Assume I want to run a game tournament with 1-on-1 games (think chess) that have (for simplicity) just win or lose as the outcome and I need a way to rank the players. Formally speaking, I want a function that takes a list of (player1, player2, who_won) triples and returns a ranking of players, e.g. by attributing each of them a number (list of (player, score)).
Because the tournament is going to be informal and unorganized, I cannot in any way influence who plays against whom when. The scoring system I am looking for should have these properties:
- The order of games should not matter.
- If two (or more) players keep playing against each other over and over, with the same winning probabilities, the scores should not change (or not change much, e.g. converge).
If necessary, new games can affect the scores of all people, and calculations might need a computer.
What scoring systems fulfil this?