The Theory of Political Coalitions

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The Theory of Political Coalitions is a book on positive political theory written by William H. Riker published in 1962. It uses game theory to formalize political theory. In it, Riker deduces the size principle. On its postulates, politicians are proved to form winning, minimal-size coalitions. The work runs contrary to a previous theory that politicians try to maximize their respective votes. Riker supposes that attracting more votes requires resources and that politicians run to win. So, a rational politician tries to form a coalition that is as large as necessary to win but not larger.

Minimal size coalitions[edit]

An example. Lets imagine a five-party system after a general election. The representation is given:

Party A Party B Party C Party D Party E
Number of representatives 5 40 26 25 4 Sum: 100

We now have three possible winning coalitions:

Party B and C Party B and D Party C and D
40+26=66 representatives 40+25=65 representatives 26+25=51 representatives

If we now presume that the power will be divided according to strength within the coalition, the parties will prefer the largest relative size within the coalition. The result is that the coalition "Party C and D" will be the winning coalition. The largest party is thus kept from power.


The assumption that governments will form on the base of minimal winning coalitions, has a poor empirical foundation in Western European multi-party systems.[citation needed]

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