Online research in philosophy

This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest to (...) largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances. (shrink)

Two themes in the theory of measurement that have been studied extensively in the past few years are numerical representations of nontransitive binary comparison structures and uniqueness in finite measurement systems. This paper brings the two together by exploring the solutions to a nontransitive, additive model that are unique up to multiplication by a positive constant. The model relates to various contexts including decision under risk, evaluation of objectives, comparative probability, and voting theory. The family of unique solutions for the (...) model is shown to be extremely rich and varied. (shrink)

The purpose of this paper is to examine the structure of individual decisions under uncertainty in extensive (i.e., decision-tree) form at a sufficient level of generality to encompass many traditional as well as novel criteria of general choice under uncertainty. Considerations both of structure and of strategic effect arise. In § 2 we define weak and strong forms of strategic equivalence of decision trees and describe partial-normalization procedures by which all economically defined complete pure strategies may be identified for the (...) decider and for “chance”. In § 3 we examine characteristics of locally randomized, “behavior” strategies for the decider as the degree of normalization is varied, and we deduce useful properties of the function which specifies an outcome lottery for each behavior strategy of the decider in conjuction with a deterministic or stochastic selection by Chance. In § 4 we list a wide variety of choice criteria which may be invoked within the framework developed here. (shrink)

Axiomatizations of ordered preference differences typically assume that preferences are ordered. However, the mere assumption that preference differences can be ordered says nothing about whether preferences themselves are ordered. Utility representations for ordered differences without ordered preferences are investigated.

Stochastic dominance is a notion in expected-utility decision theory which has been developed to facilitate the analysis of risky or uncertain decision alternatives when the full form of the decision maker's von Neumann-Morgenstern utility function on the consequence space X is not completely specified. For example, if f and g are probability functions on X which correspond to two risky alternatives, then f first-degree stochastically dominates g if, for every consequence x in X, the chance of getting a consequence that (...) is preferred to x is as great under f as under g. When this is true, the expected utility of f must be as great as the expected utility of g. Most work in stochastic dominance has been based on increasing utility functions on X with X an interval on the real line. The present paper, following [1], formulates appropriate notions of first-degree and second-degree stochastic dominance when X is an arbitrary finite set. The only ‘structure’ imposed on X arises from the decision maker's preferences. It is shown how typical analyses with stochastic dominance can be enriched by applying the notion to convex combinations of probability functions. The potential applications of convex stochastic dominance include analyses of simple-majority voting on risky alternatives when voters have similar preference orders on the consequences. (shrink)

a–b* c–d is taken to mean that your degree of preference for a over b is less than your degree of preference for c over d. Various properties of the strength-of-preference comparison relation * are examined along with properties of simple preferences defined from *. The investigation recognizes an individual's limited ability to make precise judgments. Several utility theorems relating a–b * c–d to u(a)–u(b) are included.