> Why do they have to be ill-gotten gains? Someone could invest money they've earned through productive work.
Because your hypothetical was specifically about someone who doesn't do productive work?
> Suppose you have some money and you put it in some investment fund and then live off the earnings while having no real involvement with how the fund is managed. Meanwhile the businesses you invested in are off doing productive net-positive things with your money that wouldn't have been possible had you stuffed it in your mattress, while yielding you a positive return which is nonetheless smaller than the total amount of net good created by the business.
You're begging the question - why was it your money in the first place?
If it's value you've produced, yes you can partner with someone else to compound it. But if it's just privilege that you had, then you don't get any credit for allowing it to be used productively.
> The best you can say is that the returns are zero-sum, even if the act of investing is positive sum. But isn't that true of anything? If you get a raise, that's zero sum. Someone else would have had the money in the alternative.
If you do something that produces real value in the world then that's positive sum - if you turn some planks and nails into a table, that table is more valuable than the stuff that went into it, the world is better off.