Min-wise independence is a recently introduced notion of limited independence, similar in spirit to pairwise independence. The later has proven essential for the derandomization of many algorithms. Here we show that approximate min-wise independence allows similar uses, by presenting a derandomization of the RNC algorithm for approximate set cover due to S. Rajagopalan and V. Vazirani. We also ...

Object-oriented Bayesian networks (OOBNs) facilitate the design of large Bayesian networks by allowing Bayesian networks to be nested inside of one another. Weak conditional independence has been shown to be a necessary and sufficient condition for ensuring consistency in OOBNs. Since weak conditional independence plays such an important role in OOBNs, in this paper we establish two useful resu...

Because players whose preferences violate the von Neumann-Morgenstern independence axiom may be unwilling to randomize as mixed-strategy Nash equilibrium would require, a Nash equilibrium may not exist without independence. This paper generalizes Nash’s definition of equilibrium, retaining its rationalexpectations spirit but relaxing its requirement that a player must bear as much uncertainty a...

Weak independence (WI) prevents x from socially ranking above y at profile p if y ranks above x at profile p9 and each individual ordering of hx,yj is the same at p as at p9. If f is transitive-valued and satisfies WI and Pareto then someone has veto power.  2000 Elsevier Science S.A. All rights reserved.