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Supplemental material, JTP_Mar_2019_Appendix for Voting behavior under proportional representation by Peter Buisseret and Carlo Prato in Journal of Theoretical Politics

We study dynamic international agreements when one of the negotiating parties faces a threat of electoral replacement during negotiations, when agreements made before the election are the starting point for any subsequent renegotiation, and when governments cannot commit to future negotiation strategies. Conflicts of interest between governments may be softened or intensified by the governments’ conflicts of interest with voters. We characterize when the threat of electoral turnover strengthens the prospect for successful negotiations, when it may cause negotiations to fail, and how it affects the division of the surplus from cooperation. We also show how changes in domestic politics—including uncertainty about the preferences of domestic political parties—affect a domestic government’s ability to extract greater concessions in negotiations.

We study multi-district legislative elections between two office-seeking parties when the election pits a relatively strong party against a weaker party ; when each party faces uncertainty about how voter preferences will evolve during the campaign; and, when each party cares not only about winning a majority, but also about its share of seats in the event that it holds majority or minority status. When the initial imbalance favoring one party is small, each party targets the median voter in the median district, in pursuit of a majority. When the imbalance is moderate, the advantaged party continues to hold the centre-ground, but the disadvantaged party retreats to target its core supporters; it does so to fortify its minority share of seats in the likely event that it fails to secure a majority. Finally, when the imbalance is large, the advantaged party advances toward its opponent, raiding its moderate supporters in pursuit of an outsized majority.

In democratic politics, voters delegate competing policy-making responsibilities to multiple elected agents: one agent is frequently tasked with initiating policies (the proposer ) whilst the other is charged with scrutinizing and either passing or rejecting these policies (the veto player ). A fundamental distinction lies in whether both offices are subject to direct and separate election, or whether the voter instead may directly elect only one office. Why should the voter benefit from a relatively coarse electoral instrument? When politicians’ abilities are private information, actions taken by one agent provide information about both agents’ types. A system in which their electoral fates are institutionally fused reduces the incentives of the veto player to build reputation through the specious rejection of the proposer’s policy initiatives. This can improve the voter’s welfare, relative to a system in which the survival of the veto player is institutionally separated from that of the proposer.