Games and Economic Behavior · 2026 · Hans Gersbach、Rodrigo Casado Noguerales、Samuel Schenk
中文摘要
当针对修改瑞士宪法的公民动议提出反建议时，公民要作出三项二元多数选择：动议对现状、反建议对现状，以及作为打破平局机制的动议对反建议。若这三项多数选择形成循环，现行规则会选择击败现状的备选方案。这一规则可能导致策略性投票。我们建议以不同方式打破循环，即在出现循环时选择中间备选方案，而通常该方案即为反建议。更准确地说，我们在偏好为单峰且其分布为共同知识的条件下，研究满足孔多塞一致性（Condorcet-consistent）的两两多数投票程序。随后我们表明，只要强纳什均衡存在，其结果便与真诚投票下的结果相同；并刻画了使真诚投票本身即为强纳什均衡的循环打破默认规则。特别地，在针对两种可能循环采用相同默认规则的程序中，中间备选方案是唯一的共同默认规则。
Abstract
When a counter-proposal is made to an initiative to change the Swiss constitution, the citizenry makes three binary majority choices: the initiative versus the status quo, the counter-proposal versus the status quo, and the initiative versus the counter-proposal as a tie-breaker. If the three majority choices form a cycle, the current rule selects the alternative that beats the status quo. This rule may lead to strategic voting. We suggest breaking cycles differently by choosing the middle alternative in case of a cycle, which will normally be the counter-proposal. More precisely, we study Condorcet-consistent pairwise majority voting procedures when preferences are single-peaked and their distribution is common knowledge. We then show that whenever a strong Nash equilibrium exists, its outcome is the same as under sincere voting, and we characterize the cycle-breaking defaults for which sincere voting is itself a strong Nash equilibrium. In particular, among procedures that use the same default for both possible cycles, the middle alternative is the unique common default.