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theories and methods of economics

Consider the problem of dividing $100 among three people. Suppose two of them agree to split that sum, with $60 going to one and $40 to the other. The third person, who receives nothing, has an incentive to strike a bargain with the second, offering a split of, say, $50 each, which makes them both better off than under the initial proposal. Faced with desertion, the first person can destabilize the new coalition by offering to accept $45, leaving $55 for one of the others. And so on. The game has three possible (and equally likely) outcomes in which two of the three players accept payments of $50 each, but the third player can always upset the equilibrium by cutting another deal. The same endless series of changing winning coalitions or vote “cycles” can emerge in elections involving three or more candidates or ballot issues when no one of them is strongly preferred by a simple majority of the voters.