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I have a question which I will present using a hypothetical. It's about a popular game called Sport. A game of Sport is played by two players and is recorded by one recordkeeper.

Alice and Beth love Sport, and they will go to each others' houses to play. If they play at Alice's house, the recordkeeper is always Alice's brother, Alex. If they play at Beth's house, the recordkeeper is always Beth's brother, Bob.

Alice and Beth are both part of a Sport League consisting of  hundreds of people. Whenever Alice and Beth play, their game records have to be reported to the Leaguemaster. Whoever has the most wins at the end of the season is given a cash prize, so it is important that the Leaguemaster's records are accurate.

For any given game of Sport being reported, the Leaguemaster must know:

1. Who played the game
2. That the game was played by normal league rules
3. Statistics about the game; especially, the game's winner

The problem: since Bob and Beth are related, Bob can't be trusted to not falsify the game record in Beth's favor whenever he gets to be recordkeeper. The same goes for Alex, who might falsify in Alice's favor whenever he gets the chance. Alex and Bob have also been known to rig the game itself in order to give their respective sister the advantage.

The question: How can the Leaguemaster guarantee that he is given accurate records about any given game?

>>3
What if Alice and Beth disagree about the record? Say, Alice thinks Bob's record is false, but Beth thinks it's right? Or, both Bob and Beth were playing fair and square, but Alice claims it's wrong because she doesn't want to lose?

It may be possible to track the disagreements as a third measure of reputation (Games Won, Lost, Disputed By/Against). But that still doesn't solve the problem of tracking unfair wins/losses, unless there is a set of rules that disqualifies you after a certain set conditions involving disputes is set.

And you're right, yhis still doesn't solve the problem of an unfair win that Alice and Beth don't know about.

>>4

The Leaguemaster's resources are limited. There are a lot more players that want to play than there are Leaguemasters or referees.

>>6
So Alice and Beth play at a third unknown person's house, let's say Claire, to be recorded by Claire's brother Chris (while Claire's not around -- Claire could even be playing at Beth's house at this time)? Chris might still rig the match or falsify records, but the idea is that Chris doesn't have any incentive to do so, because he doesn't know who Beth or Alice are, correct?