How does this system deal with the logarithmic value of dollars, and the asymmetry in who has them?
When you get ln(X) happiness from X dollars, you are sacrificing 1/X happiness per dollar spent. A billionaire buying a thousand votes is paying ln(10^9 - (10^3)^2) - ln(10^9) ~= 1 milli-utilon, but a thousandaire buying ten votes is paying ln(10^3 - 10^2) - ln(10^3) ~= 100 milli-utilons.
It seems like billionaires, who easily get a factor of a thousand advantage in marginal votes-per-happiness cost over 99% of the population, will massively distort a quadratic voting market.
Uniformly redistributing the voting cost makes that effect smaller, but I don't think it overcomes the logarithmic effect.
When you get ln(X) happiness from X dollars, you are sacrificing 1/X happiness per dollar spent. A billionaire buying a thousand votes is paying ln(10^9 - (10^3)^2) - ln(10^9) ~= 1 milli-utilon, but a thousandaire buying ten votes is paying ln(10^3 - 10^2) - ln(10^3) ~= 100 milli-utilons.
It seems like billionaires, who easily get a factor of a thousand advantage in marginal votes-per-happiness cost over 99% of the population, will massively distort a quadratic voting market.
Uniformly redistributing the voting cost makes that effect smaller, but I don't think it overcomes the logarithmic effect.