The Winner-Take-All Dilemma

TL;DR

This paper analyzes collective decision-making with weighted voting groups, revealing a dilemma where winner-take-all rules dominate individually but are Pareto inefficient, and proposes alternatives like proportional rules.

Contribution

It introduces a general framework for voting rules within groups, demonstrates the dominance of winner-take-all strategies, and develops asymptotic analysis techniques for evaluating rule efficiency.

Findings

Winner-take-all rule is a dominant strategy but Pareto dominated.

Proportional rule Pareto dominates winner-take-all.

Numerical analysis of US Electoral College supports the theoretical results.

Abstract

We consider collective decision making when the society consists of groups endowed with voting weights. Each group chooses an internal rule that specifies the allocation of its weight to the alternatives as a function of its members' preferences. Under fairly general conditions, we show that the winner-take-all rule is a dominant strategy, while the equilibrium is Pareto dominated, highlighting the dilemma structure between optimality for each group and for the whole society. We also develop a technique for asymptotic analysis and show Pareto dominance of the proportional rule. Our numerical computation for the US Electoral College verifies its sensibility.