War and peace in veto voting

Let I={i1,…,in}I={i1,…,in} be a set of voters (players) and A={a1,…,ap}A={a1,…,ap} be a set of candidates (outcomes). Each voter i∈Ii∈I has a preference Pi over the candidates. We assume that Pi is a complete order on A  . The preference profile P={Pi,i∈I}P={Pi,i∈I} is called a situation. A situation is called war if the set of all voters I is partitioned in two coalitions K1 and K2 such that all voters of Ki have the same preference, i=1,2,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 (peace) situations. In other words, the results depend only on the veto (or effectivity) function. We give several other examples from game (and from graph) theory with the same property.