As stated in W11 Slide #36, the Principle of Indifference says:
- When faced with n > 1 possibilities that are mutually exclusive and jointly exhaustive, and you have no evidence about their relative likelihoods, a probability equal to 1/n for each possibility.
I also gave two examples in the lecture:
- Example 1:
- Paul graduated from either JPJC, ACJC, or SAJC (and exactly one of them), but you don’t know which and you don’t know the likelihood of him going to any one of them.
Assign a probability equal to 1/3 to the possibility that he went to SAJC.- Example 2:
- You have one lucky draw coupon, and you know that one coupon from a pile (numbered 000,000,000 to 999,999,999) will be picked. Each coupon give you one chance of willing. Assign a probability equal to 1/1,000,000,000 to the outcome where your coupon is the winning coupon.
Now, the “probability” we are talking about is not something about the world–about where Paul actually went to school, or which coupon is the actual winning coupon. Rather, we are talking about the level of confidence you should have, if you are being rational, in one of the options being true, given that you don’t know yet.