The Winner-Take-All Dilemma
研究了由不同权重群体组成的社会中，赢家通吃规则作为占优策略却导致帕累托低效的困境，并证明比例规则在渐近分析中更优。
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.