Quadratic voting: A mathematical method that could offer a fairer way to vote | Hacker News Reader

Quadratic voting: A mathematical method that could offer a fairer way to vote

economist.com

126 pointsnabla9164 comments

> The first vote for a candidate costs one credit. But casting two votes for a single candidate costs four credits (ie, two squared); casting three costs nine (three squared), and so on.

This is not as bad as I imagined from the title. A lot of alternative voting systems that people like (e.g. ranked choice) are too complicated, and I think it's important for legitimacy that a voting process be so simple that even stupid or uninterested people can understand the mechanism completely. In this proposal, a winner is still determined by simple counting, and the more complicated part is entirely exposed to individual voters.

Though with anything that makes voting for alternatives easier, I think something would have to be done to limit the explosion of candidates to a reasonably small number that a voter can realistically consider, like 5 or 10.

Ranked choice voting seems far easier to me. In quadratic the total number of votes you have depends on the distribution. Very hard for innumerate people to understand.

Ranked choice is just ranking your preferences. You don’t need to understand the underlying math

> In quadratic the total number of votes you have depends on the distribution. Very hard for innumerate people to understand.

But it's something they'll encounter and have to understand to fill out the vote paper (which I imagine would look something like a simple math worksheet).

> Ranked choice is just ranking your preferences. You don’t need to understand the underlying math

Not to vote, but the problem I have it is in the end, "the algorithm" spits out who wins, and that's going to be totally opaque to most people.

On the other hand, pretty much anyone can easily figure out "which number is biggest."

You can easily fill out a quadratic worksheet incorrectly though.

Ranked choice is just whoever gets the most points win. I don’t think that’s too difficult to follow personally.

Ranked choice is only confusing if you just handwave and show the final result.

Put the thing on TV showing each and every round, with boxes moving up the list and off the list, and it’ll be completely obvious how it works.

It’s befuddling that you think it’s actually better to put the complexity on the ballot for each individual voter to wrangle with in the complete privacy of a voting booth.

Approval voting always struck me as the best way forward, though I am certainly no elections expert.

Doesn't require ballot changes. Doesn't require anyone change their voting style or keep track of which is 1, 2, etc. Obvious simplicity where you vote for whoever would be acceptable to you.

Whoever is the most acceptable to the greatest number of people gets elected. Really good at weeding out extremists and favoring folks that can appeal to the biggest tent.

Ranked choice is not that simple, and the math doesn't mean what the words say because you don't have to rank your choices honestly.

Say you have one guy you want most, A, a second much less, B, and a third abhorrent, C.

You can rank the abhorrent guy above B in order to lower B's rank even more, with the assumption that most people aren't going to rank C high.

People in A and B camps can both try this strategy and C, who only a small minority actually wants as first choice ends up winning.

I don't think this criticism makes sense, you're literally already intended to rank your least desired candidates lowest.

What you are intended to do is not the same as what people do. Strategic voting happens, arrow's impossibility theorem says there is no one way that solves all the problems.

What's too complicated about ranked choice voting as implemented in Maine?

https://www.rstreet.org/wp-content/uploads/2021/09/Final-Sho...

Thank you!! My thoughts exactly but I've never been able to express it so well.

> A lot of alternative voting systems that people like (e.g. ranked choice) are too complicated

With the quadratic method, though, all the complexity of the voting system is on the ballot rather than in the tallying process. It's pretty common to see normal people on Facebook claim that 3^2 is 6 rather than 9.

I got really into the mathematics behind voting awhile back and discovered that it's been a topic of some rigorous study for over a thousand years. There exist mathematically "perfect" voting systems that are somewhat hard for the average person to understand [0].

As it turns out, the system that makes the "best" tradeoffs between ease of implementation, ease of auditing, political buy-in, and overall fairness is ranked choice voting.

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

Isn't the main result of voting theory that there precisely isn't any perfect voting system (satisfying basic common sense constraints)?

A more concern voting is at running the elections fairly. All these math are useless if the voters base are "less informed" and elections process susceptible to fraud. 2020 elections demonstrate it is not math the issue but the implementation. You can see in Myanmar for instance who got the votes and who got the power. Same thing with USA having the guy way more popular than Obama and SCOTUS scared to hear election fraud cases. Some EU side going with fractional representation always clogged up inefficiently. Look at Brits for example. We know the referendum for the Brexit isn't done with best representation of the people votes. But it gives a way to go forward and do something about it rather than like some countries that had the run off and keep revoting multiple times until a clear majority emerged.

Stupid or uninterested people should not be allowed to vote.

I always wanted a system where you have to answer 5 questions before being given your voting card. Something like what is the current president, is Germany a neighbor country, etc.

If you do not know these thighs you cannot make an informed choice.

I even wanted to make it harder. You first say who you want to vote for. Then you are asked a question about their position on things important for the country. If you are completely off you do not get your voting card because it means you do not know what your candidate wants to do in basic areas of life.

If you get it right you hear a voting card and you can vote for whoever you want.

In th elast sentence hear → get (autocorrect...). Sorry cannot edit anymore.

It always felt to me like this was vulnerable to collusion - if Alice and Bob team up and have disjoint interests they share votes. So in elections P and Q instead of Alice spending 100 points on P (and Bob zero, as he doesn't care) then Alice can spend 25 and Bob 25. In Q, visa versa. It's a huge advantage to do so, no?

I see this brought up, but I always wonder if that's more of a feature than a bug? Coming up with a systematic way of encouraging meeting with people that think and prioritize differently than yourself? Put that way it seems like a win.

Alternatively, yes, a voting system is a means for expressing individual preferences, but it only exists in the context of groups of people trying to resolve coordination problems. The "defect" you've described shows that it strongly favors groups of people that can coordinate, avoiding the double-defect outcome in prisoner's dilemmas. Sounds like it /should/ be rewarded to some degree.

