2 CHARACTERIZATIONS OF THE UNIFORM RULE FOR DIVISION PROBLEMS WITH SINGLE-PEAKED PREFERENCES

The uniform rule is considered to be the most important rule for the p roblem of allocating an amount of a perfectly divisible good between a gents who have single-peaked preferences. The uniform rule was studied extensively in the literature and several characterizations were prov ided. The aim of this paper is to provide two different formulations a nd corresponding axiomatizations of the uniform rule. These formulatio ns resemble the Nash and the lexicographic egalitarian bargaining solu tions; the corresponding axiomatizations are based on axioms of indepe ndence of irrelevant alternatives and restricted monotonicity.