Since the question is about the average, it seems the question can be simply answered: the next-oldest person, on average, will die at the same age as the curre

Since the question is about the average, it seems the question can be simply answered: the next-oldest person, on average, will die at the same age as the current oldest person. (Obviously, assuming an unchanging mortality rate over time, but this sounds like a valid approximation for very old people. There seem to be a wall around 122.) Thus the average waiting time between two oldest-person deaths is the average age difference between the two oldest living persons. Edit: actually, an even simpler first-order approximation is possible. If we take at face-value that very old people have a 50% chance of living one more year, and that this statistics holds whatever the baseline date, then upon the death of the eldest person, the average life-span of the next eldest person is 1/2 + 1/4 + 1/8 ... IOW, 1 year.