Often, analytic philosophers give some case to elicit intuitions. Intuitions elicited by certain kinds of cases count for less. Here is one dimension of this: Intuitions elicited by worlds different from ours are, other things being equal, reliable in inverse proportion to how different the worlds are from ours. Here is the extreme case: intuitions elicited by cases of impossible worlds.
For an example of such an intuition, consider the argument against divine command theory that even if God commanded torture of the innocent, torture of the innocent would be wrong. Now, the obvious response is that it's impossible for God, in light of his goodness, to command torture of the innocent. But, the opponent of divine command theory continues, if God were per impossibile to command it, it would still be wrong, but according to divine command theory, it would be right. (E.g., Wes Morriston has given an argument like that.)
I've criticized this particular argument elsewhere (not that I think divine command theory is right).[note 1] But here is a point that is worth making. This argument elicits our intuition by a case taking place in an impossible world. But impossible worlds are very different from ours. So we have good reason to put only little weight on intuitions elicited by per impossibile cases.
This does not mean that we should put no weight on them.