Moderation in instant runoff voting

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.