Stable Coalition-Governments: The Case of Three Political Parties
We explore to what extent we can propose fixed negotiation rules as well as simple mechanisms (or protocols) that guarantee that political parties can form stable coalition-governments. We analyze the case where three parties can hold office in the form of two-party coalitions. We define the family of Weighted Rules, that select political agreements as a function of the bliss-points of the parties, and electoral results (Camson's Law and equal-share among others are included). We show that every weighted rule yields a stable coalition. We make use of the theory of implementation to design a protocol (in the form of a mechanism) that guarantees that a stable coalition will govern. We find that no dominant-solvable mechanism can be used for this purpose, but there is a simultaneous-unanimity mechanism that implements it in Nash and strong Nash equilibrium.
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