Quadratic Voting | Hacker News Reader

Quadratic Voting

en.wikipedia.org

124 pointsk2enemy53 comments

One key principle that a lot of people miss is that quadratic voting doesn't work with real money because people don't value wealth in a linear fashion. $5 is worth much more for a homeless person than for a millionaire. Proof of this can be seen in preference surveys or other studies of human behavior. This fact breaks the key assumption of quadratic voting and causes skewed results in that people with more money can buy more votes even with "weaker" preferences.

This is addressed in the Wikipedia page under "Criticisms of quadratic voting mechanisms".

Potential solutions include giving everyone the same amount of starting artificial "money", using one-person-one-vote when issues are polarized along wealth-lines, or making votes more expensive for the wealthy.

To me, the first option of delegating everyone the same starting votes seems the most reasonable. However, I think allocating vote prices based on wealth could create some interesting incentives and resulting politics.

What the wikipedia criticism doesn't mention issue flooding/packing. Quadratic voting works, on paper, when applied to set piece issues. It doesn't address the reality of legislatures, that "issues" are not fixed pieces on a chessboard. Issues can be split across multiple referendums. Whoever is in control can use splits to dilute votes, causing voters to spend their votes repeatedly winning a minor issue until their are depleted. Then those who 'lost' the first rounds now have the votes to win the last round. Giving everyone equal footing on every vote stops this.

I had the same thought. This system does not account for the introduction of legislation that can be voted on. Who decides which legislation to consider. Surely the party in power could sway the outcome by stacking the decions against each other.

This is equivalent to gerrymandering political districts. Spread out the votes on the issues based on the electors in favor of a predtermined outcome.

That's essentially the solution to this problem. Or you can think of it another way. Every person gets x votes (we'll say 100, but it should probably change dependent upon the ballot, which can get confusing but we'll ignore that). You can go all in on one candidate and designate all 100 votes to that one, but you forfeit voting elsewhere. Like on the general election ballot you will have the president, senators, congressional rep (what's the preferred gender neutral term?), governor, etc. You can assign all 100 votes in the presidential race and forfeit voting in the other races.

Of course, this brings a difficult problem on a national scale. Often many seats are run uncontested, even in large areas. So if we had a minimum of 1 vote per candidate, that would give certain areas and certain elections more power. You could then "hack" the election simply by running extra candidates and make it seem more contested. While I like cardinal systems, I think quadratic gets extremely complicated as soon as you try to expand it outside of a localized election and maybe it isn't worth it.

> what's the preferred gender neutral term?

http://enwp.org/Congresscritter

If I care strongly about an issue, but I also know it's likely to win, isn't the best tactic for me to not vote for it to save my credits for more marginal issues?

If everyone votes tacitcally, it seems like a lot of votes would be won with slim majorities. But that risks random upsets, even on issues which everyone basically agrees on!

This is why the base vote must not cost credit

Principles of game theory come into play at that time isnt it?

What frustrates me most about Quadratic Voting, and in general a lot of ideas promoted by Glen Weyl and his coterie, is that arguments in its favour almost completely ignore the significant additional cognitive burden it places on the populace. American Voters barely understand the difference between the popular vote and the electoral college -- to ask them to view the results of QV votes as fair and legitimate would be a bridge too far. Hell, I know a fair bit of math and CS, and I would feel uncomfortable quickly deciding how to divide my votes across issues, let alone advising other people on what to do.

> American Voters barely understand the difference between the popular vote and the electoral college -- to ask them to view the results of QV votes as fair and legitimate would be a bridge too far.

It is not like simpler voting methods are without subtleties (and I certainly wouldn't call electoral college simple!), but these subtleties are well-known and everybody is kind of accustomed to them. Again, immediately abandoning ordinary voting and switching to QV on the level of countries would be stupid, but I don't think they are advocating that.

> Hell, I know a fair bit of math and CS, and I would feel uncomfortable quickly deciding how to divide my votes across issues, let alone advising other people on what to do.

This can probably be less of a problem with sufficiently good UI. Imagine that you can play with some sliders and immediately see the consequences of your actions. After some fiddling you will probably get pretty close to what you want. Some friction can even be beneficial, encouraging people to be more thoughtful about issues. There was a study (link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2755844) where they used QV in opinion polls and were able to get more information about relative preferences of participants because they were forced to think about correctly allocating their credits instead of blindly answering "strongly agree"/"strongly disagree" even if they didn't really care about a particular issue.

