Happy Policeman - Patricia Anthony
Well, this was one of those rare occasions where I read through a whole book and wound up having no idea what went on. I may be beginning to sort it out a bit, here's my attempt:

One day in 1988(?), there was a blackout in Coomey, TX, and a fundamentalist preacher, for reasons I don't understand, told everyone in town it was World War III -- and everyone believed him. And as they huddled terrified in basements, their act of collective belief caught the attention of the Torku, aliens skilled in manipulating parallel universes. The Torku decided to create a pocket universe containing the town: "outside", the citizens went home in the morning feeling silly; "inside", other versions of the same people spent six years thinking the world had really ended, as the Torku kept them in comfort. The Torku's motives for doing this, apparently, were as follows: parallel universes are related to each other by pattern. (So six years equalled six months, the same people died but in different ways, and there were the same emotional entanglements.) Thoughts and beliefs are part of the pattern. The Torku think that it's a moral imperative to try to make the pattern a positive one, by not only doing what they can to improve things, but also thinking and saying positive possibilities. And they decided to try to convince one set of humans of this moral good, by having them be a captive audience in the pocket universe.

So I still haven't doped out a lot of things. I suppose I may re-read this one day; it certainly was entertaining.