[sopooneo]

If you believe the distribution of cognitive abilities to be orthogonal to race/gender, why set your a priori at 0.5? I may be misunderstanding (my stats knowledge is low) but it seems you see no reason a particular statement should be true, yet assume a fifty fifty chance that it is true.

[mjdwitt]

Because there is equally no reason that the statement should be false.

[trhtrsh]

That is completely missing the Bayesian worldview, which says you should assign a distribution to the probabilities. A uniform distribution of probabilities, 0-100%, is not perfect, captures the uncertainty better than a point distribution at 50%.

I am holding a pencil right now. Is the eraser at a higher altidude than the tip? Maybe, maybe not. Is that 50/50? Would you be willing to make a bet from me at 1:1 odds, that the the answer is yes?