Fleurbaey-Michel Conjecture on Equitable Weak Paretian Social Welfare Order

Abstract:     
The paper examines the problem of explicit description of a social welfare order over infinite utility streams, which respects anonymity and weak Pareto axioms. It provides a complete characterization of the domains of one period utilities, for which it is possible to explicitly describe a weak Paretian social welfare order satisfying anonymity axiom. For domains containing any set of order type similar to the set of positive and negative integers, equitable social welfare order satisfying weak Pareto axiom is non-constructive. The paper resolves a conjecture by Fleurbaey and Michel (2003) that there exists no explicit (that is, avoiding the axiom of choice or similar contrivances) description of an ordering which satisfies weak Pareto and indifference to finite permutations. It also provides an interesting connection between existence of social welfare function and constructive nature of social welfare order by showing that the domain restrictions for the two are identical.

Number of Pages in PDF File: 15

Keywords: anonymity, weak pareto, social welfare order, non-ramsey set, order type

JEL Classification: D60, D70, D90

Accepted Paper Series