A set of linear orders on {1,2, \Bbb{N}, n} is acyclic if no three of its orders have an embedded permutation 3-cycle {abc, cab, bca}. Let f (n) be the maximum cardinality of an acyclic set of linear orders on {1,2, \Bbb{N}, n}. The problem of determining f (n) has interested social choice...

In the first competitive election for President of the Social Choice and Welfare Society, the (official) approval-voting winner differed from the (hypothetical) Borda count winner, who was also the Condorcet winner. But because the election was essentially a toss-up, it is impossible to say who...

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...

Riker's size principle for n-person zero-sum games predicts that winning coalitions that form will be minimal in that any player's defection will negate the coalition's winning status. Brams and Fishburn (1995) applied Riker's principle to weighted-majority voting games in which players have...

Let f(n) be the maximum cardinality of an acyclic set of linear orders on {1, 2, … , n}. It is known that f(3)=4, f(4)=9, f(5)=20, and that all maximum-cardinality acyclic sets for n≤ 5 are constructed by an “alternating scheme”. We outline a proof that this scheme is optimal for n=6,...