Dominance in SSB utility theory

SSB utility theory represents preferences between probability measures by the positive part of a skew-symmetric bilinear functional φ defined on pairs of measures. Three facets of the theory are examined. First, dominance axioms are used to extend φ to an integral form. Second, the maximizing behavior of φ on subspaces of measures is investigated. Third, aspects of stochastic dominance are explored in the SSB setting.     

Comment on the Kannai-Peleg impossibility theorem for extending orders

Recent work by Y. Kannai and B. Peleg shows that two appealing axioms for extending a linear order on a set of six or more elements to a weak order on the family of non-empty subsets of that set are mutually incompatible. This comment shows that a modest restriction of their monotonicity axiom is compatible for extension with a generalization of their other axiom provided that the linear order on the basic set is a well ordering.     

IMPOVERISHING TECHNICAL AND PREFERENTIAL IMPROVEMENTS

Abstract.  Edgeworth showed that a free-trading country might be impoverished by its own technical improvements if they are confined to the export industry and if no good is inferior in consumption. More recently it has been shown that improvements confined to the country's import competing industry can never be impoverishing if, in that country, no commodity is inferior in consumption. However, in all available proofs of these propositions, it has been assumed that for each country there exists an autarkic equilibrium. It will be shown that, without that assumption, the second proposition must be severely qualified.     

Transitive measurable utility

This paper continues a study of theories of preferences under risk that do not use the independence axiom of the von Neumann-Morgenstern theory. Unlike its predecessor, it assumes that preferences are transitive. The effects of transitivity are noted in two representations of preferences. The first, which also uses continuity and dominance axioms, involves a function u on a set P of probability measures for which u(p) > u(q) if and only if p is preferred to q. Although u might be nonlinear, it has other features of a von Neumann-Morgenstern linear utility function. The second representation has linear functions u and w on P, with w strictly positive except perhaps at preference-extreme measures—where it might vanish, such that u(p) w(q) > u(q) w(p) if and only if p is preferred to q. A symmetry axiom along with the axioms for the first representation are necessary and sufficient for the second representation.     

A note on linear utility

This note shows how a spectrum of specific axiomatizations for linear utility for decision-making under risk can be integrated under a generalized axiom scheme in which one of the two binary relations used in the axioms parameterizes specific applications.     

A new characterization of simple majority

Three axiomatic characterizations of two-alternative simple majority choice are presented. The first, by Kenneth May, uses anonymity and neutrality along with a positive responsiveness condition. The third characterizes simple majority solely in terms of local dynamics and a Pareto-optimality condition. The second, noted previously by the author, provides a connecting link between the others.     

A progress report on Kelly's majority conjectures

LetC(m, n) be the proportion of n-voter profiles on m alternatives that have a majority winner. Jerry Kelly conjectured that C(m, n) > C(m + 1, n) for m ? 3 and n = 3 and n ? 5, and C(m, n) > C(m, n + 2) for m ? 3 and n ? 3. We prove these for special cases.     

An axiomatic characterization of skew-symmetric bilinear functionals,with applications to utility theory

Axioms for two generalizations of von Neumann-Morgenstern linear utility are described. The first represents preferences between risky prospects by the positive part of a skew-symmetric bilinear functional; the second is based on quotients of linear functionals.