Google already has the equivalent of upvoting without requiring anything from the users.
If you click into a site and you don't return to your search, they consider that an upvote. If you continue clicking different search results they consider that a downvote for the site you visited.
Then that's not great, based on the way I (and, from observation, many others) use search results. I often middle-click (or control+click) several links which look promising, loading them in new tabs in the background. When I have a decent number, I then go visit the sites themselves.
In addition, the best Google searches result in finding the answer directly in the preview of the page from the search results. Unfortunately there's not a clear signal to Google which site preview provided the answer in this case, or even if none of them did and I just gave up searching.
In reality, I'm sure Google's determination of which site was relevant is much more sophisticated, likely involving some machine learning.
Since google's spying on you, you'd think they'd be able to link the page you're reading to the search that triggered it, and filter the analytics back to the search. But google won't use their spying to our benefit...
If you click into a site and you don't return to your search, they consider that an upvote. If you continue clicking different search results they consider that a downvote for the site you visited.