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Eliezer_Yudkowsky comments on Two probabilities - Less Wrong
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We don't. I'm not sure what's up with that, unless it was a deliberately bad example.
I can't imagine anyone assigning the event probability 0.5 just because it's a Yes/No question. Does the probability drop to 1/3 if I added 1 more option to the question?
The person who assigns probability 1/k to all outcomes of any question with k options is NOT a Bayesian. That's someone who has misunderstood Bayes rule and should re-read all of Eliezer's posts.