Balancedness of Social Choice Correspondences

TL;DR

This paper explores the balancedness property in social choice correspondences, examining its interaction with other properties and characterizing the Borda rule among scoring rules.

Contribution

It introduces the balancedness condition, analyzes its relationship with tops-only property, and characterizes the Borda rule within scoring rules.

Findings

Balancedness interacts with other social choice properties.

Balancedness helps characterize the Borda rule among scoring rules.

The paper provides theoretical insights into social choice correspondence properties.

Abstract

A social choice correspondence satisfies balancedness if, for every pair of alternatives, x and y, and every 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 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.