Three-party competition in parliamentary democracy with proportional representation

This article studies the long-run dynamics of policy choices, government formations, and voting behavior under a parliamentary constitution and proportional representation. I develop an infinite period game where, in each period, voters participate in a proportional representation election, and three farsighted parties bargain over one-dimensional policy programs and government positions. The model incorporates the interaction between elections and coalition bargaining, which is the essence of politics in most parliamentary systems, as well as a dynamic environment of policymaking: a policy once implemented remains in effect until another replaces it. I find a Markov perfect equilibrium in which (1) there is no majority party in any election; (2) election results converge over time to a stable vote distribution; (3) policy outcomes change over time but eventually stay within a set of three points; (4) minimal winning coalitions and minority governments are formed with positive probability and alternate over time.