8 ms·

The user experience problems of quadratic voting

144 points by timdaub 5y ago

timdaub 5y ago
Hi, OP here. I'm grateful for getting this exposure. Thank you! 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_user_experience_problems_of_quadratic_voting/ https://www.reddit.com/r/programming/comments/tptbzb/the_use... <3
praestigiare 5y ago
This is fairly interesting, but I do have to note that counting the desire to not have pollution as the externality is... interesting.
dwighttk 5y ago
Yes. Every scheme I’ve seen to “improve” first past the post brings in all sorts of problems that the big brain political pundits are blind to (willfully or not).
- dane-pgp 5y ago
  Do you really think that countries which use FPTP for elections have a better political culture and public satisfaction than countries which use more proportional systems? It's not like electoral reform is some wild untested idea that we don't have any data about, globally.
celdon25 5y ago
Builds MVP-quality product Announces that the world isn't ready for the idea as a whole
- timdaub 5y ago
  Hey, despite your comment sounding mean, I want to meaningfully respond: 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.
  - onionisafruit 5y ago
    That was a weird criticism. In my mind this gives more credibility to both your article and your endeavors in quadratic voting. The article has more credibility because it isn’t from somebody who has a bias against quadratic voting, and your quadratic voting efforts have more credibility because people see you are willing to see and address flaws in the system.
- dane-pgp 5y ago
  Do you think it's never possible to determine the future success of a product by attempting to build an MVP? 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.
onionisafruit 5y ago
I generally agree with the premise of the article and don’t think quadratic voting is a good option for a democratic government — though it might make sense in other situations. 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.
- timdaub 5y ago
  You're right. After publishing, someone on Reddit told me that fractional votes are technically OK. If you look closely for it, I mention it in a footnote that I added after publishing.
  - iainmerrick 5y ago
    If you’re willing to edit the post, I suggest just removing that whole section, or at least boiling it down to a couple of sentences (here’s a thing that went wrong, here’s the fix). It seems like a rather shallow observation that just detracts from the deeper ones that follow.
    - timdaub 5y ago
      I had considered doing that. 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_user_experience_problems_of_quadratic_voting/i2e519e/ https://www.reddit.com/r/radicalxchange/comments/tprsgi/the_...
baoyu 5y ago
Here’s a quadratic voting demo that looks nice and provides more intuition: https://www.economist.com/interactive/2021/12/18/quadratic-voting https://www.economist.com/interactive/2021/12/18/quadratic-v...
- timdaub 5y ago
  thanks for sharing, I love the UI!
  - jdwyah 5y ago
    That UI really is good. 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 http://blog.forcerank.it/counting-votes-is-hard I'm going to have to think about adding quadratic as an option though.
    - dllthomas 5y ago
      For the example given, it seems like the majority criterion is actually not desirable. 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.
- amelius 5y ago
  Why do the questions never include my purchasing power, given my current financial situation? 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.
  - k__ 5y ago
captainmuon 5y ago
I don't understand how quadatic voting can deal with collusion. Say I want to give 4 credits to A, and a friend wants to give 4 credits to B. So each of us gives 2 votes to their preference. But if we join together, we each give 2 credits to each option, that is sqrt(2) votes. So each option gets 2*sqrt(2) ~= 2.8 votes instead. So we are strongly incentived to found a party and to pool our votes. I'm not sure this is what people intended. 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?
- ekelsen 5y ago
  Collusion is prevented in the same way that vote buying is prevented now -- you can't verify how other people have voted. This means that you could tell your friend you'll vote for B, but actually still vote for A and A will get more votes. Since you can't verify that collusion has worked, the best strategy is to not do it.
  - samatman 5y ago
    I wouldn't be so quick to dismiss here. 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.
    - ekelsen 5y ago
      Let's say we agree to cooperate because it's win-win. Then I go into the voting booth, do I have any incentive _at all_ to not vote for my preferences as opposed to yours? No. Why would I not defect and gain more votes for my preferred causes?
      - breuleux 5y ago
ajot 5y ago
What I would change in the Strikedao voting app (for what I can see from the videos): show people how much will next vote cost them. So, if you haven't voted for option A, your first vote costs 1. After voting for the first time, option A's cost grows to 3 to cast your second vote, then to 5 to cast your third vote, and so on. Showing an ascending odd-numbered cost for voting would be more intuitive than thinking about square roots and whatnot.
iainmerrick 5y ago
