On my Code Golf "Converting a string to lower-case (without built-in to-lower functions!)", there're two answers with the same character count (10 characters), and they're both the answer with the lowest character count. On StackExchange sites, it's not possible to accept two (or more) answers, so how can I decide which answer I should accept?
Speaking as a person who posts occasional code golf challenges (and not as a moderator), I tend to pick the earlier-posted answer in cases of a tie. Example. (In this case, Adam Davis was a proponent of Fastest Gun in the West, so this wasn't something he could dispute. :-P)
I think the ties should be broken by the number of upvotes.