The Nonlinear Library: LessWrong LW - What are your cruxes for imprecise probabilities / decision rules? by Anthony DiGiovanni
Jul 31, 2024
01:11
Link to original article
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: What are your cruxes for imprecise probabilities / decision rules?, published by Anthony DiGiovanni on July 31, 2024 on LessWrong.
An alternative to always having a precise distribution over outcomes is imprecise probabilities: You represent your beliefs with a set of distributions you find plausible.
And if you have imprecise probabilities, expected value maximization isn't well-defined. One natural generalization of EV maximization to the imprecise case is maximality:[1] You prefer A to B iff EV_p(A) > EV_p(B) with respect to every distribution p in your set. (You're permitted to choose any option that you don't disprefer to something else.)
If you don't endorse either (1) imprecise probabilities or (2) maximality given imprecise probabilities, I'm interested to hear why.
1. ^
I think originally due to Sen (1970); just linking Mogensen (2020) instead because it's non-paywalled and easier to find discussion of Maximality there.
Thanks for listening. To help us out with The Nonlinear Library or to learn more, please visit nonlinear.org
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: What are your cruxes for imprecise probabilities / decision rules?, published by Anthony DiGiovanni on July 31, 2024 on LessWrong.
An alternative to always having a precise distribution over outcomes is imprecise probabilities: You represent your beliefs with a set of distributions you find plausible.
And if you have imprecise probabilities, expected value maximization isn't well-defined. One natural generalization of EV maximization to the imprecise case is maximality:[1] You prefer A to B iff EV_p(A) > EV_p(B) with respect to every distribution p in your set. (You're permitted to choose any option that you don't disprefer to something else.)
If you don't endorse either (1) imprecise probabilities or (2) maximality given imprecise probabilities, I'm interested to hear why.
1. ^
I think originally due to Sen (1970); just linking Mogensen (2020) instead because it's non-paywalled and easier to find discussion of Maximality there.
Thanks for listening. To help us out with The Nonlinear Library or to learn more, please visit nonlinear.org