I've followed a few links that explain the mechanism of quadratic voting, but still haven't seen a simple explanation of why it might be a good idea. What makes quadratic voting better than just converting credits directly into votes -- one credit, one vote? ("Cumulative voting")
- timdaub 5y ago
  The most-comprehensive argument that motivates its existence, I've found in Glen Weyl and Eric Posner's book "Radical Markets."
  - iainmerrick 5y ago
    Is there a good summary anywhere besides just reading the book? 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 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.
aimor 5y ago
What a bizarre voting system, it values diversity of vote credits which incentives people to organize their voting strategies. Multiple people with overlapping concerns want to coordinate their credit spending. People with extra credits and no desirable issue to spend them on want to trade with others in similar situations. Seems like a great way to bias voting against smaller disorganized causes, unfairly suppressing minority representation in the vote counts.
- nopenopenopeno 5y ago
  Well put. This is the most important point. The ruling class is normally (and especially these days) far more organized than the working class. This is a voting system that will aggressively suppress the influence of working class voters.
mdavis6890 5y ago
There is a chapter in the excellent book "Why Flip a Coin" dedicated to exploring voting alternatives. The main point of the chapter is that given three intuitively obvious requirements (like adding a 3rd candidate should not change the relative order of the first two) - it can be mathematically proven that NO voting scheme will satisfy them. See https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...
- NathanielLovin 5y ago
  Arrow's impossibility theorem only applies to ordinal voting systems. Quadratic voting is a cardinal system. Cardinal voting still isn't perfect, but it does get around some of the problems with ordinal systems.
  - notahacker 5y ago
    This form of cardinal voting has a particularly egregious equivalent of the "additional candidate affects preference ordering" issue in ordinal voting systems though. Unlike the weird edge cases with preference ordering in ordinal votes, the effects of adding additional votes on reducing certain voting blocs' influence on other issues where ppeoplemust divide a budget across multiple issues often lead to intuitive (trivially simple, even) strategies to manipulate a particular outcome. 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.
  - contravariant 5y ago
    I'm not sure quadratic voting is the best cardinal voting system though. In particular it still fails to satisfy independence of irrelevant alternatives. So sure Arrow's impossibility may not apply, but the conclusion isn't actually different.
twic 5y ago
On the point of the results being hard to interpret, and sanity-check, i have a couple of thoughts. 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.
bentcorner 5y ago
On the face of it it seems weird that votes for one thing can be influenced by the existence of unrelated issues on the same ballot. 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).
malfist 5y ago
Quadratic voting seems like a very convoluted way to say: "The rich should have all the votes" 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.
- gs17 5y ago
  Quadratic voting does not require the credits to be purchasable with real money. Many implementations simply give every voter a fixed number of credits to spend with no way to gain more.
  - malfist 5y ago
    That's interesting, I did not get that from the article. It talked about voters who wanted less air pollution had to pay the economic costs of voters that didn't care about air pollution, but wanted lower electricity bills.
ComputerGuru 5y ago
This is susceptible to ballot poisoning: lobby to put something you had no intention of doing but your opposition feels very strongly about on the ballot and then watch them waste their credits “reaffirming” the status quo of the hot-button issue while educating “your” voters to prioritize the actual issue under contention. 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.
- shonenknifefan1 5y ago
  I had assumed when reading this that the voting credit budget would be allocated per question rather than across the entire ballot. However I don't think the article gave an example of a ballot with multiple questions. I'd be interested to learn which way this being implemented in practice for multi-question ballots.
  - thechao 5y ago
    I was confused by GP's post, as well! I have only seen quadratic voting used to decide amongst non-binary questions: positions with at least 3 (or more) possible outcomes. It seems weird to mix voting across a bunch of different issues.
    - ComputerGuru 5y ago
      Here’s a demo that reveals what I’m talking about: https://www.economist.com/interactive/2021/12/18/quadratic-voting https://www.economist.com/interactive/2021/12/18/quadratic-v... 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.
dane-pgp 5y ago
I wonder if there's been much research into modelling voting as an adversarial process in which different parties (and not necessarily the political parties) try to attack the various aspects of the process, including the stages before, during, and after the vote-casting and counting takes place. 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.

