Question

If Party A and B are competing on an election, and the median voter of the election has an ideal point of 1. If Party A's candidate has an ideal point of 0.55 and Party B's candidate has an ideal point of 1.45, who wins the election? From the median voter theorem, I know that the only equilibria is when both candidates stand at the ideal point 1. But then who wins the election if both parties' ideal points are in the same distance from the ideal point?

Answer 1

Yes, according to the median voter theorem the Nash equilibrium is indeed for both parties to stand at 1. But if this is not case, the party with the closest distance wins. If the distance is equal then, the problem either gives a tie-breaker rule. These are basically of two types: either one party always wins in the case of a tie or both parties can with a probability of 1/2

If the question does not specify the rule, we have a tie and both parties can win with a probability fo 1/2