My answer to the exercise, thought through before reading the remainder of the post but written down after seeing others do the same:
There is more than one direction of higher entropy to take, not necessarily towards OpenPhil’s distribution. Also, entropy is relative to a measure and the default formula privileges the Lebesgue measure. Instead of calculating entropy from the probabilities for buckets 2022, 2023, 2024, …, why not calculate it for buckets 3000-infinity, 2100-3000, 2025-2099, 2023-2024, …?
My answer to the exercise, thought through before reading the remainder of the post but written down after seeing others do the same:
There is more than one direction of higher entropy to take, not necessarily towards OpenPhil’s distribution. Also, entropy is relative to a measure and the default formula privileges the Lebesgue measure. Instead of calculating entropy from the probabilities for buckets 2022, 2023, 2024, …, why not calculate it for buckets 3000-infinity, 2100-3000, 2025-2099, 2023-2024, …?
Lol, was totally expecting “but entropy is ill-defined for continuous distributions except relative to some base measure.”