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Quadratic voting: A mathematical method that could offer a fairer way to vote
- oenetan 5y agohttps://archive.md/LnUQa https://archive.md/LnUQa
- deleted 5y ago[deleted]
- bedobi 5y agoAustralians 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.
- Ar-Curunir 5y agoThere’s no need for fatalism, especially when you admit you haven’t analyzed the protocol’s failure modes.
- Turing_Machine 5y ago> 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_theorem https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore... That said, some systems are clearly worse than others.
- ClayShentrup 5y agoArrow'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 https://www.rangevoting.org/ArrowThm
- bedobi 5y ago> 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 https://en.wikipedia.org/wiki/Condorcet_paradox (and any number of other ones that may or may not even have names)
- gpm 5y agoArrows 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?
- ClayShentrup 5y agoQuadratic voting is an extremely irrational idea. https://www.rangevoting.org/MonetizedRV https://www.rangevoting.org/MonetizedRV
- DennisP 5y agoRange 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.
- Turing_Machine 5y agoATW, 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.
- deleted 5y ago[deleted]
- notriddle 5y agoAustralia’s system (IRV) doesn’t necessarily elect the Condorcet winner, either, and it hasn’t led to mass revolts.
- bedobi 5y agoWell, 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.
- paulpauper 5y agoputting science in political science.
- Nursie 5y agoAs 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.
- bedobi 5y agoIt 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)
- jackvalentine 5y ago"Stop voting for the wrong people!" is your problem?
- bedobi 5y agoYes! 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.
- wolverine876 5y ago> 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?
- bedobi 5y agothe 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-voting 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
- mynameismon 5y agoCorrect link: https://www.economist.com/interactives/2021/12/18/quadratic-voting https://www.economist.com/interactives/2021/12/18/quadratic-...
- ssivark 5y agoIMHO, 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 https://en.wikipedia.org/wiki/Law_of_large_numbers
- timdaub 5y agoI'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 https://github.com/snapshot-labs/snapshot/issues/951
- im3w1l 5y agoA 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.
- deleted 5y ago[deleted]
- bidder33 5y agothis is where Minimum Anti-Collusion Infrastructure https://appliedzkp.github.io/maci/ 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.
- another_poster 5y ago> 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?
- bedobi 5y ago> 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
- dane-pgp 5y agoDo 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.
- bedobi 5y agoYeah, 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)
- xalava 5y agoThis 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.
- dodobirdlord 5y ago> 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.
- seph-reed 5y agoIf 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 https://www.youtube.com/watch?v=Ya1dNNzkQTE
- jude- 5y agoWhy settle for quadratic? Why not cubic? Or why not n^1.2? What's so special about quadratic that makes it the best candidate?
- ghancock 5y agoIt 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).
- bo1024 5y agoThere 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!
- nickvincent 5y agoThe 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://www.radicalxchange.org/concepts/quadratic-voting/, https://en.wikipedia.org/wiki/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 https://www.aeaweb.org/articles?id=10.1257/pandp.20181002 (appendix: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2790624 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.
- tgv 5y ago> 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?"
- biglost 5y agoWhat 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?????
- bigmattystyles 5y agoBecause 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.
- brightstep 5y agoBecause 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.
- dane-pgp 5y ago> 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.
- brightstep 5y agoNo, 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.
- noahtallen 5y ago
- chiefalchemist 5y ago> 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.
- Ar-Curunir 5y agoMany 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
- scythe 5y agoScore 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.
- cycomanic 5y agoThe 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.
- lil_dispaches 5y agoUn-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.
- nickvincent 5y agoWorth 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 https://en.wikipedia.org/wiki/Quadratic_voting#Applications), but users include Colorado's House of Reps and several civic platforms in Taiwan.
- azophy_2 5y agoIn 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 https://puaspoll.com/?ref=hn-qv
- mitchbob 5y agoArchived: https://archive.ph/YZpjj https://archive.ph/YZpjj
- assbuttbuttass 5y agoAlternative 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.
- bedobi 5y agoEconomists are universally in favor of things like carbon pricing, healthcare for all etc etc, don't be so quick to judge
- HamburgerEmoji 5y agoIf you amend your statement to "some economists are in favor of ..." then it becomes trivially true but not very useful. As is, it's obviously untrue. Does anyone care whether what they say is true or even has the appearance of reasonableness? Number of times I saw "you're posting too fast" while trying to submit this comment: 7.
- deleted 5y ago[deleted]
- Green_man 5y agoI 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.
- xrd 5y agoThis is very useful in understanding the different options. https://ncase.me/ballot/ https://ncase.me/ballot/
- nmca 5y agoIt 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?
- wolfram74 5y agoI 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.
- algo646464 5y agoAlso, 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.
- kwhitefoot 5y ago> bribing voters is a thing Is it though?
- divan 5y agoYes, 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.
- divan 5y agoWe 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.
- oli5679 5y agoThe 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.
- im3w1l 5y agoSo 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?
- motohagiography 5y agoIt'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.
- tablespoon 5y ago> 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.
- oneoff786 5y agoRanked 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
- tablespoon 5y ago> 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."
- oneoff786 5y agoYou 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.
- Zigurd 5y agoHoly hell. Now we can vote on whether "quadratic voting" or "defund the police" is the worst branding for a worthy idea.