Also, bribing voters is a thing. It would be far cheaper to pay 2X to buy X votes where each of the bribed voters keep half the money and buy a vote with other half.

> bribing voters is a thing

Is it though?

Yes, in post-soviet countries it's pretty common to bribe large number of people from elderly and poor population with food or alcohol. It's literally trucks with food or vodka and name of the party/politian that head to the semi-forgotten villages, where some decent amount of electorate lives. Needless to say those people had grown up in Soviet Union and have zero trust in elections or democracy, so they happy to vote for whoever bribes them more.

Post-Soviet countryman here!

In my country, elections are fair. If you ask people on the street -- they will say they believe in democracy. Which is reasonable since the concept of voting is easy to understand.

Offering free food for in exchange for votes is still a thing though, since voters know that everyone on the ballot is a corrupt sack of shit. They're going to end up equally fucked either way -- might as well pick up some free food along with it.

Depending on the location, oh yes it is. In the recent Serbian elections there were photos of "gift baskets" from a party if you voted for them ( of course they can't know for sure if the election is properly held, but afaik it isn't).

Yes, very much so. Probably not so much in the US and most western democracies, but yes.

At the very least tacitly. Voting blocs do exist.

One issue in the US is how certain communities organize to stack members in districts until they can affect elections, then bribe and extort politicians for concessions, to stop them from expanding into other districts, or to vote a certain way.

It's an incredible racket because it's also the system "working as intended".

It is when it scales well enough. Most voting system get around it by ensuring you need to bribe an impractical number of voters.

Not sure I understand.

Non colluding:

- Alice spends 100 on P

- Bob spends 100 on Q

Colluding

- Alice spends 75 on P and 25 on Q for Bob

- Bob spends 75 on P and 25 on Q

Like this?

I think what's confusing is credits vs votes. It's more expensive in credits for Alice to cast the first N votes than to cast the next N. However, for Bob those "next N" are his first N. So 2N votes costs fewer credits if Alice and Bob each cast N than if Alice casts 2N.

Also, Bob might end up with "leftover" credits he can't allocate to issues he cares about. So those credits might go unused in some sense.

Yes. In your first scenario P and Q get 10 votes each. In your second they get sqrt(75) + sqrt(25) = 13 point something.

One objective of voting systems is to prevent vote-selling. Usually by preventing a voter from bringing evidence of their vote out of the booth. There is no reason to presume a quadratic voting system should differ in this regard.

For Eve to maximize her impact she could pretend to collude with Bob on the issue that they both care about, but with opposing positions. Eve's false bargain would allow Bob to spend less on this issue than his interests would otherwise dictate. Eve wins by false collusion.

This dark pattern would become apparent to voters and thus unverifiable collusion would soon be distrusted amongst the electorate.

> One objective of voting systems is to prevent vote-selling.

Yes. Do we have a full list of requirements for voting systems?

It turns out that if you write down on the list of requirements that you would want from a voting system in order for it to be fair, the no deterministic voting system is fair. This is known as Arrow's theorem (https://en.m.wikipedia.org/wiki/Arrow%27s_impossibility_theo...).

Interestingly Arrow's theorem doesn't apply to randomized voting systems. In particular, the system of picking a random voter to decide the election satisfies (probabilistically) every standard notion of fairness.

I think that would covered under non-dictatorship but I see the appeal.

I don't have a list, but one that is especially important when thinking about digital voting systems:

  a voting system has to produce agreeable consent

Part of this agreeable consent is of course the goal to achieve a result that represents the intentions of those voting. But another part is that the way in which this result was achieved is transparent to all. You could then still be the sore loser, and pretend the vote was manipulated, when in fact it wasn't, but e.g. with paper ballots it would be very hard to insert fake votes or supress/manipulate real ones. As soon as digital machines enter the game this becomes very hard to proof to the layperson. And think about it this way: the person you have to proof it to might be unwilling to understand because they lost the election.

Points that come to my mind:

- anonymity (nobody should be able to find out how one individual voted)

- ability to produce agreeable consent (achieved through transparency of the process and observers from all parties involved)

- produces fair results

- values correctness over speed (better slow and correct than fast and incorrect)

- values traceability over speed (better slow and traceable than fast and untraceable)

- discourages vote selling (anonymity is one way to achieve this)

- availability (voting should be as easy as possible, otherwise hurdles will be used to control voting behaviour)

- transparent information (there should be transparent information on what the vote is about and what the choices mean)

I very much agree with your points, except for one point:

> As soon as digital machines enter the game this becomes very hard to proof to the layperson.

This is not hard to prove just to laypeople, it is hard to prove to anyone at all. I doubt for example Linus Torvalds could prove to himself beyond reasonable doubt that a digital voting system has produced the correct result.

Hah good point. Espiecially in practise. Because I could imagine a systems that are provably correct in principle, but when you start to imagine on which hardware, on which OS, with which network stack etc all of this would be running, then proving the whole stack of turtles down to the processor would take the lives of multiple CS-post graduates for one such machine alone. And even they would have to conclude something among the lines of "yeah we are reasonably sure it worked as intended, but there is not enough time to explain this to anybody, so you have to trust us".

I think you have the same problem with a system where votes are counted by hand.

Nope - you can personally go and check how votes are counted, verify the final tallies yourself etc. All parties that participated in the vote send one or a few people to all voting precincts, and each of them can carry on parallel votes, make sure votes and tallies are safe on the way to bigger centers etc.

Of course, it's not possible for literally every citizen to this themselves, but since citizens already have to trust the party they are voting for to some extent (otherwise, why care about the election?), this works out very well in practice, especially if you add a few citizens organizations and international organizations in the mix monitoring as well.

Electronic voting is orders of magnitude more complex, even in simple centralized schemes. In more decentralized schemes, it becomes completely, hopelessly intractable to ensure validity unless you chose to blindly trust hardware and base software (microcode, BIOS, disk firmware etc.). And the same argument about trust above doesn't apply here, as it's not your preferred party's representatives that have created the hardware etc.

