Let $X$ be a finite set and $2^{X}$ denote its power set excluding the empty set. Definition 1: A choice correspondence over $X$ is a map $C:2^{X}\mapsto 2^{X}$ such that $C(A)\subseteq A$ for all non-empty $A\subseteq X$. Consider the following order relation ($\succeq$) defined in $2^{...