A lot of story games leave it up to you what setting and time period you want to play in: they have rules that ensure a certain kind of fiction, but it's up to you if it's space opera, present day, fantasy, historical, whatever ... or if it's about high school students, spies, doctors, cops ...
Geiger Counter is always survival horror where the characters get picked off one-by-one: but it can happen in space, in medieval times, in a New England town, at a carnival.
Fiasco is always "incompetence porn" - the characters are always going to do stupid things to get what they want, and it's always going to end in disaster, but again - it can be in Las Vegas, on Mars, or in Olde London.
Shock: is always science fiction that uses its characters to explore some issues, so it's probably going to be in the future, but it can be any future you imagine, on Earth or another planet ... and nothing stops you from playing a 'historical shock' like the invention of the printing press or telephone ...
Microscope is always an epic history. Universalis always has conflict. Archipelago always has destinies. But where and when is still up to the players.
Because these games usually rely on the "Yes, and..." rule of improv theater - an understanding among the players that you shouldn't shoot down each other's ideas, you should build on them - a small problem emerges: the player who speaks first wins. "How about Celtic fantasy?" I might say, and if the other players are good sports, they'll get behind it, even though Celtic fantasy isn't their cup of tea. It's easy to end up with settings that one player is excited about and the other players are just okay with.
Now - it's a pretty minor problem. You're still going to have fun, even if the setting wasn't your first (or fifth) choice, because the characters and their interactions are what's important. (Although the setting isn't quite just color - with story games, when you introduce something into the story, it usually affects future play, constraining and influencing what happens next, much like setting legal precedent changes our legal system.)
But supposing we try to tackle this problem anyway. One avenue I've approached is McCarthy's consensus-building trick: somebody throws an idea out, and you vote simultaneously. Thumbs up: you're excited. Thumbs down: veto. Fist: you'll support the idea even though you're not crazy about it. Only ideas that get at least two thirds thumbs up win. This is cool, and better than "who speaks first wins" but it's about the same for the people who didn't give a thumbs up.
A second solution is what I've recently adopted for That's Drama (and only playtested twice, but have had great results with each time) - but you could use this for any of the above games (except Fiasco, where you agree on a playset):
Now we reveal the seeds - explaining what they mean if somebody doesn’t know - and we invent a setting together that includes at least one, and ideally both, of each player’s seeds.
Here's an example from a That's Drama playtest:
|Each of us write down two seeds:
So, after I explain what "orgone" is, one of the players suggests a story that takes place during the [Cold War] about a nuclear [submarine] (with a soviet [spy] on-board) on a diplomatic mission to visit the Orgonians - a race of [orgone]-infused fish-men that has just made violent contact with the USA at a particular [lighthouse]. The lighthouse keeper is on-board as well, the one human who has met Orgonians and lived...
And we couldn’t figure out how to get Volcano in there, but maybe we’ll find out as we play the Orgonians will live nearby an underwater volcano, or something to that effect.
The result of this technique is every player feels invested in the game from the start - at least one of their ideas made it in - albeit in a strange new form that they didn't originally expect ("My vampires are in space? Cool.") And although all the seeds are probably tropes or cliches, once they're mixed you'll likely end up with something pretty unique.
All that said, if the other players don't feel like playing this pre-game mini-game, and somebody else's idea is the one that got traction for the setting, you should still take responsibility for getting an idea in there you like. Maybe you were hankering for vampires, but the other players wanted science fiction. Dude. Space vampire. Bring it.