Actually, I think what would be more useful is the ability to vote directly on all things and delegate your vote on specific topics or in general when you want not every 4 years. We can have the technology to enable this and it would effectively kill a full time politician as a job. That think would instead be done by retirees in their spare time. And if things were not going to work in the right direction, you can vote immediately, any time. If, on the other hand you don’t care or don’t know enough about the subject, you can delegate your vote and that person can also delegate your and her vote too.

I love this topic and have been researching liquid democracy on the side. We need more people researching the implications of this political system.

That’s precisely what I have came up with and wish existed.

This is precisely the idea of liquid democracy: https://en.wikipedia.org/wiki/Liquid_democracy

This is exactly what the flux party is doing in Australia:

https://voteflux.org/

> Actually, I think what would be more useful is the ability to vote directly on all things and delegate your vote on specific topics or in general when you want not every 4 years.

Sounds like the ultimate form of populism: a government that just blindly follows what the majority wants. This has many problems. For example, who will care for minorities? And do you realize that everybody is part of a minority group in some ways?

I believe Switzerland is close to that model and they're doing pretty well.

The Aurora Rising books by Alistair Reynolds are set in an environment where this is the case. Basically the only automatic right is that to have a vote.

Who sets the questions?

In a parliamentary democracy, the full-time politicians decide what is debated; what is up for debate; what is possible to change through a vote (and what is not possible to change by not putting it up for a vote).

They also decide what civil servants act upon - and what they don't. What is researched and evidenced - and what is not.

Deciding what direction you want to vote on a particular single issue is relatively late in the process of democracy (and conveys relatively little power).

The power to elect a representative is thus much greater, fairer, and more desirable, than the power to flex your vote on single issues.

A liquid democracy would have to be much closer to direct democracy than representative democracy in this regard.

In California you need to collect a certain percentage of the population's signatures to get something on the ballot, and I imagine it'd have to work the same way. You could increase the frequency to yearly, or even quarterly, and build a system where you can endorse anything you want to be added to a ballot, then once a quarter you can vote on the issues you care about, and give the rest of your voting power to any other citizen, who can do the same for any other issues.

Parliaments set the agenda on a daily basis.

How do you cope with coronavirus by making decisions on a quarterly basis?

> For example, a voter with a budget of 16 vote credits can apply 1 vote credit to each of the 16 issues. However, if the individual has a stronger passion or sentiment on an issue, they could allocate 4 votes, at the cost of 16 credits, to the singular issue, effectively using up their entire budget.

It would be better for this individual "A" to find another one "B" who feels strongly about another issue, and agree to both use 2 votes each on A's cause in exchange for both using 2 votes each on B's cause. That way they each pay only 2^2+2^2 = 8 instead of 16, for the same outcome. This assumes some amount of trust between A and B in case they cannot provide each other with evidence of how they voted.

> Under various sets of conditions, quadratic voting has been shown to be much more efficient than one-person-one-vote in aligning collective decisions with doing the most good for the most people.

That's a severe misunderstanding. We don't have elections to make collective decisions that yield "the most good for the most people". We have elections because the alternatives to not having elections are worse.

Moreover, "the most good for the most people" is subjective -- any objective measures of that that you come up with will be subjectively chosen. Some will say that maximizing the health of the environment does the most good for the most people, while others will say that maximizing GDP per-capita does -- if those two are in conflict, who's right? Elections sidestep the matter: it's not about being right, but about what people want.

Sometimes people want things they really really shouldn't, and they may try to get their way via elections. For that we have institutions (e.g., constitutions, courts, separation of powers, etc.) that keep them from getting those things for some time. The alternative to all that is absolute monarchy, caudillos, dictatorship, war, anarchy (for a while until you get a strongman) -- all bad things.

If you manage to impose a technocracy not headed by a strongman, soon it will be, and either way may well lead to revolt, possibly civil war.

I too would like a better system, because "democracy is the worst system of governance, except for all the others", but like Churchill, I'm skeptical that there is something better than a constitutional, democratic republican form of government.

Utopia peddling seems very commonplace nowadays. That's a bit worrisome.

I think what they mean is it results in outcomes that better align with the preferences of the voters than other voting schemes.

