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Strategic party formation on a circle and Duverger’s Law

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Article
Author/s: 
Ronald Peeters, Rene Saran, Ayşe Müge Yüksel
Social Choice and Welfare
Issue number: 
August 2016
Publisher: 
Springer
Year: 
2016
Journal pages: 
1-31
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.
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