The user experience problems of quadratic voting
timdaub.github.io
timdaub.github.io
Imagine a ballot with one contentious question A. Opposition Y adds a question B they know will flop but is guaranteed to disproportionately attract all the attention of the other party to the ballot. Party X voters waste their credits on the red herring question B (which has greater than 50% support in the overall population anyway and would never fail them) while opposition Y advises its voters to spend the credits on the actual question A they care about.
As a completely contrived example, the real question is a controversial “add a carbon tax” that could go either way and one party either adds “ban all abortions in all cases for everyone” or “ban all firearms for all people” to the ballot to misdirect. Either of these is guaranteed to disproportionately attract all the attention of one of the parties more than the other despite neither having a remote chance of passing. Because of the phrasing and the topic chosen, even if you don’t educate your voters you can rely on the fact that their voters simply care a lot more about the topic than yours do.
I'd be interested to learn which way this being implemented in practice for multi-question ballots.
Also, mathematically a question with > 2 choices isn’t ultimately that different from a ballot with multiple binary questions. You can imagine my scenario with credits allocated to a single non-binary question as well, just substitute “poisonous question” with “poisonous option/individual” (though it is harder for me to demonstrate with non-partisan or bi-partisan examples).
Edit: Some plausible examples for distributing credits across issues include multiple open seats and top x contenders get them (so n binary yes/no “do you want x to have a seat?” questions), a ballot to determine which candidate you’re most likely to align with based off their yes/no stance on multiple questions (which is a problem if anyone’s stance is boiled down to a simple yes/no but that’s unfortunately the state of politics today with no shades of grey), etc.
The large number of votes (100) and issues (10) seems to reduce the issue around not being able to "spend" all your votes as well. When I've only got 25 it feels particularly wasteful to not be able to spend 7. But with 100 and 10 choices I really had a lot more degrees of freedom.
I run a small ranking app and have previously landed on Schulze method for calculating the rankings. http://blog.forcerank.it/counting-votes-is-hard I'm going to have to think about adding quadratic as an option though.
Picking a talk topic that everyone will like a lot is a better outcome than picking another slightly preferred by most but completely uninteresting to the rest.
This is what 50% of the population cares about, yet their votes are stolen away by focusing on things like immigration and terrorism.
The mismatch in these questions is why lower social classes often vote for populist right wing parties, instead of in their own best interest.
The problem isn't how much votes cost, it's how many questions have to be answered at once.
And it reveals another (probably unsolvable?) UX problem with quadratic voting: it takes so much longer to allocate votes by comparison to a thumbs-up / thumbs-down vote.
For myself, I did a pass through the issues, supporting or opposing each issue with a single vote. Then, I did another pass to add additional votes to each issue in proportion to how much I cared, while carefully paying attention to how many issues were left to be voted on, and my remaining "budget" of votes. Then, I did a final series of passes to rebalance everything, trying to make it as reflective of my positions as possible, while using as many votes as I could (so as not to leave any crumbs of democracy on the table, so to speak).
The whole thing was actually really complex, and not done in "linear time" like a traditional ballot. And it wasn't because I thought more about the issues, but purely because the rules of the system introduced so much more overhead.
Not saying I dislike the idea of quadratic voting, just that you can really feel the difference.
It also seems to punish caring strongly for a certain issue, whereas I wonder if that isn't maybe an indicator that you are informed about a topic, and thus your vote should count more rather than less?
Since you can't verify that collusion has worked, the best strategy is to not do it.
Collusion in 'linear' voting loses the voter their preference in exchange for some reward, double-dipping is a simple defection.
GP is talking about personal force multiplication through collaboration, it's win-win so you have a genuine prisoner's dilemma. Being unable to verify cooperation doesn't mean it won't happen in other ways.
I don't know that this is actually bad just that a simple comparison to linear votes doesn't hold up.
Unfortunately, some people do like lying, or at least they don't mind it as much, and if you create a system which rewards liars more than honest people, you shouldn't be surprised if the liars end up winning and you create more liars.
https://en.wikipedia.org/wiki/Superrationality#Prisoner's_di...
The quadratic maths tends towards making the gains from collusion very large, which means there is incentive not to defect even if detection is uncertain.
And bloc votes and ballots which aren't necessarily secret do represent some of the more plausible use cases for quadratic voting (corporate governance)
But a conversation like "I was thinking four points on A but I see why you're all in on B now, tell you what how about we go two for two on it" strikes me as a good outcome in a voting system. The fact that linear voting doesn't have an equivalent of it doesn't imply we should consider this 'collusion' rather than 'cooperation'.
[0] https://en.wikipedia.org/wiki/Vote_pairing#United_States_pre...
