Choice under complete uncertainty when outcome spaces are state dependent

One central objection to the maximin payoff criterion is that it focuses on the state that yields the lowest payoffs regardless of how low these are. We allow different states to have different sets of possible outcomes and show that the original axioms of Milnor (1954) continue to characterize the maximin payoff criterion, provided that the sets of payoffs achievable across states overlap. If instead payoffs in some states are always lower than in all others then ignoring the “bad” states is no longer inconsistent with these axioms. Similar dependence on overlap of outcome spaces across states holds for the minimax regret and maximin joy criteria.      

Choice uncertainty and the endowment effect

Journal of Risk and Uncertainty - We experimentally test for the role of choice uncertainty in generating “endowment effects” - the robust empirical finding that endowing participants...     

Welfare analysis under uncertainty

This article extends Bergsonian welfare analysis to an environment of uncertainty where preferences are not expected utility and may even be state-inconsistent. Given state-inconsistent preferences, the familiar notion of ex ante efficiency is also state-inconsistent. Other efficiency and welfare concepts achieve state consistency by ignoring entirely the prospective preferences of consumers. The framework developed in this article allows welfare judgments to be state-consistent while respecting prospective and conditional preferences. The theory is called inclusive welfare. An application to optimum insurance subsidies illustrates the practical use of the concept.     

Group cooperation under uncertainty

Previous research has shown an ‘interindividual-intergroup discontinuity effect’: intergroup interactions generally lead to less cooperative outcomes than interindividual interactions. We replicate the discontinuity effect in the deterministic prisoner’s dilemma, but find that groups are more cooperative than individuals in a stochastic version of the game. Three major factors that underlie the usual discontinuity effect are reduced in the stochastic environment: greed, fear, and persuasion power. Two group mechanisms are proposed to explain the reversed discontinuity effect: the motivation to avoid guilt and blame when making decisions that affect others’ welfare, and the social pressure to conform to certain norms when one is in a group setting.     

Intertemporal utility smoothing under uncertainty

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai (Econometrica 76:137–153, 2008) model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler (J Math Econ 18:141–153, 1989) multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.     

Production under uncertainty and choice under uncertainty in the emergence of generalized expected utility theory

Theory and Decision - Interest in the foundations of the theory of choice under uncertainty was stimulated by applications of expected utility theory such as the Sandmo model of production under...     

Expected utility theory under non-classical uncertainty

In this article, 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.     

A variational model of preference under uncertainty

A familiar example devised by Daniel Ellsberg to highlight the effects of event ambiguity on preferences is transformed to separate aleatory uncertainty (chance) from epistemic uncertainty. The transformation leads to a lottery acts model whose states involve epistemic uncertainty; aleatory uncertainty enters into the statedependent lotteries. The model proposes von Neumann-Morgenstern utility for lotteries, additive subjective probability for states, and the use of across-states standard deviation weighted by a coefficient of aversion to variability to account for departures from Anscombe-Aumann subjective expected utility. Properties of the model are investigated and a partial axiomatization is provided.     

Individual behavior under risk and under uncertainty: An experimental study

These experiments are concerned with individual behavior under risk and under uncertainty. By exploiting the isolation effect the experiments were able to offer to 134 subjects the possibility of actually gaining or losing an important sum of money.The experimental data show that under risk as well as under complete ignorance the subjects' attitudes towards prospects of gains and towards prospects of losses are totally unrelated.The data also show that when facing prospects of gains, the subjects generally take the exact probabilities of the events into account, whereas, when facing prospects of losses many of then have only recourse to coarser categories of plausibility, or even no longer use their information at all.     

Decision making under uncertainty: Starr's Domain criterion

Theory and Decision - This paper examines a decision making under uncertainty criterion first introduced by Starr, which differs from the classical criteria. The rationale and properties of this...     

