Reaching collective decisions

Collective decision-making (with voting protocols being its central tool) is a key component of many applications, including socio-economic or technological systems. Based on the fact, that voters may have incentives to strategically misreport their preferences, much of the literature in computational social choice focuses on evaluating voting mechanisms by their resistance to strategic behaviours and uses computational complexity as a barrier to them. We take another natural approach and analyse voting scenarios from a game-theoretic perspective, viewing strategic parties as players and examining possible stable outcomes of their interaction (i.e., equilibria). In particular, we are interested in the outcomes that can result from natural iterative processes, such as best-response dynamics or its restricted variants. Convergence of such procedures is a highly desirable property of the game, since, from a system-wide perspective, it implies that a system has a deterministic stable state that can be reached by the players without any centralised control and/or communication. We derive conditions on how the iterative process should (or not) be restricted to achieve convergence and, on the other hand, offer a framework where such restricted voting dynamics are justified as boundedly rational decisions under uncertainty.