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）近年来作为复数投票制在政治选举中的替代方案日益流行，支持者声称其具有一系列优势，包括比复数投票制更能产生温和的胜选者，从而有助于缓解政治极化。然而，这一主张缺乏理论基础，现有证据主要集中于案例研究和模拟。本研究在选民偏好的单维欧几里得模型中，精确证明了IRV相对于复数投票制具有调节效应。我们基于选民分布特性发展了一套排除区理论，用以揭示IRV计票过程中温和与极端候选人的互动机制。该理论证明：若选民呈对称分布且非过度集中在极端区间，IRV不可能使极端候选人击败温和候选人；相反，我们证明复数投票制可能产生此类结果，并通过计算实验验证了该结论。本方法为投票系统分析提供了新框架，通过几何方法推导胜选者精确分布，并建立了复数投票制与断棍过程之间的关联。