We consider the problem of counting straight-edge triangulations of a given set P of n points in the plane. Until very recently it was not known whether the exact number of triangulations of P can be computed asymptotically faster than by enumerating all triangulations. We now know that the number of triangulations of P can be computed in O∗(2n) time [2], which is less than the lower bound of Ω...

I show that if one is only interested in local results — that is, theorems about what is true at a state — which only depend on finitely many orders of beliefs about beliefs, then the common prior assumption is essentially irrelevant. More precisely, given any model where priors have the same support and any finite N, there is another model with common priors which has the same nth order belief...

The classic Gibbard-Satterthwaite Theorem establishes that only dictatorial voting rules are strategy-proof; under any other voting rule, players have an incentive to lie about their true preferences. We consider a new approach for circumventing this result: we consider randomized voting rules that only approximate a deterministic voting rule and only are approximately strategy-proof. We show t...

1. An interesting class of real functions of a single real variable, the approximately continuous functions, was introduced by Denjoy [l] in his work on derivatives. The two principal facts discovered by Denjoy are that these functions are of Baire class 1 and have the Darboux property. Ridder [2] showed that the arguments of Denjoy apply to real functions of n variables. In this paper we discu...