No there isn't any such mechanism. And I don't think it'd be a good idea to implement, since that's not the kind of decision I think the system can reasonably make on behalf of a user. Sometimes there is a legitimate reason to leave a question with no accepted answer... for instance, if none of the answers posted really provide the solution the questioner is looking for.
If you think one of your answers (or someone else's answer) deserves to be accepted, for example if the questioner has left a comment saying the answer worked, you can leave a comment that politely reminds them to accept the answer.
As a curiosity, the bounty system used to work in the way you're asking about; after a bounty had been outstanding for a week, if the questioner hadn't yet accepted an answer, the highest voted answer would automatically become accepted (and would receive the bounty).