DT is not my strength either, but it seems like Peterson is just doing a simple slight-of-hand trick. The trickery is concealed in this line:
Now, since you know nothing about the probabilities of the two states, you decide to regard them as equally probable
This conflicts with the earlier claim that our priors for each location are 1⁄3. Changing the way the table looks does not mean that we are allowed to change that prior information. P(P) is still 1⁄3, and P(LA or NY) is still 2⁄3. Calling these “two states” conceals the fact that you have manipulated the prior information, which is what’s creating the “paradox.”
DT is not my strength either, but it seems like Peterson is just doing a simple slight-of-hand trick. The trickery is concealed in this line:
This conflicts with the earlier claim that our priors for each location are 1⁄3. Changing the way the table looks does not mean that we are allowed to change that prior information. P(P) is still 1⁄3, and P(LA or NY) is still 2⁄3. Calling these “two states” conceals the fact that you have manipulated the prior information, which is what’s creating the “paradox.”
This. Either we know nothing about each of the three states, or we know nothing about either of the two states, not both.