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Blueberry comments on Multiple Choice - Less Wrong
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Comments (34)
If you can rule out one of four choices, you'll get the right answer 1/3 of the time, and a wrong answer 2/3 of the time, for an expected value of 1(1/3) - (1/2)(2/3) = 0, so it doesn't matter whether you guess or not.
Filling in the bubble costs time.
Inversely, filling in the bubble prevents you from getting one cell off for the following questions.
If you can firmly rule out one of the 4 options, it seems pretty unlikely that you are literally indifferent between the other three, so guessing is almost certainly positive expectation.
It was stated that a wrong answer costs a quarter point, so the expected value is 1(1/3) - (1/4)(2/3) = 1/6. A cost of 1/4 point for a wrong answer is too low though, since in that case the expected value of guessing from all four choices is still 1/16. The cost should be 1/3 to make that expectation equal 0.