An overview of lexicographic choice under uncertainty

This overview focuses on lexicographic choice under conditions of uncertainty. First, lexicographic versions of traditional (von Neumann-Morgenstern) expected utility theory are described where the usual Archimedean axiom is weakened. The role of these lexicographic variants in explaining some well-known paradoxes of choice theory is reviewed. Next, the significance of lexicographic choice for game theory is discussed. Finally, some lexicographic extensions of the classical maximin decision rule are described.The authors wish to acknowledge financial support from NSF Grant IRI-8608964, Harvard Business School Division of Research, and the Miller Institute for Basic Research in Science. We are grateful to Irving LaValle and Peter Fishburn for encouragement and helpful comments.