It may not be obvious at first glance why CCC’s response supports Eliezer’s point, so to spell it out in more detail: as of now (the night before), I expect that as of 10 am, there will be
A. 25% that cable guy already arrived, ie 25% chance of ‘before noon and before 10’.
B. 75% that cable guy has not already arrived, and 33.3% chance that he’ll arrive between 10 am and noon, ie .75 / 3 = 25% chance of ‘before noon and after 10’.
C. 75% that cable guy has not already arrived, and 66.7% chance that he’ll arrive after noon, ie .75 * 2 / 3 = 50% chance of ‘after noon’.
This illustrates Eliezer’s point nicely. Since the total ‘before noon’ chance is case A (25%) + case B (25%) and the total ‘after noon’ chance is case C (50%), my currently expected belief at 10 am tomorrow is the same as my expected belief now, and so we don’t expect our confidence in ‘before noon’ to be higher (or lower) than it is now.
As of 10 am tomorrow, we will (as CCC says) have changed our probabilities in one direction or another, but in our current expectation of our beliefs at that point, it’s still 50:50.
It may not be obvious at first glance why CCC’s response supports Eliezer’s point, so to spell it out in more detail: as of now (the night before), I expect that as of 10 am, there will be
A. 25% that cable guy already arrived, ie 25% chance of ‘before noon and before 10’.
B. 75% that cable guy has not already arrived, and 33.3% chance that he’ll arrive between 10 am and noon, ie .75 / 3 = 25% chance of ‘before noon and after 10’.
C. 75% that cable guy has not already arrived, and 66.7% chance that he’ll arrive after noon, ie .75 * 2 / 3 = 50% chance of ‘after noon’.
This illustrates Eliezer’s point nicely. Since the total ‘before noon’ chance is case A (25%) + case B (25%) and the total ‘after noon’ chance is case C (50%), my currently expected belief at 10 am tomorrow is the same as my expected belief now, and so we don’t expect our confidence in ‘before noon’ to be higher (or lower) than it is now.
As of 10 am tomorrow, we will (as CCC says) have changed our probabilities in one direction or another, but in our current expectation of our beliefs at that point, it’s still 50:50.