[论文解读] A Local-Dominance Theory of Voting Equilibria

Reshef Meir, Omer Lev+1 more|arXiv (Cornell University)|Apr 18, 2014

Game Theory and Voting Systems参考文献 38被引用 22

一句话总结

本文提出了一种在多数制规则下的策略性投票的局部占优模型，该模型考虑了有限理性与信息有限性。选民基于从民意调查中获得的可能世界状态集合，使用一种启发式方法，仅对在该集合内不被占优的候选人投票。该模型证明了均衡的存在性，并表明从真实或随机初始状态出发，均能实现快速且稳健的收敛，且均衡始终一致地再现杜弗杰定律，同时相比真实投票提升了胜者质量。

ABSTRACT

It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice. Multiple game-theoretic models have been proposed to better understand and predict such behavior and the outcomes it induces. However, these models often make unrealistic assumptions regarding voters' behavior and the information on which they base their vote. We suggest a new model for strategic voting that takes into account voters' bounded rationality, as well as their limited access to reliable information. We introduce a simple behavioral heuristic based on \emph{local dominance}, where each voter considers a set of possible world states without assigning probabilities to them. This set is constructed based on prospective candidates' scores (e.g., available from an inaccurate poll). In a \emph{voting equilibrium}, all voters vote for candidates not dominated within the set of possible states. We prove that these voting equilibria exist in the Plurality rule for a broad class of local dominance relations (that is, different ways to decide which states are possible). Furthermore, we show that in an iterative setting where voters may repeatedly change their vote, local dominance-based dynamics quickly converge to an equilibrium if voters start from the truthful state. Weaker convergence guarantees in more general settings are also provided. Using extensive simulations of strategic voting on generated and real preference profiles, we show that convergence is fast and robust, that emerging equilibria are consistent across various starting conditions, and that they replicate widely known patterns of human voting behavior such as Duverger's law. Further, strategic voting generally improves the quality of the winner compared to truthful voting.

研究动机与目标

• 解决博弈论投票模型中缺乏现实解概念的问题，这些模型假设完全理性和完全信息。
• 在有限理性和有限可靠信息获取条件下，建模策略性投票行为。
• 开发一种基于局部占优的行为启发式方法，捕捉选民在不为结果分配概率的情况下如何做决策。
• 证明在多数制投票中，对于一大类局部占优关系，该模型下存在投票均衡。
• 展示在迭代投票动态下，即使从任意或真实初始状态出发，也能快速且稳健地收敛至均衡。

提出的方法

• 选民基于潜在候选人从可能不准确的民意调查中获得的得分，构建一组可能的世界状态。
• 每位选民应用局部占优启发式：仅对在其可能状态集合中不被占优的候选人投票，其中占优通过集合内成对比较定义。
• 将投票均衡定义为所有选民均在其各自可能状态集合中投票给不被占优候选人的选票组合。
• 该模型采用迭代动态机制，选民根据局部占优更新其投票，收敛性在单个选民与群体调度器下进行分析。
• 通过在合成和真实偏好配置上进行大量模拟评估该框架，测量收敛速度、均衡一致性以及多个指标下的胜者质量。
• 在多种条件下测试该模型：真实和随机初始状态、不同选民间类型（真实偏好型、偷懒偏好型），以及多种偏好分布（均匀分布、Placket-Luce分布、单峰分布、Riffle分布）。

实验结果

研究问题

• RQ1 基于局部占优的策略性投票模型是否能在多数制规则下，即使在有限理性和信息有限的情况下，仍产生稳定均衡？
• RQ2 基于局部占优的迭代投票动态是否能从真实或随机投票配置出发，快速收敛至均衡？
• RQ3 所出现的均衡在多大程度上再现了如杜弗杰定律等已知经验模式？
• RQ4 与真实投票相比，基于局部占优的策略性投票如何影响当选胜者的质量？
• RQ5 均衡在不同初始条件和选民间类型下的一致性如何？

主要发现

• 该局部占优模型保证了在多数制规则下，对于一大类局部占优关系，均存在投票均衡。
• 从真实选票配置出发的迭代动态中，均衡收敛迅速且可靠，模拟显示在所有测试分布下均实现快速收敛。
• 均衡在模拟中高度一致：多数情况下WinnerConsistency超过0.8，单峰分布与Placket-Luce分布中TotalDuverger超过0.9，表明杜弗杰定律得到强有力再现。
• 基于局部占优的策略性投票提升了胜者质量：WinnerGroundRank显示，胜者平均而言比真实投票更接近真实理想候选人，尤其在接近理性峰值水平时表现更优。
• PluralityAgreement较高（通常高于0.7），但BordaAgreement、CopelandAgreement与CondorcetAgreement在许多分布中显著更高，表明策略性均衡通常会选择更具社会最优性的胜者。
• 即使从随机初始状态出发，策略性行为也比真实投票产生更好的平均胜者质量，WinnerGroundRank与社会福利指标的一致性改善表明了这一点。