The Effects of Voting Mechanisms on Compromise: Two Models of Collective Decision-Making

Abstract: Social choice theory studies how individual preferences are aggregated into collective decisions, considering objectives such as fairness, representation, and welfare. Growing concerns about political polarization have renewed interest in whether voting mechanisms can promote compromise rather than merely reflect existing divisions. We investigate this question through two distinct models of collective decision-making. The first model concerns proxy voting, where voters delegate their votes to active participants (proxies). Although delegation is not primarily intended to promote compromise, we show that strategic behavior can have precisely this effect. We consider a one-dimentional political spectrum, proximity-based delegation, and policy is select via weighted median. We show that, while inactive voters have no incentive to misreport their preferences, proxies can manipulate the outcome by changing their declared positions. Under mild behavioral restrictions, repeated strategic adjustments converge to the median of the entire electorate. We extend our analysis to partial-information settings, where favorable convergence guarantees persist under regret-averse behavior. The second model examines compromise through the lens of polarization in committee elections: selecting a committee that connects different parts of the electorate rather than highlighting their divisions. We study the interlacing framework for approval-based committee selection, in which each committee induces a graph connecting voters who approve common representatives. We show that existing connectivity measures can overlook important structural differences and propose edge-expansion to capture the robustness of connections across voter groups. We relate this measure to the time to reach consensus in an opinion diffusion model. We further examine limitations, notably the computational challenges of selecting optimal committees, while identifying cases where efficient computation is possible. Together, these studies illustrate how voting mechanisms can affect the prospects for compromise through policy outcomes and through structural properties of the electorate as reflected by its elected representatives.