So I think I’ve found a perfect game. I haven’t played it yet, and there are some details to be figured out, but I think it’s pretty clearly potentially a good abstraction for a certain class of mathematical and political issues, and also looks like it could be quite entertaining if you’ve got a taste for Poker or Diplomacy.

I’ll start with the simplest form I can think of.

1> There are an odd number of players

2> Each player has a vote, which can be YES or NO

3> On each round, a vote is taken, and the majority wins

4> If there are any players on the minority side, they lose

So that’s the essence. Now add some scoring.

5> At the start of each round, players put some tokens into a pot

6> The winners split the pot between them

This creates an incentive for narrow wins – in a nine player game, a 5-4 win pays out 7.2 times what an 8-1 win pays out.

One annoying problem is that this method of keeping score is impossible with beans or tokens or whatever. One simpler approach is that each loser must give one token to each winner, which also has the right properties, although I think the different risk/reward landscape would reward a different style of play to the version in which the cost of a round is the same whether you lose narrowly or by a broad margin. Somewhere in the middle is a version where on each round, the winners gain a point and the losers lose one, but then the number of points in the game is not conserved – also a problem.

I look forward to suggestions on how to resolve this scoring problem. Also note that bribery (vote with us and we’ll give you two tokens) should probably be permitted, although on an informal basis, with such promises having no in-game mechanic.

Then there are two modes of play.

7> Players make their vote by some secret mechanism, such as placing a tile face down in front of them, and all communication is face to face at the table

or

8> Players mark their votes electronically, allowing for dialog

9> There may also be issues regarding timing, such as when players decide to wait for one person to vote, and then all change their votes. These problems can be resolved at the tabletop quite easily, but may be a little less tractable in the electronic form

This game is inspired by the Byzantine Generals Problem.

I’m open to suggestions on names – I was initially thinking Byzantium, but that’s a little boring.

Oh, and for play over (for example) email, I suggest the following scheme.

1> players post a hash to a mailing list, like so

dbef29982b1ce8213ed74f626d3bb9e1

Once all hashes have been posted (possibly including multiple votes from a single player as they change their minds or bluff)

2> Players then post the string which evaluates to that hash “YES: this is randomness 2u23i4ou23p4″

3> Strings can be checked easily

MD5 (“YES: this is randomness 2u23i4ou23p4″) = dbef29982b1ce8213ed74f626d3bb9e1

It’s interesting how much of the play in the game is protocol dependent – can players revoke votes? can they see when other players have voted? how are points allocated for wins and losses? what are the victory conditions?

And, finally, what about the pathological case, where all players are on one side?