The winner‐take‐all dilemma

Abstract

We consider collective decision‐making when society consists of groups endowed with voting weights. Each group chooses an internal rule that specifies the allocation of its weight to 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.