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,...

Riker's `size principle' predicts that only minimal winning coalitions (MWCs) will form in n-person zero-sum games that satisfy certain conditions. After summarizing the logic of this principle, a model is proposed in which n players can be ordered from most to least weighty. Two different kinds...