This is kind of missing the point of Bayes. One shouldn’t “choose” a reference class to update on. One should update to the best of your ability on the whole distribution of hypotheses available to describe the situation. Neither is a ‘right’ or ‘wrong’ reference class to use, they’re both just valid pieces of evidence about base rates, and you should probably be using both of them.
It seems you are having in mind something like inference to the best explanation here. Bayesian updating, on the other hand, does need a prior distribution, and the question of which prior distribution to use cannot be waved away when there is a disagreement on how to update. In fact, that’s one of the main problems of Bayesian updating, and the reason why it is often not used in arguments.
I’m not really sure what that has to do with my comment. My point is the original post seemed to be operating as if you look for the argmax reference class, you start there, and then you allow arguments. My point isn’t that their prior is wrong, it’s that this whole operation is wrong.
I think also you’re maybe assuming I’m saying the prior looks something like {reference class A, reference class B} and arguing about the relative probability of each, but it doesn’t, a prior should be over all valid explanations of the prior evidence. Reference classes come in because they’re evidence about base rates of particular causal structures; you can say ‘given the propensity for the world to look this way, how should I be correcting the probability of the hypotheses under consideration? Which new hypotheses should I be explicitly tracking?’
I can see where the original post might have gone astray. People have limits on what they can think about and it’s normal to narrow one’s consideration to the top most likely hypothesis. But it’s important to be aware of what you’re approximating here, else you get into a confusion where you have two valid reference classes and you start telling people that there’s a correct one to start arguing from.
I agree this is an interesting philosophical question but again I’m not sure why you’re bringing it up.
Given your link maybe you think me mentioning Bayes was referring to some method of selecting a single final hypothesis? I’m not, I’m using it to refer to the Bayesian update rule.
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.
This is kind of missing the point of Bayes. One shouldn’t “choose” a reference class to update on. One should update to the best of your ability on the whole distribution of hypotheses available to describe the situation. Neither is a ‘right’ or ‘wrong’ reference class to use, they’re both just valid pieces of evidence about base rates, and you should probably be using both of them.
It seems you are having in mind something like inference to the best explanation here. Bayesian updating, on the other hand, does need a prior distribution, and the question of which prior distribution to use cannot be waved away when there is a disagreement on how to update. In fact, that’s one of the main problems of Bayesian updating, and the reason why it is often not used in arguments.
I’m not really sure what that has to do with my comment. My point is the original post seemed to be operating as if you look for the argmax reference class, you start there, and then you allow arguments. My point isn’t that their prior is wrong, it’s that this whole operation is wrong.
I think also you’re maybe assuming I’m saying the prior looks something like {reference class A, reference class B} and arguing about the relative probability of each, but it doesn’t, a prior should be over all valid explanations of the prior evidence. Reference classes come in because they’re evidence about base rates of particular causal structures; you can say ‘given the propensity for the world to look this way, how should I be correcting the probability of the hypotheses under consideration? Which new hypotheses should I be explicitly tracking?’
I can see where the original post might have gone astray. People have limits on what they can think about and it’s normal to narrow one’s consideration to the top most likely hypothesis. But it’s important to be aware of what you’re approximating here, else you get into a confusion where you have two valid reference classes and you start telling people that there’s a correct one to start arguing from.
… but that still leaves the problem of which prior distribution should be used.
I agree this is an interesting philosophical question but again I’m not sure why you’re bringing it up.
Given your link maybe you think me mentioning Bayes was referring to some method of selecting a single final hypothesis? I’m not, I’m using it to refer to the Bayesian update rule.
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.