This is why electronic voting is unconstitutional in some jurisdictions - Germany, at least.

> - discourages vote selling (anonymity is one way to achieve this)

Maybe more general: It should be infeasible to perform fraud. Ideally the infeasibility should scale exponentially with the size of the election.

Ah yeah I forgot. The (monetary, personal, logistical, time) cost of doing fraud has to be as high as possible.

This would be another point where digital solutions usually turn out far worse than traditional paper ballots. If you can hack one machine you potentially could manipulate many ballots. If you hack the manufacturer of the machine you potentially get many machines – and this could be done by a single person with the right information and skillset.

That makes a digital attack feasible for a nation-state-attacker, of which there are certainly some (and maybe more in the future).

Paper being slow, cumbersome, material-intesive is not a bug, it is a feature.

If they had disjoint interest in the issues, they would do the same without collusion.

Another example of this would be if there are three candidates X,Y,Z. Suppose Alice strongly prefers X and Bob strongly prefers Y. Rather than each of Alice and Bob allocating 100 points to their preferred candidate, they can each allocate 50 points to X and 50 points to Y. The net effect is that they have multiplied each of their voting power by sqrt(2).

I don't like any voting system that incentivizes group collusion. A much fairer system would be some form of random ballot: everyone gets to allocate some number of votes, and then a random vote gets picked to select the winner. This type of system is especially good for situations where there are many winners (eg the Congress), since it allows for even small parties (eg the Green party) to get proportionate representation.

clr.fund is a good demo of how this sort of thing can be used in online distributed communities to distribute funding across public goods and implements maci (minimal anti collusion infra) https://github.com/clrfund/monorepo

Score voting I think is one of the hardest kinds of voting to advocate (and quadratic voting is clearly score voting) because it flies in the face of the old maxim "one voter, one vote". While IRV/AV/Condorcet take pains to make sure that everything is counted "once" (be it ballots or yeas or pairwise preferences), score simply adds weights, drops the mic and leaves the stage. One must necessarily do a little extra work to move between the perspectives sometimes described as "majoritarian" and "utilitarian".

My experience with the poll was that I quickly read all of the questions to determine which ones I didn't care about very much, dropped a couple of points in those first, and then ended up putting eight votes on a carbon tax. I'm a little confused about applying this to a primary, because here we're looking at a set of independent binary questions, not a list of different responses to the same question.

The irony is that the US electoral system is anything but a "one person, one vote" system. A vote in California is very different to a vote in Utah for example.

Un-ironically, elections are all about money, and quadratic voting seems to be okay at letting populations allocate money.

So if we change the idea of "one person, one vote" to "one vote, one dollar", we not only rid ourselves of the problem of elections (sorting bad candidates) we effectively turn elections into budget resolutions.

Quadratic voting to pick candidates seems like the wrong idea. Using it to pick budget spend in place of elected budget directors is what it was invented to do.

IMHO, the concept might be more intuitively named "square-root voting" :-)

It's very interesting to note that the vote count scales/renormalizes with the population in analogy with the law of large numbers [1]. I wonder whether that would imply pathologies in cases with strongly correlated preferences, as opposed to randomly generated weak/uncorrelated preferences.

[1]: https://en.wikipedia.org/wiki/Law_of_large_numbers

I'd call it square root voting if there isn't any assumptiom about how often a single identity is eligible to vote.

E.g. for most of the crypto space, they do square root voting but claim to be quadratic. Exemplary issue here: https://github.com/snapshot-labs/snapshot/issues/951

This is very useful in understanding the different options.

https://ncase.me/ballot/

That was a very cool interactive article!

That's focused on the problems of the first-past-the-post system, isn't it?

Why settle for quadratic? Why not cubic? Or why not n^1.2? What's so special about quadratic that makes it the best candidate?

It incentivizes the welfare-maximizing result. I don’t have a short “intuitive” explanation of why handy but the math is covered in section 8.3 of Public Choice III (should be easy to get in college libraries, pdf copies can be found online if needed).

There are a few mathematical reasons. I forget the details, but I remember that a key point is to consider marginal cost: the derivative of a quadratic is linear. I think the Central Limit Theorem is also relevant, as someone else here pointed out. Anyway, if you really want to know, you can read the papers!

The core argument for x^2 is basically just that it's the only function with linear derivative, so for rational voters who calculate marginal benefit of additional votes purchased at cost x^2 (in terms of likelihood of changing the outcome of the "election"), you get a welfare maximizing outcome.

There's some assumptions underlying the theoretical result, but there's also a lot active experimentation in the real world, a few links: https://www.radicalxchange.org/concepts/quadratic-voting/, https://en.wikipedia.org/wiki/Quadratic_voting

Here's what I believe is the key paper on the topic https://www.aeaweb.org/articles?id=10.1257/pandp.20181002 (appendix: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2790624)

Lalley, Steven P., and E. Glen Weyl. 2018. "Quadratic Voting: How Mechanism Design Can Radicalize Democracy." AEA Papers and Proceedings, 108: 33-37.

> rational voters

That's a rather ridiculous assumption, isn't it? I still remember the 3rd year psychology university student, who asked: "What's a square root?"

This is a good objection. The system might be so complicated that people don't understand how to correctly express their preferences.

Definitely a challenge for many mechanism design approaches to intervening in the world. As I understand, the only really solution is to experiment in the real world, see what holds and see what doesn't, and tweak accordingly (e.g. test out different interfaces that communicate how the mechanism works!)

Rationality expectation is good if irrationality of others does not harm rational voter.

In this case, a well-organized and mathematically adept voter can and will harm less rational ones, thus skewing the balance instead of restoring it.

No. Irrational voter harms himself. Rational voter just gets what he wanted.

That's too close to calling them lesser beings for my comfort. They harm themselves, so who cares? Greed is good!

