War and Peace in Veto Voting

Let $I = \{i_1, \ldots, i_n\}$ be a set of voters (players) and $A = \{a_1, \ldots, a_p\}$ be a set of candidates (outcomes). Each voter $i \in I$ has a preference $P_i$ over the candidates. We assume that $P_i$ is a complete order on $A$. The preference profile $P = \{P_i, i \in I\}$ is called a {\em situation}. A situation is called {\em war} if the set of all voters $I$ is partitioned in two coalitions $K_1$ and $K_2$ such that all voters of $K_i$ have the same preference, $i = 1,2,$ and these two preferences are opposite. For a simple class of veto voting schemes we prove that the results of elections in all war situations uniquely define the results for all other ({\em peace}) situations.