I think research into voting systems like this shouldn't be read as coming from a point of view of "we have the correct objective function we prove that our system is unequivocably optimal under this objective function". Rather the objective function is a "toy model" which we understand does not capture all of reality, but hopefully captures enough of it to provide some interesting insight.

I mean, obviously policies and outcomes at stake in any voting system are subjective, so that's an objection that can be levelled against any objective function, but that includes anything you choose as well. E.g. if you say that your objective function will be to minimize the risk of participants getting dissatisfied enough to violently go out of the system (i.e. revolt / civil war), well, one-person-one-vote can fail like that too; who's to say that that system is really optimal with respect to this objective function?

Why not simply allocate weights of preference between choices so they sum up to 1 (100%)?

If you require that some peoples votes are of higher weight, run the same thing but on population that votes - assigning weight to every individual - so it sums up to 1 (100%) as well.

With problem defined in this way you have this intuitive tool to easily compose/merge or compare outcomes, ie. voting run for shareholders (weighted on shares) can be merged with votes of ie. employees (could be weighted on salary and/or time spent in the company) - all those can be merged givig weight to each vote run.

This can be extended with more exotic things like votes (at any level) attached to probablity of some yet unknown "fact" or time or any arbirary input which is an output of any DAG created by this voting rule. This makes the whole setup dynamic. Complexity always collapses into simple, intuitive values that can be interpreted (and used as input for other voting-like decisions).

Weighted voting all the way down.

Prussia had a three tiered voting system, which allotted electors by dividing the tax income per district in three parts and awarding equal numbers of electors to each of the subpopulations (4.7%, 12.7%, 82.6% of the population in 1849). That it was applied per district had the interesting consequence that even wealthy people could easily be in the lowest of these three brackets (https://en.wikipedia.org/wiki/Prussian_three-class_franchise)

So, for this to work - you need a reasonably large set of decisions to be decided in one big election, - rational agents, even though the topics is emotional.

And how do they reach the conclusion that "the system will be predisposed to dominance by special interest groups with strong, concentrated interests"? That might be in some limit towards infinity case, but in practice? And why that would be a good thing, is beyond me.

And who decides what the issues are that get voted on? This is an important flaw IMO against multi issue voting with this system.

If the people making the list of issues are biased they can make one big issue for all the stuff they care about, and a thousand little issues for the stuff other people care about.

Every issue needs equal footing to overcome this, meaning each issue needs to be its own independent election, effectively making QV useless.

I too think it's totally possible to rig such elections. E.g., if there's something group A wants, but you don't, you add something group A is totally against, so all their votes will go to the latter issue, and the status quo is kept as far as group A is concerned. Meanwhile, their votes are lost for other issues.

I really like the idea of this assuming it’s some kind of vote credit rather than money, and the vote credits are distributed equally per person. However, it doesn’t take into account that the number of things to vote on might not be fixed (or even finite). As more things to vote on are added, do people get more votes? How are they distributed? This would create a whole new variable to gerrymander.

This is the voting mechanism used in the game "Civilization VI" (Gathering Storm expansion), if you are interested in checking it out

Odd that they didn't mention Arrow's impossibility theorem:

https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem

https://plato.stanford.edu/entries/arrows-theorem

From the Quadratic voting Wikipedia page:

Quadratic voting is a variant of cumulative voting in the class of cardinal voting.

From the Arrow's impossibility theorem Wikipedia page:

Cardinal voting electoral systems are not covered by the theorem, as they convey more information than rank orders.

You want Gibbard's. It is an extension for cardinal systems.

[0] https://en.wikipedia.org/wiki/Gibbard%27s_theorem

Arrow's theorem is an interesting result on its own, but its practical applicability is kind of undermined by the fact that the dictatorship criterion is actually pretty rarely interesting (and is almost totally irrelevant to a ballot).

You do realise that the dictatorship criterion simply replicates the vote of one particular voter no matter what? [1]

In most realistic implementations this is likely either the first or the last voter. Surely we can agree that those wouldn't really be desirable?

[1]: See here for a somewhat easy to follow proof: https://www.math.ucla.edu/~tao/arrow.pdf

The dictatorship criterion is slightly more wide-reaching than that specific construction which makes it sound silly (though, honestly, not really tremendously unfair). Your link gives a decent enough definition:

> (No dictators) If a single voter prefers X to Y, but all other voters disagree, then the voting system should override the wishes of that single voter and rank Y higher than X.

