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Comment by troels | Hacker News Reader

Maybe I'm just a bit slow, but what's going on with the 50/50 "guessing score" reasoning? Surely, you should half the wrong answers as well, rather than just subtracting it from the right answers?!?

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If proportion X (between 0 and 1) of the population knows the right answer (we'll call A, and the wrong answer B), and the other half guesses evenly, you would expect:

    A = X + (1 - X) / 2

So to calculate X, given A,

    2A = 2X + 1 - X = X + 1
    X = 2A - 1

The author implied the formula

    X = A - 0.5

which is not correct. In particular, assume everyone got the answer right (X=A=1). Then the assertion that half of the answers are correct guesses is absurd.

The correct lucky guess fraction (amount of the right answers to discard) is:

    A - X = A - (2A - 1) = 1 - A

If A is near to 0.5 (which we would expect if our model is accurate and few people know the answer, the 50% approximation the author used is about right.)

Thanks - Not just me then.

There are two choices. If everyone guessed, the expected value is 50% correct and 50% incorrect. This is why it's 25/75 for the question with four choices.

If someone guessed incorrectly, they still didn't know the answer.

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