We consider a stronger version of the paradox of multiple elections and show that it is possible that not only the winning combination of propositions, but also all the combinations sufficiently close to it, receive zero votes.

In this paper we study some stochastic orders of positive dependence that arise when the underlying random vectors are ordered with respect to some multivariate hazard rate stochastic orders, and have the same univariate marginal distributions. We show how the orders can be studied by...

In this paper the meaning of the stochastic ordering relation is studied when the random vectors which are compared are assumed to be permutation symmetric. It is shown that in order to establish the stochastic ordering relation between two such random vectors it is enough to consider only upper...

We provide a simple characterization of the zonoid, lift zonoid, Lorenz zonoid of a random vector, as defined by Koshevoy and Mosler (J. Amer. Statist. Assoc. 91 (1996) 873; Bernoulli 4 (1998) 377). This characterization allows a direct use of Lyapunov's theorem on the range of nonatomic vector...

Several well-known stochastic orderings are defined in terms of iterated integrals of distribution or survival functions. In this note we will provide necessary conditions for some variability orderings of the above type. These conditions will be based on the comparison of mean differences,...