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 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.