144 points by timdaub 5y ago

Hi, OP here. I'm grateful for getting this exposure. Thank you! 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_user_experience_problems_of_quadratic_voting/ https://www.reddit.com/r/programming/comments/tptbzb/the_use... <3

praestigiare 5y ago

This is fairly interesting, but I do have to note that counting the desire to not have pollution as the externality is... interesting.

dwighttk 5y ago

Yes. Every scheme I’ve seen to “improve” first past the post brings in all sorts of problems that the big brain political pundits are blind to (willfully or not).

dane-pgp 5y ago
Do you really think that countries which use FPTP for elections have a better political culture and public satisfaction than countries which use more proportional systems? It's not like electoral reform is some wild untested idea that we don't have any data about, globally.

celdon25 5y ago

Builds MVP-quality product Announces that the world isn't ready for the idea as a whole

timdaub 5y ago
Hey, despite your comment sounding mean, I want to meaningfully respond: 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.
- onionisafruit 5y ago
  That was a weird criticism. In my mind this gives more credibility to both your article and your endeavors in quadratic voting. The article has more credibility because it isn’t from somebody who has a bias against quadratic voting, and your quadratic voting efforts have more credibility because people see you are willing to see and address flaws in the system.
dane-pgp 5y ago
Do you think it's never possible to determine the future success of a product by attempting to build an MVP? 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.

onionisafruit 5y ago

I generally agree with the premise of the article and don’t think quadratic voting is a good option for a democratic government — though it might make sense in other situations. 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.

timdaub 5y ago
You're right. After publishing, someone on Reddit told me that fractional votes are technically OK. If you look closely for it, I mention it in a footnote that I added after publishing.
- iainmerrick 5y ago
  If you’re willing to edit the post, I suggest just removing that whole section, or at least boiling it down to a couple of sentences (here’s a thing that went wrong, here’s the fix). It seems like a rather shallow observation that just detracts from the deeper ones that follow.
  - timdaub 5y ago
    I had considered doing that. 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_user_experience_problems_of_quadratic_voting/i2e519e/ https://www.reddit.com/r/radicalxchange/comments/tprsgi/the_...

baoyu 5y ago

Here’s a quadratic voting demo that looks nice and provides more intuition: https://www.economist.com/interactive/2021/12/18/quadratic-voting https://www.economist.com/interactive/2021/12/18/quadratic-v...

timdaub 5y ago
thanks for sharing, I love the UI!
- jdwyah 5y ago
  That UI really is good. 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 http://blog.forcerank.it/counting-votes-is-hard I'm going to have to think about adding quadratic as an option though.
  - dllthomas 5y ago
    For the example given, it seems like the majority criterion is actually not desirable. 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.
amelius 5y ago
Why do the questions never include my purchasing power, given my current financial situation? 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.
- k__ 5y ago

captainmuon 5y ago

I don't understand how quadatic voting can deal with collusion. Say I want to give 4 credits to A, and a friend wants to give 4 credits to B. So each of us gives 2 votes to their preference. But if we join together, we each give 2 credits to each option, that is sqrt(2) votes. So each option gets 2*sqrt(2) ~= 2.8 votes instead. So we are strongly incentived to found a party and to pool our votes. I'm not sure this is what people intended. 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?

ekelsen 5y ago
Collusion is prevented in the same way that vote buying is prevented now -- you can't verify how other people have voted. This means that you could tell your friend you'll vote for B, but actually still vote for A and A will get more votes. Since you can't verify that collusion has worked, the best strategy is to not do it.
- samatman 5y ago
  I wouldn't be so quick to dismiss here. 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.
  - ekelsen 5y ago
    Let's say we agree to cooperate because it's win-win. Then I go into the voting booth, do I have any incentive _at all_ to not vote for my preferences as opposed to yours? No. Why would I not defect and gain more votes for my preferred causes?
    - breuleux 5y ago

ajot 5y ago

What I would change in the Strikedao voting app (for what I can see from the videos): show people how much will next vote cost them. So, if you haven't voted for option A, your first vote costs 1. After voting for the first time, option A's cost grows to 3 to cast your second vote, then to 5 to cast your third vote, and so on. Showing an ascending odd-numbered cost for voting would be more intuitive than thinking about square roots and whatnot.

