Aggregating partitions

Abstract

Consider the following social choice problem. A group of individuals seek to partition a finite set X into two subsets. The individuals may disagree over the partition and an aggregation rule is applied to determine a compromise outcome. We permit collective indifference and so the outcome is a pair of disjoint subsets of X which may or may not partition X. Critically, neither subset can contain all of the elements in X. We present four normatively desirable properties that identify one aggregation rule uniquely. These properties are similar to those Young (J. Econ. Theory 9 (1974) 43-52) used in his characterization of the Borda rule.