Actually it's a good point and IMO for a population that may have a certain distribution of voting credits e.g. shareholders of a stock, adjusting the exponent can make sense to more fairly distribute power.

If anyone doesn't know what liquid democracy is yet, I recommend looking into it. It's not a perfect idea, but it's worth having in the toolbelt.

"Liquid Democracy in 60 Seconds"

https://www.youtube.com/watch?v=Ya1dNNzkQTE

...but how do you implement this? How do you know people are not coerced?

Assumably, with complex well thought-out systems that aren't yet fully tested or verified, but -- seemingly -- should be possible.

Worth emphasizing that, as the article states, there's a lot of ongoing experimentation with quadratic voting. Wikipedia has a good overview (https://en.wikipedia.org/wiki/Quadratic_voting#Applications), but users include Colorado's House of Reps and several civic platforms in Taiwan.

We tried quadratic voting for internal organizational stuff couple of years ago (using dApp on Ethereum). It was okay and refreshing, but in that case it didn't work well, because of the number of options (there were like 20 or 30 options). By the time you reach 15-th option, you depleted all your points and you have to go back and recalibrate your votes just to return back to 15th, and then discover 17th option that's even more important and so on. So I guess it requires by nature either good prior knowledge of all options or just having few options on the table to work well.

> It allows you to give more support to your preferred outcome.

Probably unpopular to say here but...distracting nonsense.

The preferred outcome?

Let's start with an end to thumb on the scale gerrymandering.

Then how compaigns are financed, and post-term compensation.

Congress is effectively allowed to practice insider trading.

A Fourth Estate that lacks substance to the point of undermining democracy.

The Media's shameless commitment to a two party system. A commitment so polarized that divisiveness is a natural and expected byproduct.

That two party system, effectively a cartel, corners the mrket and intentionally limits choice. They get their preferred outcome. Voters get the illusion of impact.

Finally, let's not forget the excessive amount of tax dollars that finances The MIC.

Many of those problems stem from our adoption of a shitty voting system that entrenches the existing parties. A different voting system could allow for making choices that arent possible in the existing winner-takes-all model

Alternative voting schemes sound good, because we all can recognize that our democracy is broken. But the underlying problem isn't the voting scheme, it's the lobbying and corporate money in politics. Changing out the voting system while leaving Capitalism in place would just have the corporations buying different politicians. Not surprising that the economist doesn't mention this angle.

Economists are universally in favor of things like carbon pricing, healthcare for all etc etc, don't be so quick to judge

I think your comment means that the "will of the people" isn't why democracy is broken, but it's the extra-democratic processes involved in making legislation that is the problem. Do you have an example of some policy that is generally popular, but not passed because of corporate lobbying?

I think solutions to immigration/health care/climate change are generally contentious and don't have a popular consensus. Something smaller like a "simpler" tax code seems more convincing, where a small industry of tax preparation software or something lobbies to keep income taxes complicated. At the same time, many deductions are quite popular, and these are necessarily complications to the tax code. I'm just not entirely convinced that lobbying is hurting us in any meaningful way, though a stronger example or argumentation might change my mind.

In fact health care is an example where the majority favors a government (or primarily government) paid solution [1], but it does seem unlikely to ever be implemented.

Climate change is another issue which actually has majority support in the US, but action is very little [2,3].

In fact I believe the perception of it being contentious issues is largely due to a relatively small minority which has a disproportionate influence on policy (and likely corporate lobbying will have influence as well). This is actually on e of the issues that alternative voting schemes want to address, diminishing the influence of a minority which has very strong/extreme views.

[1] https://www.pewresearch.org/fact-tank/2020/09/29/increasing-... [2] https://www.pewresearch.org/science/2020/06/23/two-thirds-of... [3] https://www.pewresearch.org/science/2019/11/25/u-s-public-vi...

When I look at these health care charts, I don't see a real consensus, even when oversimplifying health care to 4 broad categories (36 20 30 6 percent respectively). I don't know who the respective corporate interests would be for each of the categories, though I'd guess that there's big corporations that favor 2 or 3 of these potential solutions, and only a third (at most) of Americans that support one of them. A third of the populace doesn't make a popular mandate, and it certainly isn't enough for a senate majority (especially for democrats).

The climate change one might be more convincing, but I actually think we've seen some real progress on this. Alternative energy is getting cheaper, there's tax incentives for installing solar panels or EV chargers in many areas, and tax incentives for buying EVs. There's certainly more we can do, and the polls were phrased to suggest that the general public thinks so too. But if the admittedly significant oil and gas lobby is trying to hold this issue back, I'm not sure how successful they've been. Finally, this isn't an actual bill or anything. Every "green" bill I've seen is opposed by conservatives based on their constituency, whether they're a red conservative from texas, or a blue conservative from west virginia. I don't know if Joe Manchin takes donations from coal companies, but he'd unquestionably support coal either way.

> Do you have an example of some policy that is generally popular, but not passed because of corporate lobbying?

Here is an example I saw just recently: https://en.wikipedia.org/wiki/Asbestos#United_States

Really disgusting to read about it.

I'd probably support an asbestos ban for most construction (though I'm not a chemical or civil engineer, so I could have some blind spots here), and this probably comes across as pedantic, but I didn't see anything that indicated that there's broad public support for banning asbestos. Again, that's not saying that we shouldn't do it, just that I'm not sure it's a great example of the "will of the people" being overruled by a corporate interest.

I'd say it's pretty broad when so many countries banned it completely.

Well, the American public is an outlier when compared to many other democracies in other ways as well, in general I'd guess they'd view environmental/health regulations less favorably than most other developed nations. "Just don't lick the walls lol" is something I've heard regarding lead paint here in America, which sounds insane to me, but it's the insanity of democracy, not anything else.

