Ordering Pareto-Optima Through Majority Voting

M. Tvede, H. CRES

Mathematical Social Sciences

2001, n°41, pp.295-325

Départements : Finance

A commodity is shared between some individuals: there is an initial allocation; some selection procedures are used to choose an alternative allocation and individuals decide between keeping the initial allocation or shifting to the alternative allocation. The selection procedures are supposed to involve an element of randomness in order to reflect uncertainty about economic, social and political processes. It is shown that for every allocation, lambda, there exists a number, zeta(pi) is an element of [0, 1], such that, if the number of individuals tends to infinity, then the probability that a proportion of the population smaller (resp. larger) than zeta(lambda) prefers an allocation chosen by the selection procedure converges to 1 (resp. 0). The index zeta(lambda) yields a complete order in the set of Pareto optimal allocations. Illustrations and interpretations of the selection procedures are provided.