A Game Theoretical Study of “Heiritsu-sei”

Abstract

In the context of “Shou-senkyoku=Hirei-daihyou=Heiritsu-sei, “Duverger's Law” will be studied using a game theoretical model. The main result is two theorems. The Negative Theorem is that exit from an election, which means implicit alliance, occurs only if the Condorcet winner is not the biggest party. The Positive Theorem is that except for the case of a chicken game without suitable focal point, the Condorcet winner always wins the election in the equilibrium.

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33 小選挙区比例代表並立制に関す るゲーム論的一考察

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37 小選挙区比例代表並立制に関するゲーム論的一考察
表I ケ ー ス1.(#α>#β,#γ;#α>#β+#γ;#α+#β α>#β γ+#γ;;#α+#β>#γ)
A=最 大政党=コ ン ドルセ 勝 利 者=A
表II ケ ー ス2.(#α>#β,#γ;#α<#β+#γ;#α+#β α>#β γ+#γ;;#α+#β>#γ)
A=最 大政 党 ≠ コン ドル セ 勝 利 者=B
表III ケ ー ス3.(#α>#β,#γ;#α<#β+#γ;#α+#β α<#β γ+#γ;;#α+#β>#γ)
A=最 大政 党 ≠ コン ドルセ勝 利者=B
ケ ー ス 3-1.(BがCよ りもAの 勝 利 を好 む)
表IV ケ ー ス3.(#α>#β,#γ;#α<#β+#γ;#α+#β α<#β γ+#γ;;#α+#β>#γ)
A=最 大政 党 ≠ コ ン ドルセ勝 利者=B
ケ ー ス3-2.(BがAよ りもCの 勝 利 を 好 む)チ キ ン ゲ ー ム

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表V ケ ー ス4.(#β>#α,#γ;#α<#β+#γ;#α+#β α>#β γ+#γ;;#α+#β>#γ)
B=最 大 政 党=コ ン ドル セ 勝 利 者=B

39 小選挙区比例代表並立制に関するゲーム論的一考察

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A Game Theoretical Study of "Heiritsu-sei"
Junichiro WADA
In the context of "Shou-senkyoku=Hirei-daihyou=Heiritsu-sei, "Duverger's
Law" will be studied using a game theoretical model. The main result is two
theorems. The Negative Theorem is that exit from an election, which means
implicit alliance, occurs only if the Condorcet winner is not the biggest party. The
Positive Theorem is that except for the case of a chicken game without suitable
focal point, the Condorcet winner always wins the election in the equilibrium.