Suppose that there are 1,000 basement-dwelling redditors (okay, it's a caricature). Each has their basic needs taken care of, but not much money, and not much scope to improve their lot in life. What little money they have doesn't get invested, but spent frivolously.
Suppose 1,000 such people could all put in $500 and give it to a randomly selected one of them. That person wins a life-changing amount of money. They suddenly have their prospects upgraded - they can travel, buy a house, live in some comfort, pursue a dream career. Couldn't it arguably be rational for all 1,000 to participate in that game? Doesn't it make sense that the utility curve is convex, not concave - that $500,000 is more than 1,000 times better than $500, when compared to $0?
After all, suppose that $500 was a year's spare income. Even saving for most of a lifetime would only yield $20-30,000, nothing like enough for many of the opportunities that half a million would make possible. And a lump sum at age 65 could be much less useful than one at age 25. Losing the $500 might barely make a difference to one's quality of life.
Now suppose that to participate in this lottery, they have to pay 10% of the money to Wall Street, or high frequency market makers, or whoever. Couldn't it still be a rational choice for each of the 1,000 to participate?
To the person with 10 million dollars, doubling their wealth is nice for them but likely won't result in a major change in lifestyle and what they could or couldn't do before. Maybe they go from a large house to a larger house. For the person that makes 30 thousand a year, doubling it makes a huge difference in how they live. The disposable income amount doesn't double, it's likely many many times higher, because it was such a relatively small portion before.
The same thing applies to one-time payments. It would make sense in your example even if the payout was much less (like $10k) but still affected the group similarly (i.e. if they had less disposable income). That amount of money is a huge to people that have little disposable income.
The implication you're making here is that these people wouldn't mind losing $500/year, because it's otherwise being spent "frivolously". I don't think this is true because if you're spending it on something, you're getting joy out of it, otherwise you wouldn't be spending money on it in the first place. For reference, $500 can buy you a game console or several games, which can provide you with tens or hundreds of hours of entertainment.
If it's really the case that the $500/year is being spent frivolously (ie. being spent on things that don't bring joy), then the correct course of action would be some sort of intervention that forces them to save, so they receive a large enough lump sum that can be used productively. We sort of see this happen with tax refunds, where people are basically forced to save throughout most of the year, the IRS gives it back at the end of the year, and they spurge the refund on a big purchase.
>Doesn't it make sense that the utility curve is convex, not concave - that $500,000 is more than 1,000 times better than $500, when compared to $0?
What makes you think that? I think it's generally accepted that money has a diminishing returns on happiness. I guess if you go to the extremes there's some ranges where it doesn't apply (eg. it's hard to do anything fun with a $5 bill), but there's also nothing preventing you from saving up the money.
>After all, suppose that $500 was a year's spare income. Even saving for most of a lifetime would only yield $20-30,000, nothing like enough for many of the opportunities that half a million would make possible.
You're off by a factor of 2. Factoring in a 6% inflation adjusted return, you end up with a return of $77,380 if you do this for 40 years.
Things that bring me joy are being able to donate enormously to solve social problems in my quality. I can say for certainty that it will bring me 10,000 times happiness.
This almost certainly results in a worse average outcome, because of diminishing returns on income. Winning a 10M jackpot won't bring you 10,000 times the happiness compared to finding $1000 on the ground.