In my popularity contest Approximate a Bell Curve, the answer that I posted has the most votes.
In general on Stack Exchange sites, I avoid accepting my own answer and instead accept another answer that is right (when there are multiple right answers).
On this site, accepting means that the accepted answer has won the competition.
How should we handle situations like this?
There is nothing wrong with accepting your own answer, if it's the most correct one (this applies to SE in general). See: http://blog.stackoverflow.com/2009/01/accept-your-own-answers/
For my own contests, if someone posts a better answer, I set that as the accepted answer. I encourage everyone to do this. (Oh, and hence the importance of objective winning criteria: "best" is self-evident and easily verifiable.)
