A core tension in the study of plurality elections is the clash between the classic Hotelling-Downs model, which predicts that two office-seeking candidates should position themselves at the median voter's policy, and the empirical observation that real-world democracies often have two major parties with divergent policies. Motivated by this tension and drawing from bounded rationality, we introduce a dynamic model of candidate positioning based on a simple behavioral heuristic: candidates imitate the policy of previous winners. The resulting model is closely connected to evolutionary replicator dynamics and exhibits complex behavior, despite its simplicity. For uniformly-distributed voters, we prove that when there are $k = 2$, $3$, or $4$ candidates per election, any symmetric candidate distribution converges over time to a concentration of candidates at the center. With $k \ge 5$, however, we prove that the candidate distribution does not converge to the center. For initial distributions without any extreme candidates, we prove a stronger statement than non-convergence, showing that the density in an interval around the center goes to zero when $k \ge 5$. As a matter of robustness, our conclusions are qualitatively unchanged if a small fraction of candidates are not winner-copiers and are instead positioned uniformly at random. Beyond our theoretical analysis, we illustrate our results in simulation; for five or more candidates, we find a tendency towards the emergence of two clusters, a mechanism suggestive of Duverger's Law, the empirical finding that plurality leads to two-party systems. Our simulations also explore several variations of the model, including non-uniform voter distributions and other forms of noise, which exhibit similar convergence patterns. Finally, we discuss the relationship between our model and prior work on strategic equilibria of candidate positioning games.

翻译：在复数选举（plurality elections）研究中的一个核心张力，源自经典Hotelling-Downs模型（预测两位谋求公职的候选人将定位于中位选民政策）与现实民主国家常存在政策分歧的两大主要政党这一经验观察之间的冲突。受此张力启发并基于有限理性，我们引入了一个基于简单行为启发式的候选人定位动态模型：候选人模仿先前获胜者的政策。该模型与进化复制动力学（evolutionary replicator dynamics）紧密相关，尽管形式简单却展现出复杂行为。对于均匀分布的选民，我们证明当每次选举有$k=2$、$3$或$4$位候选人时，任何对称的候选人分布随时间收敛至中心聚集。然而当$k \ge 5$时，我们证明候选人分布不会收敛至中心。对于无极端候选人的初始分布，我们证明了比非收敛性更强的结论：当$k \ge 5$时，中心附近区间内的密度趋于零。在鲁棒性方面，若一小部分候选人非模仿获胜者而是均匀随机定位，我们的结论在定性上保持不变。除理论分析外，我们通过仿真验证了结果：当候选人数量达到五个或更多时，观察到两个簇群（cluster）的涌现趋势——这一机制暗示了迪韦尔热定律（Duverger's Law），即复数选举导致两党制的经验发现。我们的仿真还探索了模型变体，包括非均匀选民分布及其他形式的噪声，这些变体展现出相似的收敛模式。最后，我们讨论了本模型与先前候选人定位博弈策略均衡研究之间的关系。