The Separability Principle in Single-Peaked Economies with Voluntary Participation

We investigate the implications of the separability principle for the class of problems allocating an infinitely divisible commodity among a group of agents with single-peaked preferences and no-participation option. The separability principle requires that for two problems with the same population, but possibly different social endowments, in which the preferences of agents may change, if there is a subgroup of agents whose preferences are the same and the total amounts awarded to them are the same, then the amount awarded to each agent in the subgroup should be the same. We characterize on the basis of separability two variants of the uniform rule modified to be suitable in the current context: the family of extended uniform rules (Bergantiños et. al., 2012) and the family of generalized uniform rules introduced in this paper.