Following case: A solution is being suggested in an answer, the OP disqualifies the answer at some point as useless, after having tried it out be it a nice try or not. The answer might have already been upvoted.
See here for an example.
The question is, can the answer be upvoted further, as in "nice try!", or would we let it be and let the nature do its genetic work?
Whether the lack of success on the question author's part is an indication of this varies by the nature of the question. Ultimately, what determines this is whether the answer remains useful after the author ceases to acknowledge it as such.
Sometimes the author's specific problem isn't the only manifestation of a given question. This is especially the case of a question that has multiple solutions - the author may simply be unable to manifest the reflexes necessary to perform a certain kind of jump, or have item restrictions that prevent a particular route. However, if other people can use that solution to get past the same problem as the author, then it's absolutely worthy of upvotes.
Sometimes, though, the answer simply isn't correct for all cases. In that case, whether you want to upvote out of sympathy for trying is entirely your decision. However, keep in mind that the ultimate purpose of voting is to indicate useful content. An answer which is incorrect but which leads to a correct solution is useful, but one that is simply incorrect is not going to be useful.
I would think the voting mechanism would take care of this naturally. Presumably people are voting answers up if they are useful, and down if they are not. It would be nice if people could change their votes days later in case the asker tries a solution and reports back that it was incorrect, but the vote lock-in period is a different issue with other consequences.
In any case, personally I don't see the problem with an answer continuing to get upvotes after the asker reports it didn't work for him/her. If people are still upvoting it after its reported to be incorrect/not applicable, hopefully they are doing so because it nevertheless contains some really good information or advice.
That said, I suppose I could see an ability for the asker to mark an answer as "not the correct answer." I'm not sure if this should make it ineligible for upvotes (see above), but it might provide some utility to the community, at least as a "Got any other ideas?" flag.
