Balancedness of social choice correspondences

Abstract A social choice correspondence satisfies balancedness if, for each pair of alternatives, x and y , and each pair of individuals, i and j , whenever a profile has x adjacent to but just above y for individual i while individual j has y adjacent to but just above x , then only switching x and y in the orderings for both of those two individuals leaves the choice set unchanged. We show how the balancedness condition (satisfied by the Borda, Pareto, and Copeland rules) interacts with other social choice properties, especially tops-only. We also use balancedness to characterize the Borda rule (for a fixed number of voters) within the class of scoring rules.