Sequential decision making with partially ordered preferences

This paper presents new insights and novel algorithms for strategy selection in sequential decision making with partially ordered preferences; that is, where some strategies may be incomparable with respect to expected utility. We assume that incomparability amongst strategies is caused by indeterminacy/imprecision in probability values. We investigate six criteria for consequentialist strategy selection: Gamma-Maximin, Gamma-Maximax, Gamma-Maximix, Interval Dominance, Maximality and E-admissibility. We focus on the popular decision tree and influence diagram representations. Algorithms resort to linear/multilinear programming; we describe implementation and experiments. (C) 2010 Elsevier B.V. All rights reserved.

On the justice of voting systems

What are the best voting systems in terms of utilitarianism? Or in terms of maximin, or maximax? We study these questions for the case of three alternatives and a class of structurally equivalent voting rules. We show that plurality, arguably the most widely used voting system, performs very poorly in terms of remarkable ideals of justice, such as utilitarianism or maximin, and yet is optimal in terms of maximax. Utilitarianism is bestapproached by a voting system converging to the Borda count, while the best way to achieve maximin is by means of a voting system converging to negative voting. We study the robustness of our results across different social cultures, measures of performance, and population sizes.