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I agree. For many of the attributes of voting systems, you can actually remove the voting analogy altogether and think of any competition between individuals, like tennis. In a tennis tournament, you could easily have non-transitive results, where A defeats B, B defeats C, and C defeats A. So how do you organize a tournament to determine the "best" tennis player? Round robin tournaments (where every player plays every other player) can have non-transitive results. Of course, there's usually not enough time to do that anyway, so tournaments go with a bracket system. Brackets have their own problems, namely that it's very possible that the bracket winner would lose to a player who was knocked out of the bracket earlier by some third player.

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