If Trump doesn't win the Republican nomination, does he run a write-in campaign?

[SteveRogers]

No, because he can still run as an independent in a majority of states. Most states final deadlines for ballot access are after the convention. If it becomes clear he won't be the nominee earlier, he could get on the ballot in even more places. If it looks like the RNC might deny him the nomination, he will probably start filling in the early states as a threat to the delegates. Ballotpedia has a list of deadlines, btw.

His optimal course of action is to run as an independent in some states and as a write-in candidate in some others, depending on the logistics.
For example, it's almost impossible to run as an independent in Texas but it's actually pretty easy to run as write-in. In some other state the opposite might be true.

The Texas sore loser law bars write-in campaigns too. Trump absolutely cannot run in Texas.

[SteveRogers]

No, because he can still run as an independent in a majority of states. Most states final deadlines for ballot access are after the convention. If it becomes clear he won't be the nominee earlier, he could get on the ballot in even more places. If it looks like the RNC might deny him the nomination, he will probably start filling in the early states as a threat to the delegates. Ballotpedia has a list of deadlines, btw.

His optimal course of action is to run as an independent in some states and as a write-in candidate in some others, depending on the logistics.
For example, it's almost impossible to run as an independent in Texas but it's actually pretty easy to run as write-in. In some other state the opposite might be true.

The Texas sore loser law bars write-in campaigns too. Trump absolutely cannot run in Texas.

He could mount a legal campaign to try to overturn the sore loser law. According to "minor political party activist" Richard Winger: sore loser laws can’t apply to the presidential race because people who cast ballots in the general election aren't voting for a candidate, they're choosing electors — members of the Electoral College — who have pledged to support that same candidate.

I'm imagining Trump's legal challenge going all the way to the Supreme Court, which in turn deadlocks 4-4.

There's certainly an argument to be made there. There is of course no Constitutional principle that would compel that result. It's an issue of statutory interpretation that will vary from state to state depending on how the sore loser law is drafted. The argument has been tried before in federal court. It worked for John Anderson in at least one state in 1980 but not so much for Gary Johnson in Michigan in 2012. Trump could certainly try it. However, I find it highly unlikely that the Supreme Court would have any interest in taking up that particular claim as it's really just a state law issue of statutory interpretation.

Now I personally think there are First and Fourteenth Amendment grounds for challenging the constitutionality of sore loser laws, but the 1974 Supreme Court case Storer v. Brown seems to say I'm wrong.   

[SteveRogers]

Somewhat tangential question: whatever happened to the Reform Party?

Well Pat Buchanan basically single-handedly destroyed it in 2000 when he got the nomination and tried to inject a bunch of social issues into its platform. Now from what I can tell it's basically just a couple of groups of a dozen or so people who meet up in a hotel every four years to sue each other over whose the real Reform Party.

[SteveRogers]

I wonder if those state laws prohibiting counting write in votes would survive a court challenge. Rather doubt it as it's clearly disenfranchisement of the people's will if a write in candidate wins a state and it's invalidated by these.

Cruz has a convenient name for a write in candidate, too. Just sayin'.

I don't know the case off the top of my head, but if I recall correctly the Supreme Court has already upheld a state's right not to allow write-in votes.