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Coscott comments on Even Odds - Less Wrong
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Comments (46)
Excited to see your report.
You meant to say if p<1-q, and yes the two interpretations give the same results. The mechanism also results in no bet at all when the probabilities are the same. I did not have to make any assumptions on the probabilities, but I did for the sake of producing positive bets.
I have used it in two places. In both places, it has created some slight confusion.
In one place, two prominent users said they are dissatisfied with it and not going to use it again. This was because the bet ended up much smaller than they originally thought. It is not popular there.
I changed the rule so if you declared a probability and a max bet, the scale is set so that the largest possible bet you could end up making (if someone puts down the 100% further away from your probability) is what you declared as the max bet, instead of using the max bet as the scale directly. That would have solved the problem... but by that point the damage was done.
In the other place, I got a dozen participants to give their probability distributions for an outcome, using a pool rule which is probably equivalent to the rule for pools given elsewhere in this thread, but for more obvious reasons (round robin of 1-on-1 bets on just the observed outcome, vs all other participants). Apparently, the bandwagon jumped onto was to try it rather than the reverse. They might end up being disappointed by the small size of the results too.
Ah, didn't catch that: "Without loss of generality, assume p+q>1."