In the base scenario, Alice votes for A with 4 credits and Bob votes for B with 4 credits. A, B each gets 2 votes.
In the private deal scenario, Alice/Bob agree to each vote for A, B with 2 credits each. Then A, B each gets 2.818 votes.
Firstly, rather than just publishing the total number of votes, and vote credits, for each choice, publish the histogram of vote credits. 60 people allocated 1 credit, 40 people allocated 2 credits, 35 people allocated 3 credits, etc. That is sufficient to verify the total votes for that choice, and across all choices, to verify the total vote credits used, allowing sanity-checking. It can also be used to give some sort of visual indication of the structure of voting: imagine a bar comprising a fixed-width slice per vote, sorted in order of ascending credits per vote, coloured according to credits per vote. An option with uniform support will have a uniform colour, with the intensity of colour indicating the concentration of support; an option with some weak and some strong supporters will have a gradient of colour.
Secondly, rather than mapping credits to votes and just displaying votes, consider n^2 - n of the credits allocated by a voter to a choice 'wasted', and display a total of wasted credits as an additional part of the bar. The first part of the bar shows votes, and so which option wins, but the total bar shows credits allocated, and so some measure of total support.
However I don’t understand the point about not being able to use all credits because you have to spend them buying whole numbers of votes. Why not allow fractional votes? I realize there is probably a good reason, but I don’t see it immediately.
If you look closely for it, I mention it in a footnote that I added after publishing.
But I think it'd paint a false picture. In the half a year of developing the app, and me being mostly concerned with correctly implementing the voting algorithm and understanding the math - when reading Wikipedia and what is outlined in Weyl's book, it wasn't obvious that fractal votes can be used.
As a single tech freelancer working for a federally-funded exhibition hall, I wanted things to be correct. So I stuck to the script (aka the most credible sources accessible).
I've added the footnote in the article linking to a Reddit post where someone claims having talked to Weyl about fractal votes and that he positively reaffirmed it [1]. Anyone could comment that though.
But from a mathematical point of view, it isn't trivial (at least for me) whether fractal votes represent the same system as is currently laid as "quadratic voting".
Sure, if I end up completely understanding why fractal votes are mathematically equal to natural-numbered votes, I'll do as you suggested.
references:
- 1: https://www.reddit.com/r/radicalxchange/comments/tprsgi/the_...
I'm new to this but intuitively: The function is contiguous. Natural votes somehow behaving differently is what would be unexpected and need proof.
I wanna give a shout out to the commentators on /r/programming and that we had a meaningful discussion that may be relevant too: https://www.reddit.com/r/programming/comments/tptbzb/the_use... <3
See https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...
If you can add a proposition to the ballot paper which sufficiently threatens a particular group, they're forced to waste votes defending themselves against it, which means they have less influence on other issues they might also care about. As far as I can see the quadratic nature makes it worse, by making it more plausible a minority could actually lose a vote that threatens them if they only spent most of their credits defending themselves against it.
That's a bigger UX issue than non-sophisticated voters not really grasping the budgeting detail.
This is, I think, the least justified requirement, since humans do naturally reframe situations when extra information is given, which can cause them to change their mind about previous decisions.
To give a trivial example, suppose you were in a district which historically had a Democrat and a Republican candidate, and you always voted Democrat, but one year a far left independent candidate became popular and you feared they would attract most Democrat voters over to their camp. Given that scenario, it might make sense for you to vote for a moderate Republican instead.
In any case, I think that the significance of Arrow's impossibility theorem is generally over-estimated (and it spreads as a meme because people like to think that all voting systems are bad so there's no reason to change the terrible one they have).
For example, the theorem only applies to ordinal (ranked) voting systems, not cardinal (rated) ones, and only proves that the system cannot output "a community-wide (complete and transitive) ranking", so it is still possible to elect a small set of politicians who collectively embody the same preferences as the voters, and in direct proportion to them.
You may be interested to hear about the Gibbard–Satterthwaite theorem then. Any non-dictatorial system with more than two alternatives is subject to tactical voting. Whoops!
It does apply more broadly than Arrow's, but my understanding is that even though a tactic will exist for every voting system, that tactic may require perfect information or at least isn't guaranteed to be actually exploitable by any voters taking part.
If a tactic is so complicated and likely to backfire that no one ever attempts it (or the people that try it, on average, end up harming their cause) then I think that the threat of tactical voting is insignificant.
What I don't know, unfortunately, is which voting system is best in terms of ease of voting honestly and difficulty of voting tactically. Determining that may involve knowing things like how people respond to polling data, or to one party telling their followers to fill out their ballots in a certain way, which might be hard to model.
