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.

We must properly model attacks and the preferences of the electorate for the computational study of attacks on elections to give us insight into the hardness of attacks in practice. Theoretical and empirical analysis are equally important methods to understand election attacks. I discuss my recent work on domain restrictions on partial preferences and on new election attacks. I propose further study into modeling realistic election attacks and the advancement of the current state of empirical analysis of their hardness by using more advanced statistical techniques.