The problem is that that criterion combined with the other conditions becomes equivalent to there being no 1-man quorums. As the rest of the proof shows the negation of this implies that there is a dictator, who completely determines the result for all votes.

I guess in a ballot system it might be pretty tricky to figure out who this person is, but in the end it just boils down to the order in which the votes are put into the sorting system.

No while sortition has it's advantages it goes against most people's intuition of what a fair voting system is. And technically arrow's definition of voting systems is deterministic, although you could always shuffle the votes beforehand.

Quadratic Election Law (great article) https://www.law.uchicago.edu/news/quadratic-election-law

I wonder how it would work on popular TV shows like American Idol. Maybe it is not in the interest of the broadcaster that the voters get less frustrated/angry with the outcome?

Nice to see this here, I spent the last weekend reading about quadratic voting/funding. The core idea is that in order to decide how much "endorsement" each project amongst many receives, you take the square root of how much each person gave to that project, sum that, then square it to decide how much of a matching contribution to be given.

It has a couple interesting properties that make it appealing for the funding of "public goods" (such as software) via grant matching mechanisms. The main ones:

- Projects with distinct supporter bases will receive more funding if they join forces as a single project with more supporters

- Projects with few supporters that give a lot of money/endorsement will receive very little boost from this

- You can also implement the possibility of "negative votes/funding" that allow people to "short" the projects that they consider a net negative

Over the past year a grant matching mechanism using quadratic funding has been trialed in a platform called Gitcoin, which supports crowdfunding Ethereum development projects: https://gitcoin.co/blog/everything-you-need-to-know-about-gi...

A post by Vitalik Buterin describing quadratic funding is here: https://vitalik.ca/general/2019/12/07/quadratic.html

Vitalik also wrote about the last 3 rounds of this funding on Gitcoin, they’ve been making tweaks and the results are extremely promising:

https://vitalik.ca/general/2020/04/30/round5.html https://vitalik.ca/general/2020/01/28/round4.html https://vitalik.ca/general/2019/10/24/gitcoin.html

The idea of quadratic funding came from quadratic voting, which was discussed in the 2018 book Radical Markets: https://vitalik.ca/general/2018/04/20/radical_markets.html

In september 2018 Vitalik together with one of the book authors and another person put out a preprint describing their ideas for quadratic funding, which is very interestingly written: https://arxiv.org/pdf/1809.06421.pdf

The broader field under which this fits is called "mechanism design", which means inverse game theory: instead of specifying the rules and seeing what the outcome is, you decide which outcome you want and try to design a game that leads to it...a very enticing idea.

https://en.m.wikipedia.org/wiki/Mechanism_design

If you like this, you'll probably be interested in STAR[0]. It has a really high voter satisfaction efficiency[1]. Pretty much it is the best if you want to account for strategic voting[2] (Condorcet methods don't handle these as well, but do have a higher VSE when it isn't accounted for, but we're talking pretty close anyways).

So why Cardinal systems? They are a lot easier than ranked systems. You like two people equally? You hate two people equally? No worries, just give them the same number. You basically have all the advantages in this case (I'll mention that Gibbard's[3] is an extension of Arrow's and it applies here). But why we would want this system is because it makes for the best of both worlds between the "we need parties" and "fuck parties" groups.

Let's take an example: Pick your favorite outside candidate: Bernie, Tulsi, Warren, Yang. If the general election was using STAR it wouldn't matter who the Dems pushed. You could still vote for these candidates and it wouldn't help you're candidate win. So I'd imagine a HN ballot could look something like this

Biden: 5

Gabbard: 7

Sanders: 10

Trump: 3

Warren: 9

Yang: 8

If Bernie, Tulsi, Warren, and Yang did not get enough votes to win, it would still be like the same election where we are choosing Biden v Trump, even though Biden wasn't your first choice. This means you can vote honestly (i.e. which candidate is closest to your opinion and not which candidate you think can win). It entirely removes the "electibility" question.

Why cardinal over ranked? One simple answer is that when cardinal breaks down it turns into approval voting. Approval voting is "I like this candidate" vs "I dislike this candidate". It is essentially the way we pick where to eat with friends. Everyone says "I don't know". So you start listing off places and once enough people say "sure", you pick that. It doesn't get you the best place to eat, but no one is really unhappy either. What STAR does is basically give you the options: "Hate it", "no", "ehhh", "I guess", "fine", "yes", "hell fucking yeah" (that'd be STAR06).

