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JamesAndrix comments on Never Leave Your Room - Less Wrong
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My ex used to privately assign two menu items to the numbers one and two, and then ask me aloud to pick one or two, then see how she felt about my response.
I ask for any integer, and determine it's value modulo 2, or modulo 3 if I have an extra option.
Sorry for intruding on an very old post, but checking 'peoplerandom' integers modulo 2 is worse than flipping a coin - when asked for a random number, people tend to choose odd numbers more often than even numbers, and prime numbers more often than non-prime numbers.
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The second is also implied by the first, if "primes more often than non-primes" means "out of proportion with how many primes there are" rather than "more than 50% of the time", and I think it would be equally interesting to look at whether [odd] primes are more likely to be chosen than odd non-primes.
I wonder if the real issue is "that the person can/can't recall (part of) the factorization offhand" - that would make sense if people avoid numbers that "feel round" - something with an obscure factorization like 51 [3*17] might be more likely to be chosen than even numbers, multiples of 11, numbers that appear on a multiplication table (so, 3 times numbers 10 or less).