and try to reconcile them with the help of subjective probabilities.

2002

Economists often operate under an implicit assumption that the tastes of a decision maker are constant, while his beliefs change with the availability of new information. It is therefore customary to seek representations of preferences which cleanly separate the taste component, called 'utility,' from the beliefs component. We show that a complete separation of utility from the other components of the representation is possible only if the decision maker's preferences satisfy a mild but not completely innocuous condition, called 'certainty independence.' We prove that the preferences that obtain such separation are a subset of the biseparable preferences. * Ghirardato is grateful to the California Institute of Technology for its hospitality while parts of this research were conducted. We gratefully acknowledge the financial support of MIUR and CNR.