I was assuming you still knew something about the structure of the problem, i.e. that there would be a bunch of tickets sold, that you have only bought one, etc.
If you’ve already observed all the possible evidence, then your prediction is not a “prior” any more, in any sense of the word. Also, both total tickets sold and the number of tickets someone bought are variables. If I know that there is a lottery in the real world, I don’t usually know how many tickets they really sold (or will sell), and I’m usually allowed to buy more than one (although it’s hard for me to not know how many I have).
After updating, you have a bunch of people who all have a small probability for “the earth is flat”, but they may have slightly different probabilities due to different genetic predispositions. Are you saying that you don’t think averaging makes sense here?
I think that Hanson wants to average before updating. Although if everyone is a perfect bayesian and saw the same evidence, then maybe there isn’t a huge difference between averaging before or after the update.
Either way, my position is that averaging is not justified without additional assumptions. Though I’m not saying that averaging is necessarily harmful either.
If you are doing a log-odds average then it doesn’t matter whether you do it before or after updating.
Like I pointed out in my previous comment the question “how much evidence have I observed / taken into account?” is a continuous question with no obvious “minimum” answer. The answer “I know that a bunch of tickets will be sold, and that I will only buy a few” seems to me to not be a “maximum” answer either, so beliefs based on it seem reasonable to call a “prior”, even if under some framings they are a posterior. Though really it is pointless to talk about what is a prior if we don’t have some specific set of observations in mind that we want our prior to be prior to.
If you’ve already observed all the possible evidence, then your prediction is not a “prior” any more, in any sense of the word. Also, both total tickets sold and the number of tickets someone bought are variables. If I know that there is a lottery in the real world, I don’t usually know how many tickets they really sold (or will sell), and I’m usually allowed to buy more than one (although it’s hard for me to not know how many I have).
I think that Hanson wants to average before updating. Although if everyone is a perfect bayesian and saw the same evidence, then maybe there isn’t a huge difference between averaging before or after the update.
Either way, my position is that averaging is not justified without additional assumptions. Though I’m not saying that averaging is necessarily harmful either.
If you are doing a log-odds average then it doesn’t matter whether you do it before or after updating.
Like I pointed out in my previous comment the question “how much evidence have I observed / taken into account?” is a continuous question with no obvious “minimum” answer. The answer “I know that a bunch of tickets will be sold, and that I will only buy a few” seems to me to not be a “maximum” answer either, so beliefs based on it seem reasonable to call a “prior”, even if under some framings they are a posterior. Though really it is pointless to talk about what is a prior if we don’t have some specific set of observations in mind that we want our prior to be prior to.