Regarding betting odds: are you aware of this post? It gives a betting algorithm that satisfies both of the following conditions:
Honesty: participants maximize their expected value by being reporting their probabilities honestly.
Fairness: participants’ (subjective) expected values are equal.
The solution is “the ‘loser’ pays the ‘winner’ the difference of their Brier scores, multiplied by some pre-determined constant C”. This constant C puts an upper bound on the amount of money you can lose. (Ideally C should be fixed before bettors give their odds, because otherwise the honesty desideratum above could break, but I don’t think that’s a problem here.)
I was not aware, but I strongly suspected that someone on LW had asked and answered the question before, hence why I asked for help. Prayers answered! Thank you! Connor, are you OK with Scott’s algorithm, using C = $100?
Regarding betting odds: are you aware of this post? It gives a betting algorithm that satisfies both of the following conditions:
Honesty: participants maximize their expected value by being reporting their probabilities honestly.
Fairness: participants’ (subjective) expected values are equal.
The solution is “the ‘loser’ pays the ‘winner’ the difference of their Brier scores, multiplied by some pre-determined constant C”. This constant C puts an upper bound on the amount of money you can lose. (Ideally C should be fixed before bettors give their odds, because otherwise the honesty desideratum above could break, but I don’t think that’s a problem here.)
I was not aware, but I strongly suspected that someone on LW had asked and answered the question before, hence why I asked for help. Prayers answered! Thank you! Connor, are you OK with Scott’s algorithm, using C = $100?
Looks good to me, thank you Loppukilpailija!