Robin used a Dirty Math Trick that works on us because we're not used to dealing with large numbers. He used a large time scale of 12000 years, and assumed exponential growth in wealth at a reasonable rate over that time period. But then for depreciating the value of the wealth due to the fact that the intended recipients might not actually receive it, he used a relatively small linear factor of 1/1000 which seems like it was pulled out of a hat.
It would make more sense to assume that there is some probability every year that the accumulated wealth will be wiped out by civil war, communist takeover, nuclear holocaust, etc etc. Even if this yearly probability were small, applied over a long period of time, it would still counteract the exponential blowup in the value of the wealth. The resulting conclusion would be totally dependent on the probability of calamity: if you use a 0.01% chance of total loss, then you have about a 30% chance of coming out with the big sum mentioned in the article. But if you use a 1% chance, then your likelihood of making it to 12000 years with the money intact is 4e-53.
As I said in response to Gwern's comment, there is uncertainty over rates of expropriation/loss, and the expected value disproportionately comes from the possibility of low loss rates. That is why Robin talks about 1/1000, he's raising the possibility that the legal order will be such as to sustain great growth, and the laws of physics will allow unreasonably large populations or wealth.
Now, it is still a pretty questionable comparison, because there are plenty of other possibilities for mega-influence, like changing the probability that such compounding can take place (and isn't pre-empted by expropriation, nuclear war, etc).
Robin Hanson wrote, five years ago:
In the comments some people gave counterarguments. For those in a rush, the best ones are Toby Ord's. But I didn't bite any of the counterarguments to the extent that it would be necessary to counter the 10^100. I have some trouble conceiving of what would beat a consistent argument a googol fold.
Things that changed my behavior significantly over the last few years have not been many, but I think I'm facing one of them. Understanding biological immortality was one, it meant 150 000 non-deaths per day. Understanding the posthuman potential was another. Then came the 10^52 potential lives lost in case of X-risk, or if you are conservative and think only biological stuff can have moral lives on it, 10^31. You can argue about which movie you'll watch, which teacher would be best to have, who should you marry. But (if consequentialist) you can't argue your way out of 10^31 or 10^52. You won't find a counteracting force that exactly matches, or really reduces the value of future stuff by
3 000 000 634 803 867 000 000 000 000 000 000 777 000 000 000 999 fold
Which is way less than 10^52
You may find a fundamental and qualitative counterargument "actually I'd rather future people didn't exist", but you won't find a quantitative one. Thus I spend a lot of time on X-risk related things.
Back to Robin's argument: so unless someone gives me a good argument against investing some money in the far future (and discovering some vague techniques of how to do it that will make it at least one in a millionth possibility) I'll set aside a block of money X, a block of time Y, and will invest in future people 12 thousand years from now. If you don't think you can beat 10^100, join me.
And if you are not in a rush, read this also, for a bright reflection on similar issues.