by Alex Mennen 195 days ago | link | parent When modeling the incentives to change probabilities of events, it probably makes sense to model the payoff of changing probabilities of events and the cost of changing probabilities of events separately. You’d expect someone to alter the probabilities if they gain more in expectation from the bets than the cost to them of altering the probabilities. If someone bets on an event and changes the probability that it occurs from $$p$$ to $$q$$, then their expected payoff is $$\frac{q}{p}-1$$ times their investment, so if, in a prediction market in which there are $$n$$ possible outcomes, the expected payoff you can get from changing the probability distribution from $$(p_1,...,p_n)$$ to $$(q_1,...,q_n)$$ is proportional to $$\max_i(\frac{q_i}{p_i})-1$$. Modeling the cost of changing a probability distribution seems harder to model, but the Fisher information metric might be a good crude estimate of how difficult you should expect it to be to change the probability distribution over outcomes from one distribution to another.

### RECENT COMMENTS

This is exactly the sort of
 by Stuart Armstrong on Being legible to other agents by committing to usi... | 0 likes

When considering an embedder
 by Jack Gallagher on Where does ADT Go Wrong? | 0 likes

The differences between this
 by Abram Demski on Policy Selection Solves Most Problems | 0 likes

Looking "at the very
 by Abram Demski on Policy Selection Solves Most Problems | 0 likes

Without reading closely, this
 by Paul Christiano on Policy Selection Solves Most Problems | 1 like

>policy selection converges
 by Stuart Armstrong on Policy Selection Solves Most Problems | 0 likes

Indeed there is some kind of
 by Vadim Kosoy on Catastrophe Mitigation Using DRL | 0 likes

Very nice. I wonder whether
 by Vadim Kosoy on Hyperreal Brouwer | 0 likes

Freezing the reward seems
 by Vadim Kosoy on Resolving human inconsistency in a simple model | 0 likes

Unfortunately, it's not just
 by Vadim Kosoy on Catastrophe Mitigation Using DRL | 0 likes

>We can solve the problem in
 by Wei Dai on The Happy Dance Problem | 1 like

Maybe it's just my browser,
 by Gordon Worley III on Catastrophe Mitigation Using DRL | 2 likes

At present, I think the main
 by Abram Demski on Looking for Recommendations RE UDT vs. bounded com... | 0 likes

In the first round I'm
 by Paul Christiano on Funding opportunity for AI alignment research | 0 likes

Fine with it being shared
 by Paul Christiano on Funding opportunity for AI alignment research | 0 likes

Privacy & Terms