The third party can fill a very useful niche: when your current party has let you down, but you also don't want to support the other extreme of the political sp

The third party can fill a very useful niche: when your current party has let you down, but you also don't want to support the other extreme of the political spectrum, you can vote third party. This has no analogy in hotellings law proper. But imagine the beach had two entrances: one at 1/4 down the beach, and one 3/4 down the beach; there are more beach goers near an entrance than farther away from it. We also recognize that a beach goer is less likely to get ice cream the farther away from the ice cream stand they are. Then we will see something similar as before, with the vendors moving closer and closer together. But now they stop before they reach the center, because if they get to far from the entrance they will start losing customers. This explains why political candidates are not precisely identical, just similar: they are each catering to a block of more extreme voter. Now we add a third entrance somewhere in between the first two: what happens? We would expect three vendors to emerge, one for each entrance, all with a tendency towards their second closest entrance. This is analogous to three political parties, with two being more similar to each other than the third, as we sometimes see outside the US. In short: the political parties in the US are particular to the politics and distribution of the voters there, and efforts to paint this as inevitable given FPTP are severely overstated.