This model is no good, because it doesn’t model different difficulties of different questions, and relate the odds offered to the difficulty of the question. If the payout on a bet is very high, and person i wants to take the bet, it means most people disagree with i. That should mean that i is more likely to be wrong on that bet.
Can anyone suggest a good way of doing that? I’m thinking along the lines of using some kind of least-square error to minimize the total combined errors of the person and of society in placing bets. Or, start all over, suppose a distribution of question probabilities, and suppose that both society and person i have some error distribution.
My intuition is that:
Taking this into account will reduce the expected payoff from quadratic to linear, and obliterate it in the “no re-evaluation” case.
i will lose or break even on increasing rationality if i models their accuracy rate as being the same on all questions, instead of adjusting for the information provided in the odds offered.
I also think there’s a problem with having a uniform distribution for y. That means there are few long-odds bets offered.
This model is no good, because it doesn’t model different difficulties of different questions, and relate the odds offered to the difficulty of the question. If the payout on a bet is very high, and person i wants to take the bet, it means most people disagree with i. That should mean that i is more likely to be wrong on that bet.
Can anyone suggest a good way of doing that? I’m thinking along the lines of using some kind of least-square error to minimize the total combined errors of the person and of society in placing bets. Or, start all over, suppose a distribution of question probabilities, and suppose that both society and person i have some error distribution.
My intuition is that:
Taking this into account will reduce the expected payoff from quadratic to linear, and obliterate it in the “no re-evaluation” case.
i will lose or break even on increasing rationality if i models their accuracy rate as being the same on all questions, instead of adjusting for the information provided in the odds offered.
I also think there’s a problem with having a uniform distribution for y. That means there are few long-odds bets offered.