An allocation of indivisible items among n ≥ 2 players is proportional if and only if each player receives a proportional subset—one that it thinks is worth at least 1/n of the total value of all the items. We show that a proportional allocation exists if and only if there is an allocation...

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they fall back on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the players...

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they “fall back” on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the...

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they "fall back" on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the...

In U.S. presidential elections, voters in noncompetitive states seem not to count — and so have zero voting power, according to the Banzhaf and other voting-power indices — because they cannot influence the outcome in their states. But because the electoral votes of these states are...

Gale and Shapley (1962) proposed the deferred-acceptance algorithm for matching (i) college applicants and colleges and (ii) men and women. In the case of the latter, it produces either one or two stable matches whereby no man and woman would prefer to be matched with each other rather than with...

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they 'fall back' on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the...