Stable coalition governments: the case of three political parties

We explore to what extent we can propose …xed 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 o¢ ce in the form of two-party coalitions. We de…ne the family of Weighted Rules, that select political agreements as a function of the bliss-points of the parties, and electoral results (Gamson’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 …nd 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.