论文标题
两党选举的表现如何？
How Good Is a Two-Party Election Game?
论文作者
论文摘要
在本文中，我们提出了一个简单而直观的模型，以研究两党选举系统的效率，尤其是在提名过程中。双方中的每一个都有其自己的候选人，每个政党都为包括支持者和非支持者在内的人们带来了公用事业。在选举中，每个方提名其候选人之一与另一方的竞争。如果候选人为所有人带来更多的公用事业，候选人以更高的赔率赢得选举。我们对诸如“两党选举游戏”之类的竞争进行建模，以便每个方都是具有两个或多个纯粹策略与其潜在候选人相对应的球员，每个方的回报是来自选定的一对竞争候选人的混合效用。 通过查看三种模型，即线性链接，布拉德利 - 泰瑞（Bradley-Terry）和软马克斯（SoftMax）模型，这些模型在如何制定候选人对竞争候选人的获胜赔率上有所不同，我们表明两方选举游戏可能没有任何纯粹的纳什平衡均衡，而无政府状态的界限。然而，通过考虑传统的“利己主义”，它指出，任何候选人都比竞争党中的任何候选人都更受党派的支持者的好处，我们证明，线性链接模型和SoftMax模型中的两党选举游戏始终具有纯净的Nash Equilibria，并且还具有Anarchy的价格。
In this paper, we propose a simple and intuitive model to investigate the efficiency of the two-party election system, especially regarding the nomination process. Each of the two parties has its own candidates, and each of them brings utilities for the people including the supporters and non-supporters. In an election, each party nominates exactly one of its candidates to compete against the other party's. The candidate wins the election with higher odds if he or she brings more utility for all the people. We model such competition as a "two-party election game" such that each party is a player with two or more pure strategies corresponding to its potential candidates, and the payoff of each party is a mixed utility from a selected pair of competing candidates. By looking into the three models, namely, the linear link, Bradley-Terry, and the softmax models, which differ in how to formulate a candidate's winning odds against the competing candidate, we show that the two-party election game may neither have any pure Nash equilibrium nor a bounded price of anarchy. Nevertheless, by considering the conventional "egoism", which states that any candidate benefits his/her party's supporters more than any candidate from the competing party does, we prove that the two-party election game in both the linear link model and the softmax model always has pure Nash equilibria, and furthermore, the price of anarchy is constantly bounded.
