Strategic party formation on a circle and Duverger's Law

Ronald Peeters*, Rene Saran, Ayse Muge Yuksel

*Corresponding author for this work

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Duverger’s law states that plurality rule tends to favor a two-party system. We study the game-theoretic foundations of this law in a spatial model of party formation and electoral competition. The standard spatial model assumes a linear agenda space. However, when voters vote sincerely, electoral competition on the line under plurality rule gravitates towards a single party located at the median. We therefore depart from the linear space and instead adopt the unit circle as the space of agendas. We characterize pure-strategy (subgame-perfect) nash equilibria under both sincere and strategic voting. Under both voting behaviors, multiple configurations of parties are possible in equilibrium. We refine our predictions using a new notion called defection-proof (subgame-perfect) nash equilibrium. Under sincere voting, either two or three parties are effective in defection-proof nash equilibria, whereas under strategic voting, either one or two parties are effective in defection-proof subgame-perfect nash equilibria. These results are partially consistent with duverger’s law.
Original languageEnglish
Pages (from-to)729-759
JournalSocial Choice and Welfare
Issue number3
Publication statusPublished - Oct 2016

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