STAR is simple to understand, leads to high voter satisfaction, removes the electibility issue, let's parties exist without parties dominating (i.e. other parties can actually compete), easy to pick a winner, and more qualities we like in voting systems (if you're trying to make a fair system where people get representatives that represent their ideals). Of course, this does not fix the issues of money in politics, people lying, and all that.

This is just one component, but I think an essential component that will have huge effects on any democratically elected system and I think it is something that we really should fight for. It is also easy to sell the idea because everyone wants a more fair voting system.

[0] https://en.wikipedia.org/wiki/STAR_voting

[1]https://electionscience.github.io/vse-sim/VSE/

[2] https://en.wikipedia.org/wiki/Tactical_voting

[3] https://en.wikipedia.org/wiki/Gibbard%27s_theorem

What's the appeal over straight approval voting, which can be explained and justified in about three sentences, and almost self-evidently produces good-enough results?

There's more finesse in STAR. Because you are better able to specify __how much you approve__ this leads to higher voter satisfaction.

Is there any hard evidence for this? I'm sure there would be higher voter satisfaction among the types of folks that study alternative election systems and don't mind reading about every candidate on their ballot, but more convoluted systems generally lead to lower voter satisfaction because they're required to do more work/studying up front to maximize their voting power, and the results are more difficult to interpret.

Most voters walk into a polling place with 1 or 2 people they like, 1 or 2 people they don't like, and a bunch of people they don't care about, which is perfectly fine, and it should be taken into account with any proposed voting system.

What do you mean hard evidence? In all the sims (which you can find many more and much more detailed ones than what I listed, STAR's website has many itself[0]) it yields better satisfaction than approval. This should be obvious that it is.

> the results are more difficult to interpret.

Are you concerned about it being complicated? I'm sorry, but I just don't buy this argument. These types of scales are in questionnaires everywhere. I don't buy that people are so stupid that they can't just score a candidate. Even if they just ranked them it wouldn't have a large effect on the outcome. In fact, this can fix accidents with ranked choice where people accidentally rank candidates the same rank.

And if a significant amount of people are that dumb, well it still works out. Leaving an entry blank counts as a score of 0. You can score only a single candidate if you want, that's fine.

> but more convoluted systems generally lead to lower voter satisfaction because they're required to do more work/studying up front to maximize their voting power

You aren't required to do anything. And honestly, a lot of people do look into multiple candidates. Hell, the entire primaries are essentially people doing background research on candidates. But if they don't, sure, that's just called dishonest voting, which STAR handles better than ranked.

I honestly don't understand this type of criticism. It hinges on the idea that the average voter is dumber than a rock.

> Most voters walk into a polling place with 1 or 2 people they like, 1 or 2 people they don't like, and a bunch of people they don't care about, which is perfectly fine, and it should be taken into account with any proposed voting system.

You do realize that STAR accounts for this, right? You don't have to vote for everyone. If you just liked Biden you could just give him any number greater than 0 and your vote would be for him. At WORST STAR is identical approval.

[0] https://www.starvoting.us/

>> Using this anonymous ballot system provides identity protection from vote buying or trading since these exchanges cannot be verified by the buyer or trader.

I'm really split on that one. I'm not sure that anonymity does much to curb vote buying. I think it allows vote buying to fly under the radar. If we know how a politician votes we can then compare that to fundraising and lobbying records. With anonymous voting we are blind.

A modern lobbyist doesn't care about verifying individual votes. They lobby multiple people, entire parties, to shift trends. If they fail on an issue that only means the people they were lobbying don't have control of their party. The lobbyists move to other people for the next round. Eventually they work out where to send their money and start winning regardless. At least with non-anonymous voting outsiders have some hope of tracking what is going on.

The author is talking about anonymous votes for citizens. Not representatives.

Lobbying is very different from vote buying. Vote buying is saying to someone, "I'll buy your vote for $X". If votes are anonymous, then there's no way to verify that you actually got what you paid for.

Presumably there are reliable votes on either side that are well known : subtract those from the result and you may have a fair idea whther your puppet obeyed his master. It might not be easy to confidently disobey.

Votes by people in elections are what’s being contemplated as being bought, not votes by a much smaller group of representatives on specific legislation.

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