10 ms·

Quadratic Payments: A Primer

194 points by gabcoh 7y ago

jawns 7y ago
This post describes a system of voting/payments where you can make multiple votes, depending on how strongly you value your preferred outcome, but each vote costs more than the vote before. Identity management and collusion are big issues with these systems, as the essay points out. For programmers, one way to think about this is that each voter has a state, n, that tracks how many of times they've voted. And each vote is more expensive than the last. Eventually you either run out of money or you lack the desire to spend more money on another vote. But if you can create a new voter account as easily as you can create a new Gmail account, then once n gets sufficiently high, you just switch to a new account to lower the price of your vote. Or if a really rich voter with a high n-value pays someone with a low-n value to make a vote on their behalf, the system collapses as well. Enforcing strict identity management (e.g. requiring valid state-issued ID cards) and implementing secret voting can help address these problems, but my guess is that if there is a strong enough incentive, people will try their hardest and come up with novel ways to thwart these safeguards.
- wyldfire 7y ago
  > But if you can create a new voter account as easily as you can create a new Gmail account This is generally described as a Sybil attack [1]. > you just switch to a new account to lower the price of your vote. ... Or if a really rich voter with a high n-value pays someone with a low-n value to make a vote on their behalf AFAICT the article discusses these problems: > Perhaps the biggest challenge to consider with this concept of quadratic payments is the practical implementation issue of identity and bribery/collusion. ... Fortunately, there are technological means that can help, combining together zero-knowledge proofs, encryption and other cryptographic technologies to achieve the precise desired set of privacy and verifiability properties. [1] https://en.wikipedia.org/wiki/Sybil_attack https://en.wikipedia.org/wiki/Sybil_attack
  - joosters 7y ago
    Fortunately, there are technological means that can help, combining together zero-knowledge proofs, encryption and other cryptographic technologies to achieve the precise desired set of privacy and verifiability properties. This is placing too much trust in what is incomprehensible mathematics for 99.999% of the population. Even for those who understand it, they won't have any convincing way of being assured that 1) the maths is perfect and there are no flaws and 2) the voting technology in use is perfectly implemented. On the other hand, the 'nineteenth century technology' of secret ballots is both obvious and simple. It's a shame that people like Vitalik are so dismissive of it.
    - kortex 7y ago
      I'm a developer with a strong math background, very security-minded, with experience using cryptocurrencies, pgp/gpg, privacy tools, etc. I still would not be able to evaluate any sort of crypto program and certify its integrity, nor find any (save for the most eggregious) flaws. Even then, I have brought up questions in code reviews of "this seems to be flawed" only to learn "technically yes, but we have to do such gymnastics because of constraints xyz". I, too, was big on the "blockchain is gonna make e-voting possible! Ra ra ra!" hype train for a while, but eventually wisened up to my own naivety. I think paper is great because it's both proof of work (it had to be printed/written/modified) and proof of stake (e,g. I possess it and I can attest to its chain of custody), with zero lines of code!
    - mirekrusin 7y ago
      SHA1 "is incomprehensible mathematics for 99.999% of the population", yet we do use it to great success. Same with public key cryptography. It doesn't seem to bother people that can't implement ssh/https from top of their heads, right?
    - solveit 7y ago
      > On the other hand, the 'nineteenth century technology' of secret ballots is both obvious and simple. It's a shame that people like Vitalik are so dismissive of it. You can't write smart contracts based on secret ballots. The dream (well, one dream) is to have governance based on an ecosystem of programs that can vote perhaps hundreds of times a second. A lot of democratic procedure is built to work around the limitations of physical voting; this could qualitatively change the way decision-making works.
- 6gvONxR4sf7o 7y ago
  I don't think secret voting is as much of an issue as people make it out to be. Vote buying would in theory be a problem with today's usual voting systems, but in practice doesn't seem to be an issue. If we're voting on Proposition 1234 and I really really care but you don't, I should be willing to pay you to vote my way. But we don't see that happening.
