WELFARE BOUNDS IN THE FAIR DIVISION-PROBLEM

To any anonymous division method corresponds a lower and an upper bound function: they measure the impact on a given agent's utility of the other agents' preferences. The highest lower bound is the equal split utility; the lowest upper bound is the indirect utility from equal split at a "canonical" price. These two bounds are compatible. Yet any method with the elqual split lower bound exhibits the growth paradox, and any method with the lowest upper bound generates envy. We criticize Competitive Equilibrium from Equal Split because it puts no finite upper bound on any agent's welfare. © 1991.