The separability principle in single-peaked economies with participation constraints

•We consider how to allocate a commodity among agents with single-peaked preferences.•Bergantiños et al. (2012a) introduced a no-participation option.•We investigate the implications of the separability principle.•We introduce the family of generalized uniform rules.•We present characterization results on the basis of separability.

Bergantiños et al. (2012a) modified the class of problems allocating an infinitely divisible commodity among a group of agents with single-peaked preferences by introducing participation constraints. We investigate in this context the implications of the separability principle. It requires that for two problems with the same population but with 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 amount awarded to them is the same, then the amount awarded to each agent in the subgroup should be the same. We introduce the family of generalized uniform rules, a modification of the uniform rule to be suitable in the current context, and present characterization results on the basis of separability.