  - rkagerer 7y ago
    Like a vote-trading scheme where I can give you my vote on this issue I don't care about, to buy your support on some other issue you don't care about? I've contemplated that too, but I'm not sure it leads to better results. I think good results come from amassing voters who are genuinely engaged on an issue, and entrenching a means for them to become well-informed before casting their ballot. A system to deliver that, blocks the noise of political issues I don't care about (I simply don't participate, which is a good outcome since my participation adds little-to-negative value) and surfaces those I do. It provides me with expert analysis, arguments and counterarguments (something like StackOverflow to bubble the best content to the top?). And it makes more economical and efficient use of my attention.
    - joosters 7y ago
      It's not just whether or not vote-trading schemes are a good thing or not, but the unfortunate issue that if voter secrecy is weakened to allow for vote trading, then abuses such as forced voting, blackmail or coercion also become viable.
    - 6gvONxR4sf7o 7y ago
      I'm not advocating for any vote trading or vote buying. I think both would be terrible. I'm saying that both are incentivized in a traditional voting system but we just don't see it happening. Therefore, the fact that they're incentivized in a quadratic system doesn't mean it would actually be a problem. I'd rather be able to verify that I voted yes on prop 1234.
  - bluGill 7y ago
    You don't see it happening (much) because we have a secret ballot. If I really care about Proposition 1234 I can sell my vote to you, collect the fees, and still vote however I want. There have been cases where someone felt compelled to vote for something they didn't want because they didn't want to be seen voting the other way [their boss would fire them, or such situations], thus we no longer allow anyone to find out how an individual voted.
- snarf21 7y ago
  I don't understand how the n value is even calculated in the first place. It never really said. It seems like a rich person only needs to buy one more vote than the poor person to win. I guess this works if the number of rich people is much much lower than the number of poor people. This is also interesting mostly in a theoretical sense. The rich would never let any system like this go live.
  - QuesnayJr 7y ago
    I think he's being deliberately vague because the meaning of "n" depends on the application.
  - bluGill 7y ago
    According to the Austrian school N cannot be calculated. There are too many variables - and the people change their values in real time for various reasons (including irrational reasons). The rich don't care though, because while they cannot calculate n, they can estimate it, and then go over by a bit just to make sure.
awelkie 7y ago
Great article; very interesting and well written. A bit of a tangent, but something that bothers me is the assumption in economics that the amount of money one is willing to pay for a good is equal to the utility provided by that good. And then it follows that if I am willing to pay €2 for a coffee and another person is only willing to pay €1 for that same coffee, then I value the coffee twice as much as the other person. But to me that doesn't make much sense. What if I am a billionaire and the other person is very poor? It could very well be that the other person values the coffee a lot more than I do, but because I have so much more disposable income than they do I am willing to pay more for it. To me, the assumption should be something like the amount of money as a percentage of my total wealth that I'm willing to pay is equal to the utility of the good. And because this assumption is so fundamental to economics, it determines the conclusions that the field reaches. For example, the definition of an "efficient market" or the optimal level of production of some good both embed this assumption that willingness to pay equals utility. And then one can imagine that policy decisions and such are influenced by this assumption. (And in fact the article itself mentions this problem: "Another challenge is that quadratic payments, being a payment-based mechanism, continues to favor people with more money."). So I'm wondering if anyone has looked into an alternative formulation of economics with a different fundamental assumption (perhaps something closer to the one I proposed above). If so, do certain things that are determined to be "optimal" in classical economics turn out not to be optimal in this alternative formulation (and vice-versa)? Apologies if this is a bit of a naive question; Econ 101 is the most I've ever studied the subject.
