If the players nominated
{x1, x2, x3},
then the elections take place according to the rule
x2 if x2 = x3;
x1 if x2 ≠ x3.
Note that player 2's strategy x2 = c is dominated by strategy b, and that strategies a and b are neither dominated nor equivalent. Hence, the set of non-dominated strategies of player 2 is equal to {a, b}. Similarly, for player 3, the set of non-dominated strategies is {b, c}. On the other hand, player 1, whose vote resolves disputes, has a dominant strategy (that is, a game strategy that brings him at least as good results as any other strategy, regardless of the strategy chosen by the opposing side), namely a. Thus, if we assume that the players will not use dominated strategies, then the sets of strategies will narrow down to
for player 1 {a}, for player 2 {a, b}, for player 3 {b, c}.
With this truncation of the sets of strategies for player 2, strategy a is now dominated by strategy b and can therefore be eliminated. Similarly, player 3's strategy c is now dominated by strategy b. Therefore, after two rounds of elimination of dominated strategies, each player will have one strategy left, and candidate b will be elected, despite the fact that he is the worst candidate for player 1. Consequently, the right of the first player to resolve disputable situations turns out to be his weak point in the game, because it makes it possible to immediately foresee his strategic choice.