What it tells me is that the successful corporate lobbying against it is an outlier, meaning that in US it is a problem. No one in their right mind (unless those corrupt who profit from it) would be against such ban.

Lack of understanding the issue could be an exploited factor too. See also articles that point out how asbestos companies knew about problems for decades and hid the facts.

right but corporate lobbying isn't the only way in which America is unique. Concerns about concealed research results could be very true, but that's an entirely different question than corporate lobbying. My position isn't that companies don't do anything wrong or aren't trying to influence policy, I'm just skeptical how successful political donations are at subverting democracy.

In my opinion they are way too influential. Take a look at corporate sponsored laws that try to ban ISP competition and community / municipal broadband. Correlation between presence of such laws and corporate backing is very clear.

Sortition (random selection of politicians from the pool) is the answer. https://www.ted.com/talks/brett_hennig_what_if_we_replaced_p...

I may have heard of this once on a reddit philosophy post or something, I think this really isn't an example of a popular idea that's squashed by corporate interests. That's not to say it's not a good one (I have no idea), but I don't know if we'd pass this (or if there's even any corporate opposition).

> Do you have an example of some policy that is generally popular, but not passed because of corporate lobbying?

https://www.propublica.org/article/inside-turbotax-20-year-f...

Yeah, I brought up this idea in my parent comment, but the part I'm unsure of is whether or not there's broad public support for making taxes simpler. The devil is in the details here. If making taxes simpler included removing the mortgage interest deduction or maybe the child tax credit, I could imagine the proposal being extremely unpopular. I think some republicans have included simpler taxes on their list of campaign promises, but there hasn't been a swelling consensus around the issue. Finally, complicated tax deductions are a way for the govt to incentivize certain behavior or have some fine tuned controls over revenue, so there's a reasonable justification to keep some complications. tldr I agree that turbotax (and probably others) have lobbied to keep taxes complicated, but unless there's evidence that the broad public really cares about this, I'm unsure that those donations really did anything. It's easy to vote in your donors' interests when the vote doesn't matter (or if you were already voting that way!)

Glen Weyl (the economist who has done a lot of work on quadratic voting, mentioned in the article) has also written and talked extensively about Harberger taxes and quadratic funding; the former is a fairly deep change to how property rights work, and the latter is a way of democratically allocating funds to public projects. I would definitely encourage reading up on both of those!

(outside the United States point of view)

In Democracies with a reasonable proportional representation (PR) improving how to choose from N options, or how to allocate M resources, is secondary to the problem of how to select and parametrize N and M.

In PR democracies mechanism design should focus more on how to improve participation and deliberation before final voting.

Deliberation is a process of selecting and articulating options and figuring out problems. Mechanism design for deliberation can emphasize cooperation, dialogue, creativity and reason, as opposed to the use of power that is voting for given choices.

> the underlying problem isn't the voting scheme, it's the lobbying and corporate money in politics

There are certainly many problems, but voting schemes appear to be a very powerful lever. In particular:

- Representative democracy incentivises parties rather than independents, since like-minded candidates can pool and target their campaign resources

- Plurality/first-past-the-post voting incentivises a two-party duopoly, since voting for a third-party is a 'wasted vote' (they won't win outright, hence they'll get nothing)

- A two-party system incentivises 'least-bad' voting (i.e. voting for someone we don't actually want, to stop the other candidate who we want even less)

- A two-party system gives no choice on issues which benefit both parties (i.e. maintaining the status quo; e.g. lobbying, pork, military budgets, etc.); whilst polarising along irrelevant issues (e.g. 'culture wars')

There's no agreed-upon 'ideal' voting method; but most alternatives are regarded as better than first-past-the-post. Any system which doesn't 'waste' votes for third-parties (e.g. preferences, scores, fall-backs, proportions, etc.) would allow voters to indicate what they'd like (rather than what they'd dislike least); that gives a chance to candidates who don't benefit from the status quo; and that brings important topics like lobbying back into the political arena.

It's an interesting protocol, but given the purpose is to confer legitimacy on the winner, verifiable proofs of the integrity of the system are likely more important than nuance in preferences. Imo, quadratic and other complications (even ranked ballots) are designed to game the counting under the pretext of giving more data about preferences (which we have better ways to get), without providing a higher degree of physical integrity, or legitimacy.

Voting itself is a ritual whose integrity is maintained by showing up to cast ballots are kind of proof of work, and physical presence proves your stake in the outcome, and not the cryptographic kind. This might be fine for talent shows, party leaderships, and corporate board machinations, but voting for the peaceful transfer of power is a ritual alterantive to not-peaceful transfers. Quadratic seems fun and interesting, but probably not a good idea to run in prod.

A cooperating group could have very outsized influence in this system right? They could decide first in private which way to vote and make sure they have no cancellation and that they all use the same amount of points, this maximizes power per point.

this is where Minimum Anti-Collusion Infrastructure https://appliedzkp.github.io/maci/ becomes important, ideally someone should be able to prove they have voted without revealing any information of how they voted, which makes collusion difficult. This is achieved in person with voting booths and making it illegal to photograph your ballot. zero knowledge proofs + sybil resistance mechanisms like brightid or proof of humanity might make it possible online too.

In case anyone interested, I've made a polling website inspired by this thread, intended for everyday uses. Please let me know what you guys think! ;)

https://puaspoll.com/?ref=hn-qv

So could you make troll proposals for the purpose of getting other people to waste their votes?

"Death penalty for jaywalking" how strongly against this are you?

The interesting thing about this is that in machine learning.

- squared error loss --> conditional mean

- absolute error loss --> conditional median

And this seems to be the same thing with voting.

Holy hell. Now we can vote on whether "quadratic voting" or "defund the police" is the worst branding for a worthy idea.

https://archive.md/LnUQa

This method relies on the idea of a cost, most likely monetary, proportional to the choice. This is obviously incompatible with core principles of modern democracies.

