Axiomatic characterization of budget constrained Pareto efficient social choice for fair division problems

Abstract

In this paper, we axiomatically characterize the social choice correspondence, which picks for each economy, the set of equal income budget constrained Pareto efficient allocations. We are able to characterize this social choice correspondence uniquely, with the help of the following assumptions: Consistency, Equal Budget Property, Pareto efficiency for two agent problems and Local Independence. The most extensive use of Consistency is due to Thomson, as surveyed in Thomson [1990]; the equal budget property is due to Varian [1976], Pareto efficiency for two agent problems is due to van der Nouweland, Peleg and Tijs [1996], Local Independence is due to Nagahisa [1991]. In a final section, we replace Consistency by Converse Consistency (Thomson [1990]) and Pareto Efficiency for two agent problems by Binary Efficiency (see Lahiri [1997] to obtain yet another axiomatic characterization of the same social choice correspondence.