That's a great point, thank you. I should have tried to describe a more subtle effect where someone sees the policies of the far left candidate and it taints their view of the Democrats, who they now view with suspicion, fearing the Democrats might secretly support the same extreme policies. Alternatively, a Republican voter might see the Overton window shift and consider the Democrats a more centrist party, and so drop their support for the Republicans.
The problem is, these parties (and candidates) aren't spherical cows in a vacuum, and neither are voters. Voters have imperfect information and have to try to make predictions about which politicians are lying, and what direction the mood of the country is moving; so the addition of another party into an electoral contest can quite reasonably cause someone to change how they view the existing parties and even flip their support.
It makes more sense if you're making a selection among many people for one position, but if you have, say, 5 different issues on a ballot, you can influence the impact of those 5 by adding useless issues to the ballot. (e.g., if you are a pink legislator you can feign partisanship and add a bunch of low-importance purple issues to the ballot so that purple voters cannot easily oppose your pink issue).
For example, we've seen attacks on voter registration and availability of polling stations, and bizarre (but insidious) schemes like deceptively-named candidates and misinformation about when an election is held. We also have the problem of "fraudits" where various groups try to undermine the confidence in elections that have already taken place.
It seems like any attempt at electoral reform should take into account this adversarial context, and consider any proposed clever mathematical formula or any technology more complex than a pencil to be part of the epistemological attack surface that needs to be minimised as much as possible.
That doesn't mean that current systems are perfect, or that FUD is an unbeatable strategy for opposing reforms, but it does mean that it's not enough for a proposal to offer elections that are more convenient or that have better psephological properties.
What makes quadratic voting better than just converting credits directly into votes -- one credit, one vote? ("Cumulative voting")
I'm curious but skeptical. I would have thought that if there is a good and straightforward justification, it would be in the wikipedia page, but it's not. It simply says:
Quadratic voting is a variant of cumulative voting in the class of cardinal voting. It differs from cumulative voting by altering "the cost" and "the vote" relation from linear to quadratic.
Apart from that there's no comparison to cumulative voting, which seems a lot simpler and more robust against concerns like collusion and sybil attacks. The only other mention of "linear" is in a rather opaque paragraph marked "citation needed".
If it's purely a way to allow people to buy votes without having rich people completely corner the market, I guess it makes some sense, but it still seems rather wrongheaded. If you're going to give everybody the same number of virtual tokens, there are no rich people to begin with. If you insist on using an actual currency, there are other possible mechanisms like a universal basic income.
Edit to add: Aha, I've found a (the?) paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2343956
Rational agents maximize their utility by setting marginal cost equal to marginal benefit. This means that if John values being able to incrementally move the outcome in his favor twice as much as Sue values being able to incrementally move the outcome in her favor, John will pay twice as much at the margin as Sue does. For example, John buys 16 votes while Sue buys 8 votes. The exact number of votes that John and Sue buy depends on their estimates of how likely they will be pivotal voters, as explained below, so if John buys 16 votes for $256 (162 ), this does not mean that he values the project at $256. But it does mean that he values the project twice as much as Sue, who buys 8 votes.
This emphasis on marginal cost seems to ignore the fact that John and Sue will be working with finite budgets -- the overall real cost of the vote is important too! Unless I misunderstand, the implication is that if the cost were linear, John would buy an unbounded number of votes (as the marginal cost never goes up) which seems absurd.
Particularly in the cases where quadratic voting is actually being used in government, when e.g. lawmakers are given 100 tokens to split among different possibilities, I don't think any of the above analysis applies at all, and it's not clear that quadratic voting has any advantages over cumulative voting.
https://www.economist.com/interactive/2021/12/18/quadratic-v...
I don't think that quadratic voting is relevant for the case of "Many people need to answer a few shared questions" as it happens it elections. I believe it is for the case "one person needs to answer many questions" as it happens in polling.
Of course it can be used in elections as a sort of preference voting, but its effect is to punish extreme opinions (you might be extremely opposed to Statement A but might also want to keep some credits to express your milder opinion about B, C, and D.
(of course this also opens more venues for manipulating polling by adding duplicated similar questions...)
Unfortunately the linked article is paywalled.
The motivating example in the QV papers I've just skimmed is more about people voting on a sequence of yes-or-no questions, buying some number of votes and being compensated afterwards each time. That's totally different from this one-shot, multiple-questions, fixed-budget example.
references:
- 1: https://www.aeaweb.org/articles?id=10.1257/pandp.20181002
The use of QV in voting scenarios where you have 100 tokens to split among alternatives seems completely motiveless, beyond “QV is great because there’s a mathematical proof.” But a proof of what? Not a proof of anything relating to that voting scheme, as far as I can see.
(And by "any reason" I guess I mean "any reason besides lack of comfort with non-whole numbers").
