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ChristianKl comments on Open Thread, January 4-10, 2016 - Less Wrong Discussion
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Comments (430)
Is there a formal theory of how a rational actor should bet on prediction markets? If the prediction market says the probability is 70% and the actor thinks it's 60% is there a formal way to think about to what extend the agent thinks he knows better and should therefore bet against the market?
I'd guess that that falls under the usual paradigms like Savage or Von Neumann-Morgenstern. For example, the Kelly criterion.
Sure. Just stop thinking in terms of discrete probabilities and start thinking in terms of full distributions.
If the Superforcasting people would add a group for the next batch of forcasts that would use that method, what specific methodology should they use?
What do you mean, methodology? Operation on distributions (e.g. addition) are well-defined and while there may be no easy analytic solution, in our days you can always do things numerically.
If you would tell an average person: Please write down the probability of each event, then they can handle what they want to write.
If you would change prediction book, how would the new system look like? Would it be that someone writes 40-60% instead of 50%? Would they write something different?
We'll need to talk about the probability of the probability and I'm not sure that "an average person" is up for it.
Maybe one can ask "What do you think the probability of event X is?" and then ask "How sure are you of your answer to the previous question? What is the minimum and the maximum reasonable possibilities?"
Given this, you can construct some reasonable distribution over the [0..1] segment, e.g. Beta, and go on from there.
Let's say we talk about an average sensible person.
I'm not exactly sure about this subject but it feels to me like it would be good to move from what prediction book does to something like this.
When reading the IPCC report I would be very interested in something like this to get a better sense of the state of the science.