A Better Cycle-Breaker for Direct Democracy?

摘要

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.