# What are your cruxes for imprecise probabilities / decision rules?

By **Anthony DiGiovanni** @ 2024-07-31T15:44 (+21)

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.

^{^}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.

**MichaelStJules** @ *2024-07-31T16:27* (+6)

Some prior discussions on the EA Forum here: