We were looking for Px to disappear, indicating that the probability of a candidate no longer factors into our considerations.
I’m surprised that we are looking for Px to disappear entirely, I’m not sure I understand that. Quadratic voting shines when you have lots of votes with the same voting token pool, because you force people to allocate resources to decisions they really care about. It’s absolutely not meant to decide one decision—it’s meant to force people to allocate limited resources over a long period, and by doing so reveal their true valuation of those decisions. I would therefore fully expect Px to play a part in every agent’s considerations, as they must consider the probability of success in each vote in order to plan allocation of voting tokens for every other vote.
Interesting. But then how do you argue that it gives approximately correct results? As I understand it, Weyl sees the argument as just: votes end up being roughly proportional to utility (under a lot of differenc scenarios/assumptions). When this condition holds, the quadratic vote is a good representation of the utilitarian value of the different options.
So, the reason I think we’re looking for Px to disappear entirely is because Px is a function of x! It’s fine if c=α+γUx−√ζBB(7) or whatever, so long as none of those extra terms are a function of x, so that in the end c is still proportional to (some normalization of) Ux.
You’re effectively arguing that it’s OK to divide by Px+ϵ, because this just represents voters rationally investing less in cases where Px will probably win anyway. But this means the quadratic vote systematically undervalues the candidates who are seen as the probable winners!
Quadratic voting shines when you have lots of votes with the same voting token pool, because you force people to allocate resources to decisions they really care about. It’s absolutely not meant to decide one decision—it’s meant to force people to allocate limited resources over a long period, and by doing so reveal their true valuation of those decisions.
OK, but this should mean the quantity we are willing to spend on an election is overall adjusted up or down based on properties of that particular election (IE, how much the issue matters to us). This should not mean a dependence on Px; a dependence on Px distorts the vote, compromising it as a representation of collective utility.
Interesting, you make some great points here and I don’t think I have any good refutations to any of them. Perhaps if we play around with the auction structure by which we take away and refund these tokens?
I’m surprised that we are looking for Px to disappear entirely, I’m not sure I understand that. Quadratic voting shines when you have lots of votes with the same voting token pool, because you force people to allocate resources to decisions they really care about. It’s absolutely not meant to decide one decision—it’s meant to force people to allocate limited resources over a long period, and by doing so reveal their true valuation of those decisions. I would therefore fully expect Px to play a part in every agent’s considerations, as they must consider the probability of success in each vote in order to plan allocation of voting tokens for every other vote.
Interesting. But then how do you argue that it gives approximately correct results? As I understand it, Weyl sees the argument as just: votes end up being roughly proportional to utility (under a lot of differenc scenarios/assumptions). When this condition holds, the quadratic vote is a good representation of the utilitarian value of the different options.
So, the reason I think we’re looking for Px to disappear entirely is because Px is a function of x! It’s fine if c=α+γUx−√ζBB(7) or whatever, so long as none of those extra terms are a function of x, so that in the end c is still proportional to (some normalization of) Ux.
You’re effectively arguing that it’s OK to divide by Px+ϵ, because this just represents voters rationally investing less in cases where Px will probably win anyway. But this means the quadratic vote systematically undervalues the candidates who are seen as the probable winners!
OK, but this should mean the quantity we are willing to spend on an election is overall adjusted up or down based on properties of that particular election (IE, how much the issue matters to us). This should not mean a dependence on Px; a dependence on Px distorts the vote, compromising it as a representation of collective utility.
Interesting, you make some great points here and I don’t think I have any good refutations to any of them. Perhaps if we play around with the auction structure by which we take away and refund these tokens?