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 are assumed to rank each other as coalition partners. Two processes of coalition formation are defined and illustrated: i) Fallback (FB): Players seek coalition partners by descending lower and lower in their preference rankings until some majority coalition, all of whose members...

Ordinally single-peaked preferences are distinguished from cardinally single-peaked preferences, in which all players have a similar perception of distances in some one-dimensional ordering. While ordinal single-peakedness can lead to disconnected coalitions that have a "hole" in the ordering,...

In the much-studied Centipede Game, which resembles the Iterated Prisoners' Dilemma, two players successively choose between (1) cooperating, by continuing play, or (2) defecting and terminating play. The subgame-perfect Nash equilibrium implies that play terminates on the first move, even...

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...

We extend approval voting so as to elect multiple candidates, who may be either individuals or members of a political party, in rough proportion to their approval in the electorate. We analyze two divisor methods of apportionment, first proposed by Jefferson and Webster, that iteratively...

Assume two players, A and B, must divide a set of indivisible items that each strictly ranks from best to worst. If the number of items is even, assume that the players desire that the allocations be balanced (each player gets half the items), item-wise envy-free (EF), and Pareto-optimal (PO)....

We apply a fallback model of coalition formation to decisions of the U.S. Supreme Court, focusing on the seven natural courts, which had the same members for at least two terms, between 1969 and 2009. The predictions of majority coalitions on each of the courts are generally bourn out by the 5-4...