- hderms 7y ago
  it seems like in the event that quadratic payments are applied to a situation where multiple parties are competing for a single good that it reduces to something similar to an auction. Imo it's clear that auctions, corresponding with what you said, favor those with the most income.
  - lisper 7y ago
    Yes, and adding a non-linear transfer function won't help in this case. To win an auction, I only need to outbid you by epsilon. Non-linear payments only help where the value of the thing being purchased can vary (non-linearly) with the purchase price.
6gvONxR4sf7o 7y ago
This is a fascinating collective decision making scheme. One potentially serious nitpick. In the "one dollar one vote" scheme, it makes a simplification that seems really bad. It's the same flavor of mistake as when you have the option of making a bet. If the expected return is positive, it says you should bet all of your money. In reality, people don't do this. Rational actors shouldn't even do this. I'd love to see what an attempt at this same sort of number-of-votes-is-proportional-to-value comes to with a less simplified model of behavior. If I value outcome A at price $x and outcome B at price $y, I might not be able to afford $x^2+y^2, and this model doesn't say what I would or should do. A corresponding model that talked about how people allocate their finite money rather than a unit by unit spending description seems like it would better apply to reality.
- joosters 7y ago
  It's simply not true that if EV is positive, you should bet all of your money. There's a classic formula called the 'Kelly criterion' to calculate how much of your money should be bet given your expected edge. The original paper (which came out of Bell labs, based upon noise over a transmission channel!) is a good read: https://en.wikipedia.org/wiki/Kelly_criterion https://en.wikipedia.org/wiki/Kelly_criterion http://www.herrold.com/brokerage/kelly.pdf http://www.herrold.com/brokerage/kelly.pdf
  - 6gvONxR4sf7o 7y ago
    I think you misread me. That's exactly what I'm saying. Or I misread you and you aren't actually trying to disagree.
    - joosters 7y ago
      Oops, sorry, I misread your comment and thought that you were saying the opposite!
  - lifeisstillgood 7y ago
    Can I check something - reading the wikipedia article on Kelly Bets it seems that one should take the expected chance of winning, double it and subtract 1.0 and use that as percentage of bet size So when I win 3/4 times, that's .75 -> 1.5 -> .5 of my total wealth. But this basically means never gamble till the odds are in your favour. (ie above .5 chance of winning) What does this say about founding a startup?
slowhand09 7y ago
Interesting article.
creeble 7y ago
It seems like solving the Sybil problem (a prerequisite to this scheme having any use whatsoever) might be something better on which to focus attention first, as it has other useful applications, even in one-person, one-vote democracies.
- rytill 7y ago
  Pushing this idea doesn't mean other problems in the space aren't being thought about.
say_it_as_it_is 7y ago
Really great to see Vitalik working with Glen Weyl's ideas. Weyl's collection of "radical ideas" may actually become more than just thought experiments.
- DennisP 7y ago
  They actually authored a paper together: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3243656 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3243656 On arxiv: https://arxiv.org/abs/1809.06421 https://arxiv.org/abs/1809.06421
seangrogg 7y ago
I've always enjoyed the concept of exponential costs for incremental gains. I've had the benefit of only really utilizing them in strong-identity systems (games) but I've considered some of the drawbacks of using them in weak-identity systems and come to a few ideas: 1) A participation barrier can be used to prevent identities from participating until they've overcome something. A simple example would be an age barrier (identity must exist for some period of time before participating) which prevents spinning up multiple identities on-demand to try to increase voting power. Ideally, in practice there would be multiple barriers that would be naturally-occurring for a real participating identity but too expensive to create/maintain several identities. 