A Satisficing Heuristic Decision-Making Model under Limited Attention and Incomplete Preferences

Classical choice theory assumes that a decision-maker considers all feasible alternatives. However, a decision-maker in the real world can not consider all alternatives because of limited attention. In this paper, we propose a satisficing choice model to describe the choice procedure based on the incomplete preferences under the limited attention of the decision-maker. Moreover, the existence and rationality properties of the satisficing choice model on the different domains are studied combined with some proposed rationality conditions. Further, the proposed satisficing choice model is applied to a case of quality competition. Results show that the satisficing choice model of this paper is of a certain theoretical guiding significance to a kind of emergency decisions made by decision-makers under the circumstance of time pressure and limited information. It can also be the theoretical foundation for the study on the boundedly rational decision-making.

Joint desirability foundations of social choice and opinion pooling

We develop joint foundations for the fields of social choice and opinion pooling using coherent sets of desirable gambles, a general uncertainty model that allows to encompass both complete and incomplete preferences. This leads on the one hand to a new perspective of traditional results of social choice (in particular Arrow’s theorem as well as sufficient conditions for the existence of an oligarchy and democracy) and on the other hand to using the same framework to analyse opinion pooling. In particular, we argue that weak Pareto (unanimity) should be given the status of a rationality requirement and use this to discuss the aggregation of experts’ opinions based on probability and (state-independent) utility, showing some inherent limitation of this framework, with implications for statistics. The connection between our results and earlier work in the literature is also discussed.

Multi-utility representations of incomplete preferences induced by set-valued risk measures

We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for representations that are both parsimonious (the family of representing functionals is indexed by a tractable set of parameters) and well behaved (the representing functionals satisfy nice regularity properties with respect to the structure of the underlying space of alternatives). The key to our results is a general dual representation of set-valued risk measures that unifies the existing dual representations in the literature and highlights their link with duality results for scalar risk measures.

Decision Making and Equilibrium under Uncertainty

Rational choice under uncertainty for individuals with incomplete preferences is examined for three choice environments: the standard financial portfolio model, producer choice in the absence of financial markets, and producer choice in the presence of financial markets. Each problem is analyzed using distance functions and the zero-maximum (zero-minimum) principle. General equilibrium is analyzed using the zero-maximum (zero-minimum) principle and related to equilibrium representation in a nonstochastic setting. Choice under uncertainty for individuals with complete preferences is examined