Re: Which Twin has the Tony?
I disagree with the analogy to the 2 envelope problem. In that case, the apparent paradox, as you've said in a past thread, relates to an incorrect assumption on the probability distribution:
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This is the heart of the problem - the distribution from which the envelope amounts are chosen. Even advanced probabilty students miss the underlying bogus assumption that all envelope amounts are equally likely. ie. that the envelope amounts were chosen from a uniform distribution over the positive real numbers. Of course there is no such probabilty distribution.
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However, in this case, the probability distribution of haircuts onto twins is a lot simpler than money in envelopes. We're talking discretes and Booleans, not analysis across the real number line. I'm still unconvinced that we cannot model it as an equal probability of each twin having the haircut and get useful results.
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