Answer
The median voter would be the most likely to get their way since the the median voter's preferred outcome beats any other outcome in a two-outcome race.
Work Step by Step
Mathematically, if we ordered the desired outcomes of a set number of voters, the outcome would be that of the median voter (since we would find the outcome that is in the exact middle of the outcomes). The average voter's preferred outcome would be likely either higher or lower than the median voter's preferred outcome.
As an example, there are 100 voters voting on the amount of a tax increase. 25 voters want no increase, 15 want an increase of 5 dollars, 20 want an increase of 10 dollars, 35 want an increase of 15 dollars, and 5 want an increase of 20 dollars. The median voter voted for a 10 dollar increase, and the average voter wanted a 9 dollar increase.
More than half of the voters want less than a 10 dollar increase, and more than half of the voters want more than a 10 dollar increase. If someone proposes a increase of less than (more than) a 10 dollar increase, then everyone who prefers more than (less than) a 10 dollar increase will have the median vote.