From here it seems like the general principle of social cost still applies / doesn't have anything to do with the step-function nature of things.
In Weyl and Posner's book "Radical Markets" they motivate quadratic voting as outlined as a way of preference voting where a voter's desire intensity is represented in the vote.
Their argument is practically outlined in the pollution + city example I make in the original blog post and where, with the sloppy figure I have attached [1], they reason geometrically that "Nils" should "pay" for reducing the electricity plant's pollution. If you look closely at that figure (which is nicer in the book), you can see that the plane where the cost functions intersect is a triangle.
I can't fully reproduce the mathematical reasoning here, but how I understood it is that dependent on Nils's choice, the externality he imposes has quadratic cost given that the triangle's change is affected quadratically. In an isosceles triangle, where volume V is defined dependent on two same length sides, I can see that work out. But I've never worked through that.
More intuitively, an example, I'm just making up is if you're annoyingly snorting during a visit to the cinema.
If you're the only person snorting and you think that's OK, but nobody else can understand the dialogue - you're not only wasting your money but everybody else's. It's quadratic because of the opportunity cost of everybody wasting 2 hours but having all paid for the film. So both the cost of the cinema running the movie for two hours and everybody paying but not understanding makes your snorting square the cost. Does that make sense? Please correct me if I'm wrong.
So essentially, if Nils is picky with anti-pollution, his pickiness costs the town's society quadratically - which is why he should pay the quadratic cost of his pickiness during governance.
references:
- 1: https://timdaub.github.io/assets/images/cost-of-externality....
I've seen in proposed for voting in the real world where you buy the credits with real money in some growing cost-per-credit, as an attempt to control for rich people being able to buy so much more voting power right now through lobbiests. It has a certain cryptonanarchist or radical libertarian appeal, but the engineer in me points out there doesn't appear to be a path from here to there, since among other things you have to figure out how to fully ban any other form of lobbying by the rich, which is simply not practical. Not even if I include "have a violent" revolution as an option, because no plausible violent revolution would adopt this system at the end of it either. I dunno if it's fair to say people are really hardcoded to "one person, one vote", but for whatever reason it is something that you can get people to generally agree as fair, possibly just because everyone can easily see that the instant you visibly deviate from that there's no longer in point in voting because you will never get to the voting phase; the voting body will never again do anything but argue about how to vote.
While I think it's still hopelessly impossible, at least in this context there's some meat to discuss to the proposal, rather than just Yet Another Exotic Voting Method for small groups.
(I have to add visibly there because as previous sentences show in that paragraph, I'm well aware we don't have a "one person, one vote" system in practice. In theory it's a Republic, after all, not a Democracy, and in practice, anyone who buys lobbiests has vastly more voting power than you do. But it looks like we do, so it's stable enough for now. It can even be the case that everyone pretty much realizes it, but it's stable enough. But make it visibly obvious that's not what's happening and the fireworks will fly.)
In fact, if a society could work out how to do that, they should do that first, and then they might find that all these "let rich people have more voting power" proposals would coincidentally disappear.
> it's a Republic, after all, not a Democracy
Please don't perpetuate that awful meme. A country can be both, and the US is only "not a democracy" under the most idiosyncratic definition of "democracy".
https://mises.org/wire/stop-saying-were-republic-not-democra...
https://www.bloomberg.com/opinion/articles/2019-04-11/is-u-s...
https://thebaffler.com/latest/were-a-republic-not-a-democrac...
Point!
As for "democracy", I'm not particularly convinced the US is a democracy under any definition at this point, honestly, so I can't find it in myself to particularly care which flavor of democracy we most aren't.
The fact that you have a finite budget, so you can't just arbitrarily keep buying votes until some threshold is met, seems like a big flaw in the argument.
If voting incurs a cost, and the more of that cost you can pay, the greater your vote, then all that does is disenfranchise people who cannot afford to vote.
This is just poll taxes 2.0, now with extra feudalism.
It's not like electoral reform is some wild untested idea that we don't have any data about, globally.
Announces that the world isn't ready for the idea as a whole
Where do you set the personal boundry for evaluating an experiment as a failure or success?
E.g. in the case of social networks and what consequences Facebook brought us. When is the right time for Mark Zuckerberg to announce conclusive failure or success for his actions?
Pessimists say he should have admitted it years ago.
He himself doesn't even accept the premise of the argument. Rather he sees it as his personal calling or responsibility to build (source: see Lex Friedman podcast).
Who's right here?
Anyways, it isn't my intention to negatively associate digital or quadratic voting. Rather the post is an attempt at adding to a currently inconclusive picture through critique.
You could maybe try to argue that the implementation hadn't reached the minimum level yet, and therefore wasn't an MVP and it was too early to draw conclusions, but it sounds like you're just assuming that.