This article reasoning compares the Brexit and Trump votes, and speculates that they might have had a different result by changing their voting mechanism, almost exchanging them. Rather than a good argument, this is exactly the reason why voting mechanisms should be dealt with carefully.

More generally, the idea of voting mechanisms using preferences is a few centuries old. There is an abondant literature analyzing its potential merits but also failures.

> This method relies on the idea of a cost, most likely monetary, proportional to the choice. This is obviously incompatible with core principles of modern democracies.

A standard non-monetary proposal is to have all issues voted on separately, and allow voters who choose not to vote on a particular issue to bank their votes for the next election. This is obviously incompatible with voting by representatives in a representative democracy, but isn’t incompatible with direct democracy, which is how many issues are decided in local elections.

> An individual who felt strongly about a single issue could hoard their credits until its moment arrives, then blow all of their saved credits on it. That would allow passionate minorities occasionally to outvote indifferent majorities.

In other words, hoarders and impulsive spenders would decide policy?

Ultimately political systems are judged by the quality of their policies. Why would passionate minorities produce better policy than median voters?

> Ultimately political systems are judged by the quality of their policies

thanks for putting into words exactly what I thought without really being able to explain it

"fair" voting systems feel good but from what I've seen they seem to kind of end up amplifying extremism and bad policy

Do you have some examples where there is a clear causative link between the "fair" voting system and the amplified extremism / bad policy? Alternatively, can you point to examples where an "unfair" voting system has prevented such bad outcomes that were otherwise unavoidable?

It's actually very hard to predict what sorts of government would emerge, or constitutional crises would occur, under a counterfactual voting system, and countries can fail for any number of reasons, regardless of their voting system. Ideally we'd need a dataset covering dozens of countries and multiple decades, with some sort of measure of "extremism" and "bad policy", which a political scientist might be reluctant to try quantifying.

Yeah, I posted one elsewhere in the thread

> It also makes it easier for people to vote for trash parties like One Nation. In other countries people would think twice before voting for small, extremist parties like that lest they waste their vote if the party doesn't make it past the threshold for getting a seat. (this is just one of the many problems I see with the Australian system)

But has the ability for people to vote for One Nation specifically lead to bad government policies? Under a less fair voting system, might a minority of extremists have been able to take over one of the major parties (or at least might one of the major parties have adopted extremist policies in order to secure the vote of the extremists)?

I think it would be very naive to imagine that making the voting system less representative would make people just give up on their extremism and peacefully accept the policies of one of the major parties. If anything, I would guess that showing how little support an extremist party has would disabuse its voters from believing they represent some sort of oppressed majority.

So you're arguing for removing the ability of those whose opinions you dislike to have their opinions represented, in other words.

I love in the UK, which uses FPTP, and personally I don't consider countries which uses this system to be democratic countries at all. I'm de facto disenfranchised.

> you're arguing for removing the ability of those whose opinions you dislike to have their opinions represented

as I said elsewhere, I think the cost for voting for minority extremist parties and policies should be higher, not lower, yes, and frankly, I don't have a problem with disenfranchising extremism, no.

> I don't consider countries which uses FPTP to be democratic countries at all. I'm de facto disenfranchised

I think that's great. More "fair" voting systems to me are bad because it seems to me all they do is just to cater to people's extremism.

On a side note, probably the fundamental reason why we disagree is because you and people like you seem to think democracy should mean the will of the people and the voting system should serve to cater to and express the will of the people as closely as possible, including the ugly stuff,

while I and people like me think in liberal democracies there are a lot of things which are not and should not be subject to the will of the people, no matter how popular, and the voting system should not cater to peoples extremisms, no matter how popular.

Your side will make a point out of that, saying you're more democratic. Maybe that's true! But I don't want to live in a society where eg fundamental human rights are subject to the whims of popular opinion. (which is often ugly, misinformed etc etc)

It's worth remembering that a particular flaw of IRV which is not shared by all multiple selection voting systems is that it can incentivize putting a low-popularity party ahead of your more popular preference, since your vote will very likely transfer. This is called "non-monotonicity" and has been documented e.g. here:

https://www.abc.net.au/news/2011-05-04/an-example-of-non-mon...

But the Australian system is still much better than the first-choice-only method used in most electorates. You don't have the situation (discussed in the article) where an extreme faction can usurp a major party by being unified in the primaries. By shuttling "One Nation" voters to their own party, you give them a little representation, but you keep a lid on it. Meanwhile, you give a voice to new perspectives that might be ignored for a long time in a two-party system.

It's really the other way around, our current systems (to different degrees) give extreme positions disproportionate influence. Just look at the republican party in the US, which has moved considerably to the extreme right over the last 20 years due to the influence of extreme single issue minorities (tea party/fundamentalist christian).

The point is that generally hoarders and impulsive spenders can’t have a big impact in QV. Your influence scales as the sqrt of the number of votes you cast. It’s much more effective to have many “small” voters than a few big voters.

I've long thought that every economic policy should be required to include an objective measure of its success, and that rather than explicitly voting, citizens could wager "vote credits" on the success or failure of that policy. This would produce a market-implied success rate, and whether or not the policy passed would depend on whether there was a positive expectation outcome (i.e., whether the risk-adjusted rewards of success outweighed the risk-adjusted cost of failure).

Those who exceeded a certain amount of credits would receive a stipend, which adds financial incentive to participate.

The hard part of this is ensuring that the objective measure of success is a fair one. There'd be tremendous incentive to pervert the metrics. You'd need a social class of incorruptible and cloistered "oracles" or something.

Or just cut out the middleman and go straight to AI overlords :)

What you're describing is basically Futarchy[0]. Its catchphrase is "vote on values, bet on beliefs".

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

Thanks. Figured it wasn't an original idea but never had a word for it before.

Oh this is great!

America is now The handmaids tale, with more solar panels

Is it just me, or was this idea of a lifetime number of votes rather than tying them to a given election kinda slipped in at the end? And kind of a big deal?

