It seems the updating rule doesn’t tell you anything about the original argument even when you view information about reference classes as evidence rather than as a method of assigning prior probabilities to hypotheses. Or does it? Can you rephrase the argument in a proper Bayesian way such that it becomes clearer? Note that how strongly some evidence confirms or disconfirms a hypothesis also depends on a prior.
What argument are you referring to when you say “doesn’t tell you anything about the original argument”?
My framing is basically this: you generally don’t start a conversation with someone as a blank pre-priors slate that you get to inject your priors into. The prior is what you get handed, and then the question is how people should respond to the evidence and arguments available. Well, you should use (read: approximate) the basic Bayesian update rule: hypotheses where an observation is unlikely are that much less probable.
I think you’re underestimating the inferential gap here. I’m not sure why you’d think the Bayes updating rule is meant to “tell you anything about” the original post. My claim was that the whole proposal about selecting reference classes was framed badly and you should just do (approximate) Bayes instead.
You’re having a conversation with someone. They believe certain things are more probable than other things. They mention a reference class: if you look at this grouping of claims, most of them are wrong. Then you consider the set of hypotheses: under each of them, how plausible is it given the noted tendency for this grouping of claims to be wrong? Some of them pass easily, eg. the hypothesis that this is just another such claim. Some of them less easily; they are either a modal part of this group and uncommon on base rate, or else nonmodal or not part of the group at all. You continue, with maybe a different reference class, or an observation about the scenario.
Hopefully this illustrates the point. Reference classes are just evidence about the world. There’s no special operation needed for them.
It seems the updating rule doesn’t tell you anything about the original argument even when you view information about reference classes as evidence rather than as a method of assigning prior probabilities to hypotheses. Or does it? Can you rephrase the argument in a proper Bayesian way such that it becomes clearer? Note that how strongly some evidence confirms or disconfirms a hypothesis also depends on a prior.
What argument are you referring to when you say “doesn’t tell you anything about the original argument”?
My framing is basically this: you generally don’t start a conversation with someone as a blank pre-priors slate that you get to inject your priors into. The prior is what you get handed, and then the question is how people should respond to the evidence and arguments available. Well, you should use (read: approximate) the basic Bayesian update rule: hypotheses where an observation is unlikely are that much less probable.
I meant leogao’s argument above.
I think you’re underestimating the inferential gap here. I’m not sure why you’d think the Bayes updating rule is meant to “tell you anything about” the original post. My claim was that the whole proposal about selecting reference classes was framed badly and you should just do (approximate) Bayes instead.
And what would this look like? Can you reframe the original argument accordingly?
It’s just Bayes, but I’ll give it a shot.
You’re having a conversation with someone. They believe certain things are more probable than other things. They mention a reference class: if you look at this grouping of claims, most of them are wrong. Then you consider the set of hypotheses: under each of them, how plausible is it given the noted tendency for this grouping of claims to be wrong? Some of them pass easily, eg. the hypothesis that this is just another such claim. Some of them less easily; they are either a modal part of this group and uncommon on base rate, or else nonmodal or not part of the group at all. You continue, with maybe a different reference class, or an observation about the scenario.
Hopefully this illustrates the point. Reference classes are just evidence about the world. There’s no special operation needed for them.