Bloc Voting on Single Peaked Preferences
Ariel Calver, Serena Pallan, Alice, Park, Jennifer Wilson
TL;DR
This work characterizes the structure of winning coalitions under Bloc voting when voter preferences are single-peaked. It derives exact and asymptotic results on adjacency, Gehrlein-stability, and local stability, with complete characterizations for small candidate sets and general insight for larger ones, complemented by Monte Carlo simulations across distinct voter-behavior models. A key finding is that when $k \\ge\\lceil m/2 ceil$, winning sets are adjacent and Gehrlein-stable, while for smaller $k$ non-adjacent and non-Gehrlein-stable configurations can occur yet remain locally stable in many cases; simulations show model-dependent frequencies and agreements with Copland. The results illuminate when Bloc voting approximates Condorcet-consistent behavior in single-peaked electorates and highlight center-squeeze phenomena, offering guidance for practical multi-winner elections and further theoretical exploration across arbitrary $m$.
Abstract
We analyze the winning coalitions that arise under Bloc voting when voters preferences are single-peaked. For small numbers of candidates and numbers of winners, we determine conditions under which candidates in winning coalitions are adjacent. We also analyze the results of pairwise contests between winning and losing candidates and assess when the winning coalitions satisfy several proposed extensions of the Condorcet criterion to multiwinner voting methods. Finally, we use Monte Carlo simulations to investigate how frequently these coalitions arise under different assumptions about voter behavior.