Two outcomes that I find pretty undesirable:

1) A small group of super intense extremists save up their votes their whole life and use them to jam through their wackiest idea.

2) A group tries that trick, fails, and now we have a population of dejected, permanently disenfranchised hardcore extremists.

I had a similar reaction about the way the article was written. I was confused about the benefits of this over a much simpler rating system, until they started talking about tying credits to external resources of some kind. Holding credits over seems to have similar issues.

What I dont get it is, why in our presidential elections, candidates promise but are not liable for not doing their promise, we vote trusting them!!!! Who in his right mind would trust a polítician promise?????

Because they're not elected tyrants. They may want to do things but, for instance, in the US, an elected president may not get the legislature (s)he wants.

Because elections are for a different purpose than we are taught. We are told to vote for candidates who most closely match our preferences but see them turn from their promises, time after time, toward a bipartisan project of war, environmental destruction, enrichment of corporations, etc. What our votes really do is provide legitimacy to this system. Your choice is to vote for the bipartisan consensus or to abstain.

> What our votes really do is provide legitimacy to this system.

Are you really hoping that you can convince enough people to abstain that eventually the two major parties will have an epiphany and feel so ashamed that they'll fix the voting system to allow more competition and better representation?

I think you really need to consider who you are up against here, which is people who are prepared to fight dirty for unchecked and undeserved power, who will treat your abstention as being consent for their misrule.

No, I'm not advocating abstention from voting. Maybe I was a little too harsh. Sometimes voting can make a big difference, but more often than not it doesn't. That doesn't mean we shouldn't engage.

How do you make someone liable? For example, democrats can correctly claim that they can’t get votes to pass most of their legislation right now, which means Biden can’t achieve his goals. Did Biden lie? I mean perhaps some, but a lot of the big policy pieces would get passed if democrats had a bigger majority in the senate. Also, our system isn’t very competitive, so how do you get rid of someone who lied?

- No term limits in Congress, so people have a huge edge as incumbents

- It’s very hard to primary someone and defeat the current person in your own party.

- There are only two parties which have an impact, which means you end up voting for “one of two.” And when neither are great options, neither will turn out to be great options.

Essentially, the number of times you can make a choice is very limited. (Basically to when someone resigns or steps down or runs against the opposite party.) and then when you have a choice, you don’t have very many compelling alternatives.

Australians love to hype their voting system, not knowing or caring to know it too is fraught with problems, just like this proposed one probably is.

That's not to say the US or UK or what have you systems are better or worse. All voting systems kind of suck and suffer from mathematical and political paradoxes.

> All voting systems kind of suck and suffer from mathematical and political paradoxes.

Yes. Arrow's Impossibility Theorem.

https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...

That said, some systems are clearly worse than others.

> Arrow's impossibility theorem

Ah, that's it, thanks, I was looking for it but forgot what it was called. There's also https://en.wikipedia.org/wiki/Condorcet_paradox (and any number of other ones that may or may not even have names)

Arrows impossibility theorem only proves things about voting systems where the method of voting is simply ranking the candidates in an order, so it doesn't actually apply to this quadratic voting system.

Does anyone happen to know if an analogous theorem does apply to this quadratic voting system?

Range voting and approval voting aren't subject to anything similar, according to William Poundstone's book Gaming the Vote. If that's correct then I'd think quadratic voting is the same.

ATW, score voting (which some call range voting) and approval voting both suffer from the defect that a choice that is favored by an absolute majority (which would thus win in a "normal" election) can wind up losing.

That wouldn't have to happen very often to lead to a lot of very angry voters.

Australia’s system (IRV) doesn’t necessarily elect the Condorcet winner, either, and it hasn’t led to mass revolts.

Well, you have to be aware of the potential quirks in the system, and Australians are not, they uncritically know their system is infallible and the best.

How can approval voting suffer from this defect? Is the idea here that we factor in people who don’t vote for things they actually favor because they’re hoping to avoid tipping the result away from something they favor even more? Or do you mean an election could end up selecting a result that is favored by the majority even though there is a different result that is more favored by a smaller majority?

https://en.wikipedia.org/wiki/Approval_voting#Effect_on_elec...

This isn't a defect, it's a benefit. It's mathematically proven that an electorate can prefer X even if a majority of its members prefer Y.

Commonly proposed "majoritarian" methods using rankings can, for instance, elect X even though Y is preferred to X by a huge majority of voters and Y has twice as many first-place votes as X. http://scorevoting.net/CoreSuppPocket

And there's not even a clear mathematical definition of "majority winner". https://web.archive.org/web/20190219005032/https://sites.goo...

The goal of voting methods is to produce the most satisfying results possible (highest expected utility). And score/approval voting are excellent at that, and also radically simpler than ranked methods.

https://electionscience.org/library/approval-voting-versus-i...

https://rpubs.com/Jameson-Quinn/VSE5key

https://medium.com/election-science/star-voting-is-simpler-t...

etc.

In practice, approval voting and score voting will almost always elect the Condorcet winner. Possible even more often than real Condorcet methods.

http://www.rangevoting.org/AppCW

Try the online demo they made at

https://www.economist.com/interactives/2021/12/18/quadratic-...

it's cool but tbh I would rather have infinite points to spend, at which point you might as well have binary endorse / oppose votes (maybe with an added option abstain)

point being that I don't think the intensity of my endorsement of policies to combat climate change should cost anything for my equally intense endorsement of paying reparations for colonialism - I consider both incredibly important and essential policies.

Quadratic voting is an extremely irrational idea.

https://www.rangevoting.org/MonetizedRV

putting science in political science.

Arrow's theorem only really applies to social welfare functions not voting methods. You use a utilitarian social welfare function when you calculate Bayesian regret for a voting method.

https://www.rangevoting.org/ArrowThm

As a Brit that now lives in Australia, from what I can tell the voting is just better here. With preferential voting you (hopefully) end up with more of a consensus for the winner, rather than purely a representative of the largest minority as with FPTP.