iainmerrick 5y ago

I've followed a few links that explain the mechanism of quadratic voting, but still haven't seen a simple explanation of why it might be a good idea. What makes quadratic voting better than just converting credits directly into votes -- one credit, one vote? ("Cumulative voting")

timdaub 5y ago
The most-comprehensive argument that motivates its existence, I've found in Glen Weyl and Eric Posner's book "Radical Markets."
- iainmerrick 5y ago
  Is there a good summary anywhere besides just reading the book? 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 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.

aimor 5y ago

What a bizarre voting system, it values diversity of vote credits which incentives people to organize their voting strategies. Multiple people with overlapping concerns want to coordinate their credit spending. People with extra credits and no desirable issue to spend them on want to trade with others in similar situations. Seems like a great way to bias voting against smaller disorganized causes, unfairly suppressing minority representation in the vote counts.

nopenopenopeno 5y ago
Well put. This is the most important point. The ruling class is normally (and especially these days) far more organized than the working class. This is a voting system that will aggressively suppress the influence of working class voters.

mdavis6890 5y ago

There is a chapter in the excellent book "Why Flip a Coin" dedicated to exploring voting alternatives. The main point of the chapter is that given three intuitively obvious requirements (like adding a 3rd candidate should not change the relative order of the first two) - it can be mathematically proven that NO voting scheme will satisfy them. See https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...

NathanielLovin 5y ago
Arrow's impossibility theorem only applies to ordinal voting systems. Quadratic voting is a cardinal system. Cardinal voting still isn't perfect, but it does get around some of the problems with ordinal systems.
- notahacker 5y ago
  This form of cardinal voting has a particularly egregious equivalent of the "additional candidate affects preference ordering" issue in ordinal voting systems though. Unlike the weird edge cases with preference ordering in ordinal votes, the effects of adding additional votes on reducing certain voting blocs' influence on other issues where ppeoplemust divide a budget across multiple issues often lead to intuitive (trivially simple, even) strategies to manipulate a particular outcome. 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.
- contravariant 5y ago
  I'm not sure quadratic voting is the best cardinal voting system though. In particular it still fails to satisfy independence of irrelevant alternatives. So sure Arrow's impossibility may not apply, but the conclusion isn't actually different.

twic 5y ago

On the point of the results being hard to interpret, and sanity-check, i have a couple of thoughts. 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.

bentcorner 5y ago

On the face of it it seems weird that votes for one thing can be influenced by the existence of unrelated issues on the same ballot. 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).

malfist 5y ago

Quadratic voting seems like a very convoluted way to say: "The rich should have all the votes" 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.

gs17 5y ago
Quadratic voting does not require the credits to be purchasable with real money. Many implementations simply give every voter a fixed number of credits to spend with no way to gain more.
- malfist 5y ago
  That's interesting, I did not get that from the article. It talked about voters who wanted less air pollution had to pay the economic costs of voters that didn't care about air pollution, but wanted lower electricity bills.

ComputerGuru 5y ago

This is susceptible to ballot poisoning: lobby to put something you had no intention of doing but your opposition feels very strongly about on the ballot and then watch them waste their credits “reaffirming” the status quo of the hot-button issue while educating “your” voters to prioritize the actual issue under contention. 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.

shonenknifefan1 5y ago
I had assumed when reading this that the voting credit budget would be allocated per question rather than across the entire ballot. However I don't think the article gave an example of a ballot with multiple questions. I'd be interested to learn which way this being implemented in practice for multi-question ballots.
- thechao 5y ago
  I was confused by GP's post, as well! I have only seen quadratic voting used to decide amongst non-binary questions: positions with at least 3 (or more) possible outcomes. It seems weird to mix voting across a bunch of different issues.
  - ComputerGuru 5y ago
    Here’s a demo that reveals what I’m talking about: https://www.economist.com/interactive/2021/12/18/quadratic-voting https://www.economist.com/interactive/2021/12/18/quadratic-v... 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.

dane-pgp 5y ago

I wonder if there's been much research into modelling voting as an adversarial process in which different parties (and not necessarily the political parties) try to attack the various aspects of the process, including the stages before, during, and after the vote-casting and counting takes place. 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.