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

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.)