It also makes it easier for people to vote for trash parties like One Nation. In other countries people would think twice before voting for small, extremist parties like that lest they waste their vote if the party doesn't make it past the threshold for getting a seat. (this is just one of the many problems I see with the Australian system)

"Stop voting for the wrong people!" is your problem?

Yes! I don't think liberal democracies should tolerate parties and policies that dismantle them. In many European countries people like Pauline Hanson would have been put jail (where she belongs) for hate speech (and probably any number of other things) a long time ago.

The irony being, that FPTP has resulted in Trump which is arguably not much better than One Nation.

Trump has far more to do with the electoral college and other quirks of the US system than FPTP

Don't we want voters to be able to just honestly write that they like these small extremist parties? Are you suggesting that we want all the voters to vote for one of the top two parties, out of a fear of wasting their vote?[0] Besides, those small parties are obviously eliminated almost immediately, so the only thing those votes are worth is a bit of money from the Australian Electoral Commission.[1]

[0]: https://en.wikipedia.org/wiki/Duverger's_law

[1]: https://en.wikipedia.org/wiki/Australian_Electoral_Commissio...

I think the cost for voting for minority extremist parties and policies should be higher, not lower, yes.

That's government by the majority, not the whole. Democracy is “a system of government by the whole population or all the eligible members of a state” (OED; emphasis added).

Just because you think the cost of voting for small extremist parties should be high doesn't mean you're in favor of absolutist majority rule?

+ liberal democracies have (at least in theory) unalienable basic rights that can't be taken away, even by majority. Eg just because a 90+% majority votes to revoke citizenship from all muslims that doesn't mean that it will go through.

The effect of eg. FPTP is to effectively disenfranchise large portions of the population. A country with a voting system like that makes a mockery of the very term democracy.

As for these "inalienable" right, I'm not aware of any system without a mechanism for altering their constitutional laws.

To your specific example, the UK just had a government representing a minority of voters vote through a law that allows them to strip citizenship from millions as they please.

Who determines what is extremist and what is small? It’s not like the dominant parties dropped from the sky with their existing “bigness”. They too started out as small parties.

> Who determines what is extremist

we're not talking about some ambiguous grey zone stuff here

* proposed a drastic reduction in immigration with particular reference to immigrants from Asia.

* stated that African immigrants were bringing diseases into Australia and were of "no benefit to this country whatsoever"

* called for a ban on Muslim immigration to Australia

* announced policies including installing CCTV cameras in all existing mosques

* stated "all terrorist attacks in this country have been by Muslims"

it's safe to call the above extremist and xenophobic

But you're not solving that problem by pretending they have less support than they do.

A huge danger of systems that downplay the support for extremist parties is that they create an incentive for infiltrating the bigger parties instead.

In a single-winner election, why would you think that? The "minority extremist parties" are going to lose anyway, so why not try to let people vote more honestly, so that they don't need to strategize? For example, I don't want people who naively vote Green to end up wasting their vote just because they don't know how the voting system works.

Personally I think that makes it a better system.

I may not agree with the politics of One Nation (in fact I'm almost certain I don't, without even going to read what they are) but having a system where I can place a vote for what I really want and then put an acceptable compromise candidate as second choice seems to me a much better way of allowing newer parties and newer politics in than the more or less institutionalised stagnation of something like the US system.

From what I can tell the Australian system rarely lets such smaller parties gain very much anyway.

For all that we have instant-runoff preferential voting, we still have single-member districts for our House of Representatives (and 150 members of said House). We also have compulsory voting and (at the federal level, and in most states), a full-preferential ballot.

When you have 150 single-member districts you're probably going to get two major parties regardless of whether you have FPTP or IRV or even Approval voting. What compulsory voting and preferencing add on top of that is both of Australia's majors have to win the centre, rather than energising their base per the US.

What our system does allow for is for smaller parties in our Senate. It's generally elected 6 people at a time, allowing for e.g. 1 Green, 2 Labor, 2 Liberal-National and 1 One Nation (this is a very plausible result for Queensland next year).

So what does the US system allow then? Well, every system has to let its steam out somewhere. The US has its primaries, which often has a level of access and openness that greatly surpasses any Australian preselection (generally still getting out of the smoke-filled-room era).

The primaries still only really allow people who have climbed the ranks in an existing party to get a shot, AFAICT. But I'm no expert.

I like the idea that the main parties have to capture the centre, and I really like that I can vote for something a bit out there, without the fear that my vote is effectively a vote for my least favourite big incumbent. The "You must vote Labour or the Tories win!" thing has always rubbed me up the wrong way, as someone who isn't especially fond of either of those options.

> That's not to say the US or UK or what have you systems are better or worse. All voting systems kind of suck and suffer from mathematical and political paradoxes.

The argument that everything has >0 flaws, therefore everything is the same, is a bit bizarre to find on HN. Is every solution in every category the same?

> just like this proposed one probably is

Even when we don't know what it is?

the point is, Australians in particular are very very quick to hype their system

and they have a fairly good understanding of the alleged benefits of their system

and they get told this over and over throughout their schooling and by the electoral commission

but not once have I ever seen any Australian ask themselves if the alleged benefits of their systems are really true in the first place, and even if they are, what the inescapable downsides of their system are

it doesn't even occur to them, the question doesn't even make sense to them

as for this quadratic one,

try the online demo they made at

https://www.economist.com/interactives/2021/12/18/quadratic-...

it's cool but tbh I would rather have infinite points to spend, at which point you might as well have binary endorse / oppose votes (maybe with an added option abstain)

Correct link: https://www.economist.com/interactives/2021/12/18/quadratic-...

There’s no need for fatalism, especially when you admit you haven’t analyzed the protocol’s failure modes.

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