Translate your problem into a space where differences seem approximately linear. For many problems with long tails, this means estimating the magnitude of a quantity rather than the quantity directly, which is just “use lognormal”.
Aggregate in the linear space and transform back to the original. For lognormal, this is just “geometric mean of original” (aka arithmetic of the log).
My generalized heuristic is:
Translate your problem into a space where differences seem approximately linear. For many problems with long tails, this means estimating the magnitude of a quantity rather than the quantity directly, which is just “use lognormal”.
Aggregate in the linear space and transform back to the original. For lognormal, this is just “geometric mean of original” (aka arithmetic of the log).