I still don’t think the position I’m trying to defend is circular. I’ll have a go at explaining why.
I’ll start with aswering your question: in practice the way I would come up with probabilities to assess a charitable intervention is the same as the way you probably would. I’d look at the available evidence and update my priors in a way that at least tries to approximate the principle expressed in Bayes’ theorem. Savage’s axioms imply that my decision-describing-numbers between 0 and 1 have to obey the usual laws of probability theory, and that includes Bayes’ theorem. If there is any difference between our positions, it will only be in how we should pick our priors. You pick those before you look at any evidence at all. How should you do that?
Savage’s axioms don’t tell you how to pick your priors. But actually I don’t know of any other principle that does either. If you’re trying to quantify ‘degrees of belief’ in an abstract sense, I think you’re sort of doomed (this is the problem of induction). My question for you is, how do you do that?
But we do have to make decisions. I want my decisions to be constrained by certain rational sounding axioms (like the sure thing principle), but I don’t think I want to place many more constraints on myself than that. Even those fairly weak constraints turn out to imply that there are some numbers, which you can call subjective probabilities, that I need to start out with as priors over states of the world, and which I will then update in the usual Bayesian way. But there is very little constraint in how I pick those numbers. They have to obey the laws of probability theory, but that’s quite a weak constraint. It doesn’t by itself imply that I have to assign non-zero probability to things which are concievable (e.g. if you pick a real number at random from the uniform distribution between 0 and 1, every possible outcome has probability 0).
So this is the way I’m thinking about the whole problem of forming beliefs and making decisions. I’m asking the question:
″ I want to make decisions in a way that is consistent with certain rational seeming properties, what does that mean I must do, and what, if anything, is left unconstrained?”
I think I must make decisions in a Bayesian-expected-utility-maximising sort of way, but I don’t think that I have to assign a non-zero probability to every concievable event. In fact, if I make one of my desired properties be that I’m not susceptible to infinity threatening Pascal muggers, then I shouldn’t assign non-zero probability to situations that would allow me to influence infinite utility.
FWIW, I think most of us go with our guts to assign probabilities most of the time, rather than formally picking priors, likelihoods and updating based on evidence. I tend to use ranges of probabilities and do sensitivity analysis instead of committing to precise probabilities, because precise probabilities also seem epistemically unjustified to me. I use reference classes sometimes.
I still don’t think the position I’m trying to defend is circular. I’ll have a go at explaining why.
I’ll start with aswering your question: in practice the way I would come up with probabilities to assess a charitable intervention is the same as the way you probably would. I’d look at the available evidence and update my priors in a way that at least tries to approximate the principle expressed in Bayes’ theorem. Savage’s axioms imply that my decision-describing-numbers between 0 and 1 have to obey the usual laws of probability theory, and that includes Bayes’ theorem. If there is any difference between our positions, it will only be in how we should pick our priors. You pick those before you look at any evidence at all. How should you do that?
Savage’s axioms don’t tell you how to pick your priors. But actually I don’t know of any other principle that does either. If you’re trying to quantify ‘degrees of belief’ in an abstract sense, I think you’re sort of doomed (this is the problem of induction). My question for you is, how do you do that?
But we do have to make decisions. I want my decisions to be constrained by certain rational sounding axioms (like the sure thing principle), but I don’t think I want to place many more constraints on myself than that. Even those fairly weak constraints turn out to imply that there are some numbers, which you can call subjective probabilities, that I need to start out with as priors over states of the world, and which I will then update in the usual Bayesian way. But there is very little constraint in how I pick those numbers. They have to obey the laws of probability theory, but that’s quite a weak constraint. It doesn’t by itself imply that I have to assign non-zero probability to things which are concievable (e.g. if you pick a real number at random from the uniform distribution between 0 and 1, every possible outcome has probability 0).
So this is the way I’m thinking about the whole problem of forming beliefs and making decisions. I’m asking the question:
″ I want to make decisions in a way that is consistent with certain rational seeming properties, what does that mean I must do, and what, if anything, is left unconstrained?”
I think I must make decisions in a Bayesian-expected-utility-maximising sort of way, but I don’t think that I have to assign a non-zero probability to every concievable event. In fact, if I make one of my desired properties be that I’m not susceptible to infinity threatening Pascal muggers, then I shouldn’t assign non-zero probability to situations that would allow me to influence infinite utility.
I don’t think there is anything circular here.
Ok, this makes more sense to me.
FWIW, I think most of us go with our guts to assign probabilities most of the time, rather than formally picking priors, likelihoods and updating based on evidence. I tend to use ranges of probabilities and do sensitivity analysis instead of committing to precise probabilities, because precise probabilities also seem epistemically unjustified to me. I use reference classes sometimes.