[jwarden]

Author here. @sokoloff also pointed this out in their comment. You are right, the example confuses by making the group sizes different.

I will update the article so it reads like this:

    Ten wealthy art patrons each contribute €1,000,000 to the local public art museum.
        Total Contributions: 10×€1,000,000=€10,000,000
        QF allocates:  (10×sqrt(1,000,000))²=€100,000,000
    Subsidy: €90,000,000

    Ten lower‑income individuals each contribute €100 to replace lead pipes in their neighborhood
        Total Contributions: 10×€100=€1,000
        QF allocates: (10×sqrt(100))²=€10,000
    Subsidy: €9,000.

Here, both groups get their contributions multiplied 10x. But the high-income group gets 10,000x the subsidy.

Given the assumption of wealth equality (and other assumptions), the QF paper proves that allocating more money to art maximizes social welfare, because if people contribute more to the art, it means art it has more utility.

But given the reality of wealth inequality, and the theory of diminishing marginal utility of wealth, the wealthy may contribute more to art simply because they can afford it, and because 1,000,000 may not have any more utility to them than 100 has to a very poor person.

[Sweepi]

"the example confuses by making the group sizes different" But isn't that also realistic, since there a lot more people with little income and "small" problems than ultra-wealthy potential art patrons?

Today, if I get 1000 people to give $10 to the local library or public sport place, I have $10.000. (1000xsqrt(10))² are $10.000.000.

For me, an obvious fix for potential exploitation would be to cap the individual contribution to 10k or 100k. However, as I said I know nothing about qf and this has prob. already been discussed to death.