2) Similar to (1), have an ongoing cost to maintaining identities. Something such as a "subscription fee" may serve as a deterrent as the value of one identity needs to be weighed against the cost of maintaining it. This can be made additionally effective if the issue being voted on recurs every period rather than one-time (i.e. revisiting regulation votes every cycle instead of just voting once and having the regulation remain until stricken). For the normal participant, the value of this subscription could be offset by access to a non-scaling benefit - i.e. access to private content/events. 3) While the article focuses on the economics in terms of dollars there's the very real question of allowing votes to be purchased with other forms of currency that either complement or replace traditional currency. This is common in MMOs where you can have multiple characters (weak identities) each with their own in-game currency that can be acquired from in-game activities and may or may not be exchanged with real-world currency depending on the stance the owners of the game take. Suffice it to say there aren't really silver bullets to "general purpose quadratic payments with weak identities" but you could create some limited-purpose constraints that are particular to the problem/community and make some strides from there.
miki123211 7y ago
I don't think this idea is actually implementable in a large-scale, real-world setting. One person, one vote democracy is pretty understandable to an average Joe who doesn't even remember what "squared" means. I think that a normal person would have no idea how much to spend on a particular decision, as the formulas would seem like black magic to them. Normal voting is pretty intuitive, quadratic is not. This problem is not that noticable for HN people, as our average intelligence is probably way above the societys', but before deploying this on a large scale, it has to be considered. I don't think that internal workings of democracy should be something that an average school child can't easily grasp.
- rytill 7y ago
  > I don't think that internal workings of democracy should be something that an average school child can't easily grasp While it would be a regression in this aspect, I'm not sure this outweighs the potential benefits.
- naringas 7y ago
  part of the reason the so-caleld "average Joe" doesn't remember what squared means is becuase they don't really have to. If this scheme were part of the world form the minute "Joe" is born, Joe would have to understand this. education must improve. the current paradigm of education is reminiscent of an assembly line. if kids aren't manufactured goods, why is their education treated as such?
rajacombinator 7y ago
The main topics of interest here are how non “quadratic” voting converges to quadratic via influence peddling or subquadratic in the form of rigged/kabuki elections.
moultano 7y ago
We tried quadratic voting for our team choosing a new name, and we did not find it to work well. I think the analysis that the scheme even converges makes simplifying assumptions that aren't well justified, particularly that everyone knows the marginal probability of each candidate winning (when that itself is behind a fairly inscrutable voting method.) Without that assumption I think it falls apart. The optimal strategy is to vote maximally for your preferred most likely contender, and maximally against the nearest competitor, but if you don't know who those are, the system provides no means of discovery. So strategic voting is not just possible, it is critical to have any influence, but the evidence needed for optimal strategic voting is neither obvious, nor revealed by the system, (and from our experience I don't think it has any stable Nash equilibria.) After a few days with the system, we finally abandoned it and switched to a condorcet election.
steenreem 7y ago
While reading I wasn't convinced this was going to work due to the collusion problem, until I read the comments on collusion which add an extra condition: "we need votes to be so private that even the person who made the vote can't prove to anyone else what they voted for." However, this condition is not enough, it doesn't cover the case where someone is being watched while they are voting. The condition should be something like: "we need votes to be so private that only the voter can know what he voted on" I don't see many solutions to this, except the '19th century' way of voting at a voting station, or a voting machine that can read minds. Obviously it would be pretty strange inputting your vote through thoughts, especially since this system might never allow you to confirm what you voted on. However, I guess even ballot voting could suffer from collusion since it's not fundamentally private. You could take a hidden camera into the voting box and record your vote, and afterwards get a payout.

