Ordering Pareto-optima through majority voting

A commodity is shared between some individuals: there is an initial allocat ion; 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 inv olve an element of randomness in order to reflect uncertainty about economi c, social and political processes. It is shown that for every allocation, l ambda, 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) pref ers 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 opti mal allocations. Illustrations and interpretations of the selection procedu res are provided. (C) 2001 Elsevier Science BN. All rights reserved.