Question: Why does median voter theory require that there be only two parties? Is it not always electorally efficient to align with the preferences of the median voter?

Answer: This is a good question and the answer centres on parties outflanking the party that positions itself at (or nearest) the median voter. So, let’s imagine a two-party system with a left party and a right party, in which the left party has positioned itself almost at the median voter whilst the right party is further away. Of course, the latter party picks up the votes of everyone in the electorate to the right of their position, as well as everyone to their left who is closer to them than the (almost-median) position of the left party. The left party does the same for all voters to their left and everyone between them and the median voter, as well as picking up the crucial median voter (because they are closer than the right party).

Now let’s imagine that a new left party enters the electoral arena to represent those voters on the left who feel alienated by the central position of the original left party. The new party will pick up all the votes to the left of their position, and all the votes of those to their right who are, nonetheless, closer to their position than that almost median position of the original left party. So, the left vote is split and the right party, which remains unchallenged on the right, can win without positioning themselves at the median voter. The right party can still count on everyone to their right (and those to their left who are closer to them than they are to the median) but the original left party cannot count on the votes of everyone to their left. In other words, they have been outflanked on the left as well as on the right, and there are not enough votes around the median to deliver victory. Of course, this depends on the precise positions of the parties because there are, in a normal distribution, more votes to be won around the median voter. So, if the new left and original right parties move to the extremes it still makes sense for the original left party to go to the median, where there are more votes.

Of course, all of this turns on other assumptions including, for instance, that voters turn out to vote. If parties moving to the median would alienate voters on the left or right to the extent that they stopped voting then that would also undermine the simple calculus involved in moving to the median voter (hence the idea of shoring up the base).