A possibilistic hierarchical model for behaviour under uncertainty

Hierarchical models are commonly used for modelling uncertainty. They arise whenever there is a `correct' or `ideal' uncertainty model but the modeller is uncertain about what it is. Hierarchical models which involve probability distributions are widely used in Bayesian inference. Alternative models which involve possibility distributions have been proposed by several authors, but these models do not have a clear operational meaning. This paper describes a new hierarchical model which is mathematically equivalent to some of the earlier, possibilistic models and also has a simple behavioural interpretation, in terms of betting rates concerning whether or not a decision maker will agree to buy or sell a risky investment for a specified price. We give a representation theorem which shows that any consistent model of this kind can be interpreted as a model for uncertainty about the behaviour of a Bayesian decision maker. We describe how the model can be used to generate buying and selling prices and to make decisions.     

Empirical rules of thumb for choice under uncertainty

A substantial body of empirical evidence shows that individuals overweight extreme events and act in conflict with the expected utility theory. These findings were the primary motivation behind the development of a rank-dependent utility theory for choice under uncertainty. The purpose of this paper is to demonstrate that some simple empirical rules of thumb for choice under uncertainty are consistent with the rank-dependent utility theory.     

Frames and decisions under uncertainty in economics theory

Theory and Decision -     

On a statistical approach to choice under uncertainty

This article is concerned with criteria of choice under uncertainty which are based on long sequences of independent experiments. To state a rule of comparison for such sequences, we first specify it for sequences of certain numbers (say, of certain incomes). Eventually, the problem is reduced to a connection between preferences on sequences ofcertain numbers and thoseon probability distributions. We take into consideration a notion of statistically stable criteria for which choice based on a single random experiment does not disagree with that based on a “sufficiently long” sequence of independent replicas of the same experiment. The main aim of the article is to establish conditions under which a statistically stable criterion exists and to give its explicit representation.     

Ordinal utility models of decision making under uncertainty

This paper studies two models of rational behavior under uncertainty whose predictions are invariant under ordinal transformations of utility. The quantile utility model assumes that the agent maximizes some quantile of the distribution of utility. The utility mass model assumes maximization of the probability of obtaining an outcome whose utility is higher than some fixed critical value. Both models satisfy weak stochastic dominance. Lexicographic refinements satisfy strong dominance.The study of these utility models suggests a significant generalization of traditional ideas of riskiness and risk preference. We define one action to be riskier than another if the utility distribution of the latter crosses that of the former from below. The single crossing property is equivalent to a minmax spread of a random variable. With relative risk defined by the single crossing criterion, the risk preference of a quantile utility maximizer increases with the utility distribution quantile that he maximizes. The risk preference of a utility mass maximizer increases with his critical utility value.     

Decision problems under uncertainty based on entropy functionals

This essay intends to define the role of entropy, in particular, the role of the maximum entropy criterion with respect to decision analysis and information economics. By considering the average opportunity loss interpretation, the basic hypothesis for Shannon's derivation can be derived from properties of decision problems. Using the representation Bayes Boundary it is possible to show that selecting a single probability from a set by the Maximum Entropy Criterion corresponds to a minimax criterion for decision-making. Since problems of randomly accessing and storing information as well as communicating information can often be stated in terms of coding problems, this result might be used to develop strategies for minimizing retrieval time or communication costs.     

A Theory of Rational Choice under Ignorance

This paper contributes to a theory of rational choice for decision-makers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of `Complete Ignorance' which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a `Principle of Preference-Basedness', according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called `Simultaneous Expected Utility Maximization'. It can be interpreted as agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the (extremal) `acceptable priors' among which the decision maker has suspended judgment. An essential but non-standard feature of Simultaneous Expected Utility choices is their dependence on the entire choice set. This is justified by the conception of optimality as compromise rather than as superiority in pairwise comparisons.     

Coherent bets under partially resolving uncertainty and belief functions

By considering situations of partially resolving uncertainty, a one-to-one correspondence between belief functions and coherent betting systems à la de Finetti is shown to exist.