世界银行-排名重要时的投票：真实的平衡、效率和弃权（英）-2024.7-43页_490kb

🐾 Voting when Rankings Matter: Analysis of Truthful Equilibria, Efficiency, and Abstention

This paper addresses the use of ranked-choice voting systems, examining their properties in terms of truthful voting (individuals reveal their true preferences) and overall efficiency.

Key points:

1. Truthful Nash Equilibrium: The work demonstrates that truthful voting always represents a pure-strategy Nash equilibrium across various voting rules and individual preference structures. This means no voter can strictly benefit by deviating from their true ranking, regardless of the complexity or any restrictions imposed on preferences or voting methods. This is a major finding, as it contrasts with some traditional voting systems (like plurality) which can incentivize strategic ("false") voting to manipulate outcomes.
2. Robustness: The conclusion that truthful voting is an equilibrium remains valid even if the resulting social ranking is cyclic (ranking cycles like the Condorcet Paradox can occur) or if preferences and voting rules are restricted to ensure an acyclic/socially transitive outcome. Thus, the result isn't limited to specific narrow scenarios.
3. Pareto Efficiency (Limited Cases): While truthful voting is robustly an equilibrium, it is Pareto efficient (beneficial for balancing everyone's interests to the maximum extent) only under specific conditions. This includes scenarios where:
   • There are exactly two candidates.
   • Voters have strict linear preferences (no indifference).
   • A more general condition is met where voter preferences are neutral (valuing all candidate pairs equally in terms of social comparison weight), social incomparability is resolved probabilistically, and the truthful vote results in a complete social ranking (ranking established priorities for all candidate pairs).
4. Comparison to Traditional Systems: Ranking voting mechanisms can mitigate issues associated with traditional systems like plurality or range voting, such as vote-splitting (where multiple similar candidates' votes divide support, potentially altering the winner). However, it also faces challenges like strategic abstention when individual participation is costly but voluntary, partially built on earlier research.

In essence, ranked voting emerges as a system where individuals have a strong incentive to vote truthfully due to its equilibrium properties. The high rate of truthful reporting can lead to outcomes better reflecting societal preferences than systems encouraging strategic behavior. This offers a potential improvement in efficiency over some traditional ordinal voting methods but requires careful consideration of specific conditions for full Pareto efficiency.