To resolve the conflict, elections were organized, in which it was necessary to choose the ruler of the village. People who came to the aid of the inhabitants at a decisive moment, in gratitude, received the right to exert a decisive influence on the result of the vote in case of equality of votes.
The situation in the village after the battle developed in such a way that the preference of one or another candidate for these three groups was as follows.
groups: u = (u1, u2, u3),
candidates: Xi = {a, b, c},
where
u1 - a group of aliens, votes for candidate a;
u2 - a group of soldiers, votes for candidate b;
u3 - a group of workers, votes for candidate c;
u1(b) < u1(c) < u1(a),
u2(c) < u2(a) < u2(b),
u3(a) < u3(b) < u3(c)
(the sign "<" means that for this group the candidate on the right is preferable to the candidate on the left).
Three days after the battle, this distribution of strategies is no longer a secret to anyone in the village. Elections tomorrow, on the fourth day.