Uniform, equal division, and other envy-free rules between the two - Toyotaka Sakai; Takuma Wakayama (Osaka University, Institute of Social and Economic Research (ISER), 2008)
This paper studies the problem of fairly allocating an amount of a divisible resource when preferences are single-peaked. We characterize the class of envy-free and peak-only rules and show that the class forms a complete lattice with respect to a dominance relation. We also pin down the subclass of strategy-proof rules and show that the subclass also forms a complete lattice. In both cases, the upper bound is the uniform rule, the lower bound is the equal division rule, and any other rule is between the two.
Keywords: D71; D63; 330; Uniform rule; Choice of rules; Lattice; Pareto dominance; Singlepeaked preference; Fair allocation