| HPS 0628 | Paradox | |
Back to doc list
A square has been selected among those of the diamond-shaped checkerboard above. Use Keynes' Principle of Indifference to determine the probability that the selected square is the square marked "a."
1. If our judgments about the selected square are indifferent over all the squares of the figure, not distinguishing the light from the dark, what is the probability that the selected square is "a"?
2a. If our judgments about the selected square are indifferent over which of the horizontal rows of the checkerboard contains the selected square, what is the probability that the second row contains the selected square?
2b. Under the same indifference as 2a, what is the probability that the selected square is "a"?
3a. If our judgments about the selected square are indifferent over whether it is dark or light, what is the probability that that the selected square is dark?
3b. If we could know that a dark square has been chosen but we would otherwise be indifferent in our judgments over which that dark square is, what is the probability that the selected square is "a"?
3c. If the answers to 3a and 3b are combined, what is the probability that selected square is "a"?
4. Your answers to questions 1-3 should be different. What is the significance of that difference for Keynes' Principle of Indifference?