If Republican means nothing else than non-Democrat and Democrat nothing else than non-Republican, then Republican means nothing else than Republican and Democrat nothing else than Democrat.

The demonstration is straightforward. The hypotheses in the conditional part of the above sentence implies that Republican is non-non-Republican, that is, Republican is Republican. A similar demonstration can show that Democrat is Democrat.

The identity principle “A is A” prevents one from building castles on contradiction sand, but it does not tell us anything useful about A—including whether or not to vote for A.

The median voter theorem is one way to make practical sense of that. In this perspective, the Republican Party and the Democratic Party are intentionally nearly identical because each is trying to capture the median voter  (or the median voter group) at the middle of the political spectrum. Given certain assumptions, no one cannot get more than  50% of the vote without the median voter. But then, why do the two parties vociferously claim to be different?

I prefer the hypothesis of economist Daniel Kian Mc Kiernan:

I suppose that people who try to define both terms “Democrat” and “Republican” or “left” and “right” negatively are tribalists who don’t want simply to say “us” and “everybody else”.

A practical implication is that not too much meaning or normative value should be attached to elections where all candidates say, “We are us; vote for us and we will do what you want.” James Buchanan’s and Gordon Tullock’s constitutional political economy correctly argues, only unanimity has normative value. If unanimity is impossible even at the level or general and abstract rules, anarchy is the only ethical solution, at least in theory, as Anthony de Jasay argues.