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Misha comments on Example of poor decision making under pressure (from game show) - Less Wrong
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Comments (22)
I don't see how this can be true in conjunction with Vaniver's post. In particular, suppose you start with 0 wealth, and get a question right by being honest. Now you have e.g. £10,000 in winnings.
Then wouldn't the problem of answering the second question be isomorphic to the problem of answering the first question when you don't start with zero wealth, which as we've seen involves being dishonest?
I have two hypotheses explaining this. One is that I don't understand something about the game show rules. Another is that you're combining winnings improperly: winning £X then £Y should give you log(X+Y) utility, not log(X) + log(Y) (and if you mistakenly do the latter, then I think honesty is the best option in all cases).
You start with zero wealth. The quiz show host "gives" you a million pounds to play with, but you can only take home the money left after the last round. The intermediary levels of imaginary wealth do not affect the calculation.
Oh, I see, I was completely misunderstanding the problem.