by Alex Mennen 358 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.

### NEW DISCUSSION POSTS

Note: I currently think that
 by Jessica Taylor on Predicting HCH using expert advice | 0 likes

Counterfactual mugging
 by Jessica Taylor on Doubts about Updatelessness | 0 likes

What do you mean by "in full
 by David Krueger on Doubts about Updatelessness | 0 likes

It seems relatively plausible
 by Paul Christiano on Maximally efficient agents will probably have an a... | 1 like

I think that in that case,
 by Alex Appel on Smoking Lesion Steelman | 1 like

 by Sam Eisenstat on No Constant Distribution Can be a Logical Inductor | 1 like

A: While that is a really
 by Alex Appel on Musings on Exploration | 0 likes

> The true reason to do
 by Jessica Taylor on Musings on Exploration | 0 likes

 by Vadim Kosoy on Musings on Exploration | 1 like

I'm not convinced exploration
 by Abram Demski on Musings on Exploration | 0 likes

Update: This isn't really an
 by Alex Appel on A Difficulty With Density-Zero Exploration | 0 likes

If you drop the
 by Alex Appel on Distributed Cooperation | 1 like

Cool! I'm happy to see this
 by Abram Demski on Distributed Cooperation | 0 likes

Caveat: The version of EDT
 by 258 on In memoryless Cartesian environments, every UDT po... | 2 likes

[Delegative Reinforcement
 by Vadim Kosoy on Stable Pointers to Value II: Environmental Goals | 1 like