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The Inventor's Tournament is a good idea. But how will it work for more than two people? Some options are (A) All participants besides each inventor vote on which of his games to play. (B) One participant has the responsibility of choosing which game to play by another participant. There are multiple ways of choosing who gets to pick whose variant. (1) Who picks whose game is randomly chosen after all participants sign up, according to (a) a completely random pattern, (b) a linked list pattern, or (c) a reciprocal pattern. Since a reciprocal pattern requires an even number of players, the other options are better. A linked list pattern may be best, because it prevents bargaining between participants who get to choose each other's game. (2) Each participant picks the game to be played by the inventor who signed up before him, and when signing up is finished, the first player to sign up picks a game invented by the last player to sign up. This allows most participants to sign up and pick a game immediately, but it forces the first participant to wait until the end to pick a game. (3) Each inventor picks the game of the inventor who signed up after him, and when signing up is finished, the last inventor to sign up picks a game by the first inventor to sign up. This makes everyone wait between signing up and picking a game, but it minimizes how long anyone has to wait.

Of these options, B2 and B3 are natural linked list patterns that help get things going quickly. They give people some knowledge of what games will be played before signing up is finished. The other methods require everyone to sign up before knowing what any of the games in the tournament will be. With B2, all but the first participant have some degree of choice over whose game they pick. With B3, no one signs up knowing whose variants he will be able to pick a game from.

I would suggest the following amendments to this process. (A1) Each participant can exercise one veto on a game chosen by someone else after he has already signed up. Then the person who picked that game has to pick another one by the same inventor. (A2) Each participant may vote against games chosen after he has signed up, and if the majority of people who have already signed up oppose it, the person who picked it has to pick another. These two amendments give people who sign up early some guarantee that they won't be unhappy with the games selected after they sign up. People who sign up late tacitly give their approval to the games already picked.

After posting the preceding, I thought of some other ways to choose who picks whose game. (4) Each participant picks a game by any other inventor in the tournament who hasn't had one of his games picked. (5) Each participant picks a game by any other inventor who signed up after him, and the last person to sign up has to pick a game by the first person. (6) Each participant picks a game by any other inventor who signed up before him, the first person to sign up picking a game by the last person to sign up. (7) Same as 4 with the added provision that no two participants may pick each other's game, which prevents collusion.

Although I thought B7 would work out, methods 4 and 7 both have some problems mathematically. A group of people could create a looped linked list among each other that leaves someone out. Method 7 stops closed pairs from forming, but it doesn't stop closed loops of three or more people. I think methods 5 & 6 may not be subject to this problem, but I haven't worked out the math, and it remains more of a hunch.