Instant runoff voting (IRV) has gained popularity in recent years as an alternative to traditional plurality voting. Advocates of IRV claim that one of its benefits relative to plurality voting is its tendency toward moderation: that it produces more moderate winners than plurality and could therefore be a useful tool for addressing polarization. However, there is little theoretical backing for this claim, and existing evidence has focused on simulations and case studies. In this work, we prove that IRV has a moderating effect relative to traditional plurality voting in a specific sense, developed in a 1-dimensional Euclidean model of voter preferences. Our results show that as long as voters are symmetrically distributed and not too concentrated at the extremes, IRV will not elect a candidate that is beyond a certain threshold in the tails of the distribution, while plurality can. For the uniform distribution, we provide an approach for deriving the exact distributions of the plurality and IRV winner positions, enabling further analysis. We also extend a classical analysis of so-called stick-breaking processes to derive the asymptotic winning plurality vote share, which we use to prove that plurality can elect arbitrarily extreme candidates even when there are many moderate options.

翻译：即时决选（IRV）近年来作为传统多数决投票的替代方案日益普及。支持者声称，相较于多数决投票，IRV的优势之一在于其趋向温和性：即它比多数决投票更容易产生温和的获胜者，从而可能成为应对政治两极分化的有效工具。然而，这一主张缺乏充分的理论支撑，现有证据主要基于模拟与案例研究。本研究证明，在选民偏好的一维欧几里得模型中，IRV相对于传统多数决投票具有特定意义上的温和效应。结果表明，只要选民分布对称且不过度集中于极端区间，IRV将不会选出位于分布尾端某一阈值之外的候选人，而多数决投票则可能选出这类候选人。针对均匀分布，我们提出了一种方法，可推导出多数决投票与IRV获胜者位置的确切分布，从而支持进一步分析。此外，我们拓展了经典"断棍过程"的分析，推导出多数决投票获胜者的渐进得票率，籍此证明即便存在众多温和选项，多数决投票仍可能选出极为极端的候选人。