We study a model of voting with two alternatives in a symmetric environment. We characterize the interim allocation probabilities that can be implemented by a symmetric voting rule. We show that every such interim allocation probability can be implemented as a convex combination of two families...

Theorem 1 in Bhargava, Mohit et al. (2015) provides a necessary condition for a social choice function to be LOBIC with respect to a belief system satisfying top-set (TS) correlation. In this paper, we provide a counter example to that theorem and consequently provide a new necessary condition...