33. Assume that and take different positions, with one possibly being at . What position should take to maximize his or her vote total? Is ’s position always a winning one?
33.
If, say, takes a position at , and takes a position to the right of , should take a position just to the left of that is closer to than ’s position, giving essentially half the votes and enabling him or her to win the election. If neither nor takes a position at , should take a position next to the candidate closer to . The position that takes to maximize his or her vote may be either closer to (if the candidates are far apart) or farther from (if the candidates are closer together), but this position may not be winning.