Approval voting (AV) is a voting system in which voters can vote for, or approve of, as many candidates as they like in multicandidate elections. In 1987 and 1988, four scientific and engineering societies, collectively comprising several hundred thousand members, used AV for the first time....

Political parties in Northern Ireland recently used a divisor method of apportionment to choose, in sequence, ten cabinet ministries. If the parties have complete information about each others' preferences, we show that it may not be rational for them to act sincerely by choosing their...

IN his classic novel, "Catch-22" (1961), Joseph Heller describes a thoroughly frustrating situation faced by a combat pilot in World War II. This is generalized to a "generic" 2x2 strict ordinal game, in which whatever strategy the column player chooses, the best response of the row player is to...

Fallback bargaining is a bargaining procedure under which bargainers begin by indicating their preference rankings over all alternatives. They then fall back, in lockstep, to less and less preferred alternatives - starting with first choices, then adding second choices, and so on - until an...

This paper focuses on the fair division of a set of indivisible items between two people when both have the same linear preference order on the items but may have different preferences over subsets of items. Surprisingly, divisions that are envy-free, Pareto-optimal, and ensure that the less...

A cornerstone of game theory is backward induction, whereby players reason backward from the end of a game in extensive form to the beginning in order to determine what choices are rational at each stage of play. Truels, or three-person duels, are used to illustrate how the outcome can depend on...