The conjunction fallacy really says nothing about prior probabilities. The conjunction rule is a theorem in probability. Occam’s razor is a working rule for assigning prior probabilities to hypotheses.
Prior and posterior probabilities are not made of fundamentally different stuff, and posterior of one calculation can turn out the be prior in the next. Assuming fundamentally distinct sets of probabilities and new ways of popping probabilities into existence seems uncalled for.
You were also suggesting to first use conjunction rule to weed out hypotheses that are less likely, and then summoning Occam’s razor to do the exact same thing again. This too seems redundant.
Agreed, there is no fundamental distinction. You can certainly update existing probabilities which did not take into account Occam’s Razor, to take it into account. What makes Occam pertinent to priors in particular is that you can apply it to anything, which means it can always also be the first thing you apply to hypotheses. So think of Occam as ‘evidence’ that applies to all hypotheses. (note that the conjunction rule is not similarly ‘evidence’)
Yes it is ideally redundant, but i did emphasize I was suggesting it as a working rule. It seems to me less computationally expensive to remove extraneous elements from hypotheses than to calculate or at least rank their complexity.
Prior and posterior probabilities are not made of fundamentally different stuff, and posterior of one calculation can turn out the be prior in the next. Assuming fundamentally distinct sets of probabilities and new ways of popping probabilities into existence seems uncalled for.
You were also suggesting to first use conjunction rule to weed out hypotheses that are less likely, and then summoning Occam’s razor to do the exact same thing again. This too seems redundant.
Agreed, there is no fundamental distinction. You can certainly update existing probabilities which did not take into account Occam’s Razor, to take it into account. What makes Occam pertinent to priors in particular is that you can apply it to anything, which means it can always also be the first thing you apply to hypotheses. So think of Occam as ‘evidence’ that applies to all hypotheses. (note that the conjunction rule is not similarly ‘evidence’)
Yes it is ideally redundant, but i did emphasize I was suggesting it as a working rule. It seems to me less computationally expensive to remove extraneous elements from hypotheses than to calculate or at least rank their complexity.