Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. We develop a theory of exclusion zones, derived from properties of the voter distribution, which serve to show how moderate and extreme candidates interact during IRV vote tabulation. The theory allows us to prove that if voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can and validate our results computationally. Our methods provide new frameworks for the analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.

翻译：即时决选投票（IRV）近年作为单轮多数投票的替代方案在政治选举中日益普及，支持者声称其具备多重优势，包括比多数投票制更能产生温和型获胜者，从而有助于缓解政治极化。然而，这一主张缺乏理论支撑，现有证据主要基于案例研究与模拟分析。本研究在选民偏好的一维欧几里得模型中，从精确意义上证明了IRV相对于多数投票具有调节效应。我们基于选民分布特性构建了排斥区理论，用以揭示温和候选人与极端候选人在IRV计票过程中的交互机制。该理论证明，当选民呈对称分布且非过度集中于极端立场时，IRV不会选举出极端候选人取代温和候选人；相反，我们证明多数投票制可能产生此类结果，并通过计算实验验证了结论。本研究为投票系统分析提供了新框架，通过几何方法推导获胜者精确分布，并建立了多数投票与断棍过程之间的关联。