This conference is part of the MAST Lecture Series organised by the Mathematics Department of the University of Luxembourg with the support of the FNR. The objective is to share the most recent developments of mathematics and their applications in the Luxembourg scientific community.
Abstract
Much of economic and political theory is based on the notion of choice. Consumers choose commodity bundles, firms choose production plans, governments choose public projects, and voters choose their representatives by means of elections, for example. A central hypothesis is that choices are rational in the sense that they are made with a
purpose, and purposive choice is typically associated with a goodness relation: observed choices are rational if there is an at-least-as-good-as relation such that, according to this relation, the selected objects are best among those that are available. An immediate question is what coherence properties such a goodness relation should possess. This usually involves the exclusion of goodness cycles, and the standard condition is transitivity. Because transitivity can be considered very demanding (especially in group decisions), it is desirable to explore weaker conditions. One
possibility is the use of a consistency property that rules out specific cycles but does so without requiring full transitivity. The presentation is focused on the use of consistency in individual and collective choice.