194 points by gabcoh 7y ago

This post describes a system of voting/payments where you can make multiple votes, depending on how strongly you value your preferred outcome, but each vote costs more than the vote before. Identity management and collusion are big issues with these systems, as the essay points out. For programmers, one way to think about this is that each voter has a state, n, that tracks how many of times they've voted. And each vote is more expensive than the last. Eventually you either run out of money or you lack the desire to spend more money on another vote. But if you can create a new voter account as easily as you can create a new Gmail account, then once n gets sufficiently high, you just switch to a new account to lower the price of your vote. Or if a really rich voter with a high n-value pays someone with a low-n value to make a vote on their behalf, the system collapses as well. Enforcing strict identity management (e.g. requiring valid state-issued ID cards) and implementing secret voting can help address these problems, but my guess is that if there is a strong enough incentive, people will try their hardest and come up with novel ways to thwart these safeguards.

wyldfire 7y ago
> But if you can create a new voter account as easily as you can create a new Gmail account This is generally described as a Sybil attack [1]. > you just switch to a new account to lower the price of your vote. ... Or if a really rich voter with a high n-value pays someone with a low-n value to make a vote on their behalf AFAICT the article discusses these problems: > Perhaps the biggest challenge to consider with this concept of quadratic payments is the practical implementation issue of identity and bribery/collusion. ... Fortunately, there are technological means that can help, combining together zero-knowledge proofs, encryption and other cryptographic technologies to achieve the precise desired set of privacy and verifiability properties. [1] https://en.wikipedia.org/wiki/Sybil_attack https://en.wikipedia.org/wiki/Sybil_attack
- joosters 7y ago
  Fortunately, there are technological means that can help, combining together zero-knowledge proofs, encryption and other cryptographic technologies to achieve the precise desired set of privacy and verifiability properties. This is placing too much trust in what is incomprehensible mathematics for 99.999% of the population. Even for those who understand it, they won't have any convincing way of being assured that 1) the maths is perfect and there are no flaws and 2) the voting technology in use is perfectly implemented. On the other hand, the 'nineteenth century technology' of secret ballots is both obvious and simple. It's a shame that people like Vitalik are so dismissive of it.
  - kortex 7y ago
    I'm a developer with a strong math background, very security-minded, with experience using cryptocurrencies, pgp/gpg, privacy tools, etc. I still would not be able to evaluate any sort of crypto program and certify its integrity, nor find any (save for the most eggregious) flaws. Even then, I have brought up questions in code reviews of "this seems to be flawed" only to learn "technically yes, but we have to do such gymnastics because of constraints xyz". I, too, was big on the "blockchain is gonna make e-voting possible! Ra ra ra!" hype train for a while, but eventually wisened up to my own naivety. I think paper is great because it's both proof of work (it had to be printed/written/modified) and proof of stake (e,g. I possess it and I can attest to its chain of custody), with zero lines of code!
  - mirekrusin 7y ago
    SHA1 "is incomprehensible mathematics for 99.999% of the population", yet we do use it to great success. Same with public key cryptography. It doesn't seem to bother people that can't implement ssh/https from top of their heads, right?
  - solveit 7y ago
    > On the other hand, the 'nineteenth century technology' of secret ballots is both obvious and simple. It's a shame that people like Vitalik are so dismissive of it. You can't write smart contracts based on secret ballots. The dream (well, one dream) is to have governance based on an ecosystem of programs that can vote perhaps hundreds of times a second. A lot of democratic procedure is built to work around the limitations of physical voting; this could qualitatively change the way decision-making works.
6gvONxR4sf7o 7y ago
I don't think secret voting is as much of an issue as people make it out to be. Vote buying would in theory be a problem with today's usual voting systems, but in practice doesn't seem to be an issue. If we're voting on Proposition 1234 and I really really care but you don't, I should be willing to pay you to vote my way. But we don't see that happening.
- rkagerer 7y ago
  Like a vote-trading scheme where I can give you my vote on this issue I don't care about, to buy your support on some other issue you don't care about? I've contemplated that too, but I'm not sure it leads to better results. I think good results come from amassing voters who are genuinely engaged on an issue, and entrenching a means for them to become well-informed before casting their ballot. A system to deliver that, blocks the noise of political issues I don't care about (I simply don't participate, which is a good outcome since my participation adds little-to-negative value) and surfaces those I do. It provides me with expert analysis, arguments and counterarguments (something like StackOverflow to bubble the best content to the top?). And it makes more economical and efficient use of my attention.
  - joosters 7y ago
    It's not just whether or not vote-trading schemes are a good thing or not, but the unfortunate issue that if voter secrecy is weakened to allow for vote trading, then abuses such as forced voting, blackmail or coercion also become viable.
  - 6gvONxR4sf7o 7y ago
    I'm not advocating for any vote trading or vote buying. I think both would be terrible. I'm saying that both are incentivized in a traditional voting system but we just don't see it happening. Therefore, the fact that they're incentivized in a quadratic system doesn't mean it would actually be a problem. I'd rather be able to verify that I voted yes on prop 1234.
- bluGill 7y ago
  You don't see it happening (much) because we have a secret ballot. If I really care about Proposition 1234 I can sell my vote to you, collect the fees, and still vote however I want. There have been cases where someone felt compelled to vote for something they didn't want because they didn't want to be seen voting the other way [their boss would fire them, or such situations], thus we no longer allow anyone to find out how an individual voted.
snarf21 7y ago
I don't understand how the n value is even calculated in the first place. It never really said. It seems like a rich person only needs to buy one more vote than the poor person to win. I guess this works if the number of rich people is much much lower than the number of poor people. This is also interesting mostly in a theoretical sense. The rich would never let any system like this go live.
- QuesnayJr 7y ago
  I think he's being deliberately vague because the meaning of "n" depends on the application.
- bluGill 7y ago
  According to the Austrian school N cannot be calculated. There are too many variables - and the people change their values in real time for various reasons (including irrational reasons). The rich don't care though, because while they cannot calculate n, they can estimate it, and then go over by a bit just to make sure.

