I think the core issue is that the lottery wins you government dollars, which you can’t actually spend freely. Government dollars are simply worth less, to Pablo, than Pablo’s personal dollars. One way to see this is that if Pablo could spend the government dollars on the other moonshot opportunities, then it would be fine that he’s losing his own money.
So we should stipulate that after calculating abstract dollar values, you have to convert them, by some exchange rate, to personal dollars. The exchange rate simply depends on how much better the opportunities are for personal spending, versus spending government money.
The fact that opportunities can get larger than your budget size seems not to be the core issue for the reason that you mention—that at realistic sizes of opportunity, it is possible to instead buy a lottery for a chance at the opportunity instead.
I think the core issue is that the lottery wins you government dollars, which you can’t actually spend freely. Government dollars are simply worth less, to Pablo, than Pablo’s personal dollars. One way to see this is that if Pablo could spend the government dollars on the other moonshot opportunities, then it would be fine that he’s losing his own money.
So we should stipulate that after calculating abstract dollar values, you have to convert them, by some exchange rate, to personal dollars. The exchange rate simply depends on how much better the opportunities are for personal spending, versus spending government money.
The fact that opportunities can get larger than your budget size seems not to be the core issue for the reason that you mention—that at realistic sizes of opportunity, it is possible to instead buy a lottery for a chance at the opportunity instead.