Positions and votes Candidate who gets most votes wins.

(x + x )/2 12

^{x}1

m

^{x}2

vote for 1

vote for 2

In this case, candidate 1 wins.

# Best responses

# Best response of candidate i to x_{j}:

•

x

_{j }< m:

^{x}j

m

any position for i in here wins

candidate i wins if x_{i }> x_{j }and ^{1 }(x_{i }+ x_{j }) < m or in , 2

other words x_{j }< x_{i }< 2m − x_{j}. Otherwise she either ties or loses. Thus every position between x_{j }and 2m − x_{j }is a best response of candidate i to x_{j}.

•

x

_{j }> m: symmetrically, every position between 2m − x_{j }and x_{j }is a best response of candidate i to x_{j}.•

x

_{j }= m: if candidate i choose x_{i }= m she ties for first place; if she chooses any other position she loses. Thus m is the unique best response of candidate i to x_{j}.

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