On Tournaments and negative dependence

Abstract Negative dependence of sequences random variables is often an interesting characteristic their distribution, as well a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations, the rate increase maximum, and more. In study probability models tournaments, negative participants’ outcomes arises naturally, with application to results. particular, property orthant was proved in several articles different tournament models, special proof each model. this note we unify these results by proving stronger property, association , generalization leading very simple proof. We also present natural example knockout where scores are negatively dependent but not associated. The requires new result on preservation that independent interest.