awelkie 7y ago

Great article; very interesting and well written. A bit of a tangent, but something that bothers me is the assumption in economics that the amount of money one is willing to pay for a good is equal to the utility provided by that good. And then it follows that if I am willing to pay €2 for a coffee and another person is only willing to pay €1 for that same coffee, then I value the coffee twice as much as the other person. But to me that doesn't make much sense. What if I am a billionaire and the other person is very poor? It could very well be that the other person values the coffee a lot more than I do, but because I have so much more disposable income than they do I am willing to pay more for it. To me, the assumption should be something like the amount of money as a percentage of my total wealth that I'm willing to pay is equal to the utility of the good. And because this assumption is so fundamental to economics, it determines the conclusions that the field reaches. For example, the definition of an "efficient market" or the optimal level of production of some good both embed this assumption that willingness to pay equals utility. And then one can imagine that policy decisions and such are influenced by this assumption. (And in fact the article itself mentions this problem: "Another challenge is that quadratic payments, being a payment-based mechanism, continues to favor people with more money."). So I'm wondering if anyone has looked into an alternative formulation of economics with a different fundamental assumption (perhaps something closer to the one I proposed above). If so, do certain things that are determined to be "optimal" in classical economics turn out not to be optimal in this alternative formulation (and vice-versa)? Apologies if this is a bit of a naive question; Econ 101 is the most I've ever studied the subject.

hderms 7y ago
it seems like in the event that quadratic payments are applied to a situation where multiple parties are competing for a single good that it reduces to something similar to an auction. Imo it's clear that auctions, corresponding with what you said, favor those with the most income.
- lisper 7y ago
  Yes, and adding a non-linear transfer function won't help in this case. To win an auction, I only need to outbid you by epsilon. Non-linear payments only help where the value of the thing being purchased can vary (non-linearly) with the purchase price.

6gvONxR4sf7o 7y ago

This is a fascinating collective decision making scheme. One potentially serious nitpick. In the "one dollar one vote" scheme, it makes a simplification that seems really bad. It's the same flavor of mistake as when you have the option of making a bet. If the expected return is positive, it says you should bet all of your money. In reality, people don't do this. Rational actors shouldn't even do this. I'd love to see what an attempt at this same sort of number-of-votes-is-proportional-to-value comes to with a less simplified model of behavior. If I value outcome A at price $x and outcome B at price $y, I might not be able to afford $x^2+y^2, and this model doesn't say what I would or should do. A corresponding model that talked about how people allocate their finite money rather than a unit by unit spending description seems like it would better apply to reality.

joosters 7y ago
It's simply not true that if EV is positive, you should bet all of your money. There's a classic formula called the 'Kelly criterion' to calculate how much of your money should be bet given your expected edge. The original paper (which came out of Bell labs, based upon noise over a transmission channel!) is a good read: https://en.wikipedia.org/wiki/Kelly_criterion https://en.wikipedia.org/wiki/Kelly_criterion http://www.herrold.com/brokerage/kelly.pdf http://www.herrold.com/brokerage/kelly.pdf
- 6gvONxR4sf7o 7y ago
  I think you misread me. That's exactly what I'm saying. Or I misread you and you aren't actually trying to disagree.
  - joosters 7y ago
    Oops, sorry, I misread your comment and thought that you were saying the opposite!
- lifeisstillgood 7y ago
  Can I check something - reading the wikipedia article on Kelly Bets it seems that one should take the expected chance of winning, double it and subtract 1.0 and use that as percentage of bet size So when I win 3/4 times, that's .75 -> 1.5 -> .5 of my total wealth. But this basically means never gamble till the odds are in your favour. (ie above .5 chance of winning) What does this say about founding a startup?

slowhand09 7y ago

Interesting article.

creeble 7y ago

It seems like solving the Sybil problem (a prerequisite to this scheme having any use whatsoever) might be something better on which to focus attention first, as it has other useful applications, even in one-person, one-vote democracies.

rytill 7y ago
Pushing this idea doesn't mean other problems in the space aren't being thought about.

say_it_as_it_is 7y ago

Really great to see Vitalik working with Glen Weyl's ideas. Weyl's collection of "radical ideas" may actually become more than just thought experiments.

