Are 1v1 matches a good way to determine who is the better player?

I had this discussion with a couple of friends today, and it was a very contested debate. Some of us believe that under the right conditions, a one versus one game can dictate which player is superior. Whilst on the other hand, this evidence is not entirely definitive, it's possibly the best way to make a judgement on whom has the higher skill level.

In my opinion there is a way to have a feasibly close contest; albeit not entirely fair. First, both players choose the same champion. One that they both feel comfortable playing and confident on. Once you have selected this character, proceed to a game using your own decision on runes and summoner spells. I feel it would be a better competition if both champions are confined to one lane, just to make sure both players are consistently in contest with each other.

Since one match won't guarantee a certain result, the best of three to five games is ideally the best way to decide who is the overall winner.

My question to everyone reading this post is: what do you think is the best way to solve a dispute between two players? How would you stage a competition that would reliably prove which person is exceptional, and which is a baddie?