Context and decision : three approaches to representing preferences

• Main Author: O'Callaghan, Patrick H. D.
• Published: University of Warwick 2011
• Subjects: 510; QA Mathematics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.560300

We present three approaches to representing families of preference relations indexed by context over a set of alternatives. Our main motivation is that existing models of preferences typically assume that there is a unique order that ranks alternatives and contexts alike, that is preferences are context-free. We argue that this is often an unnecessary and unrealistic burden on the decision-maker’s capacity to decide. The first chapter is a geometric approach that improves upon the model of Gilboa and Schmeidler (2003) and casebased decision theory. The second is a general, topological approach with applications to choice under uncertainty; for context preferences it emulates the classical representation of Debreu (1954) and (1964). Finally, as a practical alternative the previous two models we extend the model of Herstein and Milnor (1953) and hence von Neumann and Morgernstern (1944) to obtain a representation for unions of mixture spaces.