Social Choice and Welfare | 2021
Generalized medians and a political center
Abstract
I propose two generalizations of the classic simple majority rule, unicameral yolk (Ferejohn, McKelvey and Packel (1984); McKelvey (1986)), and I characterize them building on properties of the median. A P -ball (for pivotal) is a smallest radius ball such that a winning coalition prefer one alternative over another if all individuals in that ball share that preference. A W -ball (for winning) is a smallest radius ball such that for all pairs of alternatives, if there exists a winning coalition that prefer one alternative over the other, then there exists an individual in that ball that shares that preference. Using these constructs, I generalize and sharpen McKelvey’s (McKelvey (1986)) circular bounds on the set alternatives socially preferred to any alternative, and bound the core and the uncovered set for general voting rules. I study comparative statics on the effect of changes in the voting rule.