Resource-monotonic solutions to the problem of fair division when preferences are single-peaked
The author considers the problem of allocating an infinitely divisible commodity among a group of agents who have single-peaked preferences, i.e. there is an optimal amount of the commodity for each agent and the further he moves from it, in either direction, the worse off he is. The author considers the effects of an increase in the amount to divide. Whereas for classical preferences it is natural to consider the property, that all agents benefit from such an increase (since more is better) this requirement does not make sense if preferences are single peaked. Two more general properties are considered: resource monotonicity and one sided resource monotonicity. In the first case it is assumed that all agents are affected in the same direction by an increase of the amount. Resource monotonic selections exist from the Pareto solution. In general the property is quite strong. One sided resource monotonicity characterizes special changes: If there is not enough of the commodity to satisfy all agents before the increase there is not enough afterwards (similarly for a decrease). This requirement is compatible with important distributional requirements. There exists a one sided resource-monotonic selection from the envy-free and efficient solution. The main result shows that there is a unique selection on a large subdomain of the primary domain.
scientific article; zbMATH DE number 617484