TY - JOUR

T1 - Universal Pareto dominance and welfare for plausible utility functions

AU - Aziz, Haris

AU - Brandl, Florian

AU - Brandt, Felix

N1 - Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using lotteries whereas uncertainty over the agents' preferences over lotteries is modeled using sets of plausible utility functions. A lottery is universally Pareto undominated if there is no other lottery that Pareto dominates it for all plausible utility functions. We show that, under fairly general conditions, a lottery is universally Pareto undominated iff it is Pareto efficient for some vector of plausible utility functions, which in turn is equivalent to affine welfare maximization for this vector. In contrast to previous work on linear utility functions, we use the significantly more general framework of skew-symmetric bilinear (SSB) utility functions as introduced by Fishburn (1982). Our main theorem generalizes a theorem by Carroll (2010) and implies the ordinal efficiency welfare theorem. We discuss three natural classes of plausible utility functions, which lead to three notions of ordinal efficiency, including stochastic dominance efficiency, and conclude with a detailed investigation of the geometric and computational properties of these notions.

AB - We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using lotteries whereas uncertainty over the agents' preferences over lotteries is modeled using sets of plausible utility functions. A lottery is universally Pareto undominated if there is no other lottery that Pareto dominates it for all plausible utility functions. We show that, under fairly general conditions, a lottery is universally Pareto undominated iff it is Pareto efficient for some vector of plausible utility functions, which in turn is equivalent to affine welfare maximization for this vector. In contrast to previous work on linear utility functions, we use the significantly more general framework of skew-symmetric bilinear (SSB) utility functions as introduced by Fishburn (1982). Our main theorem generalizes a theorem by Carroll (2010) and implies the ordinal efficiency welfare theorem. We discuss three natural classes of plausible utility functions, which lead to three notions of ordinal efficiency, including stochastic dominance efficiency, and conclude with a detailed investigation of the geometric and computational properties of these notions.

KW - Ordinal efficiency

KW - Pareto optimality

KW - SSB utility

KW - Social welfare

KW - Stochastic dominance

UR - http://www.scopus.com/inward/record.url?scp=84940737034&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2015.06.014

DO - 10.1016/j.jmateco.2015.06.014

M3 - Article

AN - SCOPUS:84940737034

SN - 0304-4068

VL - 60

SP - 123

EP - 133

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

ER -