Let’s walk through the median voter theorem in a little more detail. Consider a town with three voters, Enrique, Nandini, and Torsten. The big issue in the upcoming election is how high the sales tax rate should be. As you’ll learn in macroeconomics (and in real life), on average, a government that wants to do more spending has to bring in more taxes, so “higher permanent taxes” is the same as “higher government spending.” Enrique wants low taxes and small government, Nandini is in the middle, and Torsten wants the biggest town government of the three. Each one is a stubborn person, and his or her favorite position—what economic theorists call the “ideal point”—never changes in this problem.Their preferences can be summed up like this, with the x denoting each person’s favorite tax rate:
Suppose there are two politicians running for office, N and O (so ignore P for now). Enrique will vote for 2rtXH4xyxFE=, Nandini will vote for Gy14tCcIxQw= and Torsten will vote for Gy14tCcIxQw=. Candidate Gy14tCcIxQw= will win the election.
O drops out of the campaign after the local paper reports that he hasn’t paid his sales taxes in years. P enters the race, pushing for higher taxes, so it’s N vs. P. Voters prefer the candidate who is closest to them. Enrique will vote for UW3vrr+H0DA=, Nandini will vote for RDkj89EdyJY= and Torsten will vote for RDkj89EdyJY=. Candidate RDkj89EdyJY= will win the election.