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The Winner-Take-All Dilemma

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  • Kazuya Kikuchi
  • Yukio Koriyama

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.

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  • Kazuya Kikuchi & Yukio Koriyama, 2022. "The Winner-Take-All Dilemma," Papers 2206.09574, arXiv.org.
    • Handle: RePEc:arx:papers:2206.09574
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    Cited by:

    1. Héloïse Cloléry & Yukio Koriyama, 2020. "Elections présidentielles américaines : comment sortir du dilemme du prisonnier ?," Post-Print halshs-03019443, HAL.
    2. Kazuya Kikuchi & Yukio Koriyama, 2023. "A General Impossibility Theorem on Pareto Efficiency and Bayesian Incentive Compatibility," Papers 2303.05968, arXiv.org, revised Mar 2024.
    3. Héloïse Cloléry & Yukio Koriyama, 2020. "Trapped by the Prisoner’s Dilemma, the United States Presidential Election Needs a Coordination Device," Post-Print halshs-03019446, HAL.

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