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Coscott comments on Even Odds - Less Wrong
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I thought it was very interesting that my natural assumptions lead to a Brier score like system rather than Bayes score. I really don't think Bayesianists respect Brier score enough.
I thought it was interesting too. As far as I can tell, your result is special to the situation of two bettors and two events. The description I gave describes a betting method when there are more than two alternatives, and that method is strategy proof, but it is not fair, and I can't find a fair version of it.
I am really stumped about what to do when there are three people and a binary question. Naive approaches give no money to the person with the median opinion.
I wrote up an answer to this here http://bywayofcontradiction.com/?p=118
You could just do all three pairwise bets. That will not be fair, since not everyone participates in all bets. The middle man might just be guaranteed to make money though. (for some probabilities)