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komponisto comments on BHTV: Eliezer Yudkowsky & Razib Khan - Less Wrong
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The conjunction fallacy applies only when you already have a probability law. (a specification of a probability space). It applies to events in a probability space. The conjunction rule proscribes assigning a subset event higher probability than the event containing it.
Occam's razor is prescription for what probability laws should look like (e.g each program having a prior probability of (1/2) to the power of its code length in bits). i.e. what constitutes an outcome in the probability space, all outcomes having equal probability.
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.
These are two distinct, legitimate uses of the term "Occam's Razor". The conjunction rule is the everyday sense; what you're talking about is a deeper, philosophical sense.
Well I agree. In our everyday lives, Occam tells us to chose the simplest hypotheses. Conjunction rule tells us to keep any particular hypothesis we have as simple as possible.
Also, maybe we should apply conjunction rule first to our candidate hypotheses and then only Occam to chose the simplest among them. (of course, Occam by itself already picks out the simplest hypotheses, but i'm talking about a working procedure here)