DennisP 7y ago
They actually authored a paper together: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3243656 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3243656 On arxiv: https://arxiv.org/abs/1809.06421 https://arxiv.org/abs/1809.06421

seangrogg 7y ago

I've always enjoyed the concept of exponential costs for incremental gains. I've had the benefit of only really utilizing them in strong-identity systems (games) but I've considered some of the drawbacks of using them in weak-identity systems and come to a few ideas: 1) A participation barrier can be used to prevent identities from participating until they've overcome something. A simple example would be an age barrier (identity must exist for some period of time before participating) which prevents spinning up multiple identities on-demand to try to increase voting power. Ideally, in practice there would be multiple barriers that would be naturally-occurring for a real participating identity but too expensive to create/maintain several identities. 2) Similar to (1), have an ongoing cost to maintaining identities. Something such as a "subscription fee" may serve as a deterrent as the value of one identity needs to be weighed against the cost of maintaining it. This can be made additionally effective if the issue being voted on recurs every period rather than one-time (i.e. revisiting regulation votes every cycle instead of just voting once and having the regulation remain until stricken). For the normal participant, the value of this subscription could be offset by access to a non-scaling benefit - i.e. access to private content/events. 3) While the article focuses on the economics in terms of dollars there's the very real question of allowing votes to be purchased with other forms of currency that either complement or replace traditional currency. This is common in MMOs where you can have multiple characters (weak identities) each with their own in-game currency that can be acquired from in-game activities and may or may not be exchanged with real-world currency depending on the stance the owners of the game take. Suffice it to say there aren't really silver bullets to "general purpose quadratic payments with weak identities" but you could create some limited-purpose constraints that are particular to the problem/community and make some strides from there.

miki123211 7y ago

I don't think this idea is actually implementable in a large-scale, real-world setting. One person, one vote democracy is pretty understandable to an average Joe who doesn't even remember what "squared" means. I think that a normal person would have no idea how much to spend on a particular decision, as the formulas would seem like black magic to them. Normal voting is pretty intuitive, quadratic is not. This problem is not that noticable for HN people, as our average intelligence is probably way above the societys', but before deploying this on a large scale, it has to be considered. I don't think that internal workings of democracy should be something that an average school child can't easily grasp.

rytill 7y ago
> I don't think that internal workings of democracy should be something that an average school child can't easily grasp While it would be a regression in this aspect, I'm not sure this outweighs the potential benefits.
naringas 7y ago
part of the reason the so-caleld "average Joe" doesn't remember what squared means is becuase they don't really have to. If this scheme were part of the world form the minute "Joe" is born, Joe would have to understand this. education must improve. the current paradigm of education is reminiscent of an assembly line. if kids aren't manufactured goods, why is their education treated as such?

rajacombinator 7y ago

The main topics of interest here are how non “quadratic” voting converges to quadratic via influence peddling or subquadratic in the form of rigged/kabuki elections.

moultano 7y ago

We tried quadratic voting for our team choosing a new name, and we did not find it to work well. I think the analysis that the scheme even converges makes simplifying assumptions that aren't well justified, particularly that everyone knows the marginal probability of each candidate winning (when that itself is behind a fairly inscrutable voting method.) Without that assumption I think it falls apart. The optimal strategy is to vote maximally for your preferred most likely contender, and maximally against the nearest competitor, but if you don't know who those are, the system provides no means of discovery. So strategic voting is not just possible, it is critical to have any influence, but the evidence needed for optimal strategic voting is neither obvious, nor revealed by the system, (and from our experience I don't think it has any stable Nash equilibria.) After a few days with the system, we finally abandoned it and switched to a condorcet election.

steenreem 7y ago

While reading I wasn't convinced this was going to work due to the collusion problem, until I read the comments on collusion which add an extra condition: "we need votes to be so private that even the person who made the vote can't prove to anyone else what they voted for." However, this condition is not enough, it doesn't cover the case where someone is being watched while they are voting. The condition should be something like: "we need votes to be so private that only the voter can know what he voted on" I don't see many solutions to this, except the '19th century' way of voting at a voting station, or a voting machine that can read minds. Obviously it would be pretty strange inputting your vote through thoughts, especially since this system might never allow you to confirm what you voted on. However, I guess even ballot voting could suffer from collusion since it's not fundamentally private. You could take a hidden camera into the voting box and record your vote, and afterwards get a payout.