Objection #1: Quadratic voting discourages voting on losing propositions.
The idea that quadratic voting incentivises you to vote proportionately to your preferences is based on the idea that the derivative of the quadratic formula is linear, so the cost of one additional vote is proportional to the number of votes you’ve already purchased. (In the example table above, the cost of one additional vote is precisely the number of votes you’ve already purchased.) This means if you stop when cost=benefit, your number of votes represents the amount of benefit.
The problem with this argument is that the benefit of one additional vote is based on the chance that it tips the election in your favor. So we shouldn’t expect your votes to be proportional to the utility of a given option. Rather, we should expect your votes to be proportional to utility times probability.
This means that quadratic voting, like plurality voting, has a high incentive to avoid voting on losing propositions.
I think the point of quadratic voting was as follows:
Each legislative term, each legislator starts with one thousand votes. They can use these votes however they want; they might blow all 1K votes on a single big important issue, or use just one vote on each issue, or whatever. This allows strength-of-preference to be expressed, which hopefully helps pass both bills.
The legislature has a set of ideas to vote on. a) How are they prioritized, or b) What passes and what fails?
If everyone blows 1K votes on a handful of issues, then another round of voting may be needed, with another set of 1K votes, and it’s a bit of a mess. Quadratic voting is supposed to even out the distribution—everyone’s time is wasted if there are more rounds of voting required.*
This post also worried about issues still existing, while not performing calculations, which might have revealed whether quadratic voting made things worse, better, etc.
For example, by decreasing votes for things desired, does it increase the risk of these ‘What if they vote for the time travelers?’ effects dominating, or decrease it because things both sides care about are more important to get a little bit of votes on to show preference ordering, and they don’t have so many votes to spare on time travelers just to mess with the other side (because sort(100) is 10, maybe it’s harder to mess with things).
(*The radicalxchange website may have had an article on this, or maybe it was a news article about its use in practice, but they’ve since had a redesign, so, I haven’t found it.)
This post also worried about issues still existing, while not performing calculations, which might have revealed whether quadratic voting made things worse, better, etc.
Agreed, but, calculations are difficult. Also, the issues seem severe. I think all the options I’ve mentioned here are probably significantly worse than business as usual.
I think the point of quadratic voting was as follows:
The legislature has a set of ideas to vote on. a) How are they prioritized, or b) What passes and what fails?
If everyone blows 1K votes on a handful of issues, then another round of voting may be needed, with another set of 1K votes, and it’s a bit of a mess. Quadratic voting is supposed to even out the distribution—everyone’s time is wasted if there are more rounds of voting required.*
This post also worried about issues still existing, while not performing calculations, which might have revealed whether quadratic voting made things worse, better, etc.
For example, by decreasing votes for things desired, does it increase the risk of these ‘What if they vote for the time travelers?’ effects dominating, or decrease it because things both sides care about are more important to get a little bit of votes on to show preference ordering, and they don’t have so many votes to spare on time travelers just to mess with the other side (because sort(100) is 10, maybe it’s harder to mess with things).
(*The radicalxchange website may have had an article on this, or maybe it was a news article about its use in practice, but they’ve since had a redesign, so, I haven’t found it.)
Agreed, but, calculations are difficult. Also, the issues seem severe. I think all the options I’ve mentioned here are probably significantly worse than business as usual.