Positions and votes Candidate who gets most votes wins.
(x + x )/2 12
vote for 1
vote for 2
In this case, candidate 1 wins.
Best response of candidate i to xj:
xj < m:
any position for i in here wins
candidate i wins if xi > xj and 1 (xi + xj ) < m or in , 2
other words xj < xi < 2m − xj. Otherwise she either ties or loses. Thus every position between xj and 2m − xj is a best response of candidate i to xj.
xj > m: symmetrically, every position between 2m − xj and xj is a best response of candidate i to xj.
xj = m: if candidate i choose xi = 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 xj.