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Quadratic voting (2014) (ericposner.com)
84 points by alansammarone on Sept 9, 2017 | hide | past | favorite | 109 comments



This is fascinating, as I've done some work with weighted voting systems in the past.

If I understand correctly, some emergent effects would occur.

1. The poor would collectively have less voting power.

2. The poor would likely become less poor due to distribution of voting funds. This would be roughly proportional to the amount of voting power lost.

3. The middle class, assuming it still exists the way we know it, may or may not have increased collective voting power.

4. Upper-middle class will gain proportionally more collective voting power than what middle class gained, but they are fewer in population. The 1% will gain even more, but they are only 1% of the population. Each social class (aside from the poor) will have more representation, while the poor will receive money (and a tiny amount of representation).

5. More passionate voters will pay more, and polarizing or strongly motivating issues will create a less-predictable situation at the polls. This could be a very good thing or a very bad thing, I don't know. Perhaps this is where the magic happens.

6. Political groups will form voting coalitons to vote certain ways, and may be paid to do so, beyond the voting fees, unless legally prohibited. However, this may prove to be not the most viable use of resources.

I think that this could work in positive ways. However, I wouldn't bet on it, as there are as many things that could go wrong. When dealing with complex strategy or architecture choices with unknown consequences, it is a hard sell to willingly go with one that brings significant risk. However, one can argue, especially with the current political climate and lack of faith in the system, that not switching to this would be the bigger risk.

I'm interested in finding smaller scale applications of such a system, as a crude proof of concept.


I accept that this is a superior voting system to one-person-one-vote. However, for it to succeed, it should not merely be superior, it should also appear superior. The trust the voters put into the system is paramount. And for that to be true, the vast majority of the voters have to understand exactly how it works. Unfortunately, and, yes, I'm a cynic, I don't believe we are close to having a voter base that is capable of understanding, and hence accepting an outcome of such a voting system.

Disclaimer: I'm not a US citizen.


A possible counter-point may be the existence of the Australian System of voting. Complex, debatably widely misunderstood...yet I'd argue widely accepted.

I realise of course, there is a world of difference between pointing out there is a country with a different/more complex voting system, and migrating a country with culture/history of a given voting system to a more complex alternative...


I love the Australian voting system. It is based on two seeming unrelated, but intertwined rules.

1. Instant runoff voting (preferencing the candidates from 1 to x).

2. Compulsory voting (actually a fine for not visiting the polling station and getting your name crossed off, voting is optional).

The two systems together work to keep everyone involved to a certain extent in the political system, a choice in who you can actually vote for, and historically, stable centralist governments. We have over the last decade or so ended up with less stable governments, but this is more a reflection of a convergence to the centre. The differences between the major parties is now so small that changing does not make much difference in policy.

The one downside is it does make Australia a rather boring place to live :)


> The one downside is it does make Australia a rather boring place to live :)

That's not a bug, it's a feature. There's a reason that "may you live in interesting times" is considered a curse.


Wouldn't it also be a negative?

Basically, you cannot have radical societal or cultural changes because you have to get everyone on board ahead of time.

In a two party system and optional voting, you can have only a small fraction of the population who particularly want some changes actually get those changes. Also, this strategy can be used to destabilize a system away from local maximum (if we are searching for some better state).


Yes if you want radical change it is a negative. Having said this radical change does not have a good history. I think that gradual change that has the support of the majority is the best way to achieve lasting change for the better.

A really good current example is same sex marriage. Australia is one of the last western countries to allow this (should be implemented before the end of the year), but it now has the support of 70% of the population. I would rather see change occur that lasts, than a small minority impose their will on the majority and having to deal with the resulting backlash.


Another way of looking at this is that gay marriage is banned because of the will of 30% of the population

Granted a lot of this is about stickiness of laws but it seems like a huge battle has to be fought for removing systemic inequalities, when that seems to be a major problem in the current system

It's only very recently that reproductive rights have broad majority support. The Civil Rights Act could never be enacted if it had required 70% support.

Once the battle is won then these rights get protected. At a time when systemic inequalities are at the forefront, inhibiting change seems like something that would go against the general political currents.


SSM was banned when it did not have popular support and will now be unbanned when it has popular support. It is a philosophical position, but I think large change should come with popular support and if you don't have popular support for your idea then keep working until you do.

It is worth debating if the civil rights act should have been enacted before it had popular support. Rather than undermining the basis of suppression, imposing something on the majority without their support brings a resulting backlash that can last generations. We only have to look what drove the last 50 years of politics in the US south to see the result. From my comfortable perspective it might have been better to let the south come to its own opinion (with a lot of outside nudging) that things really had to change.


Well these things have popular support, it's just there's a gulf between 50% and 60%, and yet another between 60% and 70%

Its hard because laws that ensure basic civil rights go through the same process as tax law, but one is vitally more important for a better future for all


The move in support for legalising SSM has come rather fast - 5 years ago it was less than 50%.

Yes relying on achieving popular support before acting will always mean that change happens later than it really should, but I think this price is worth paying to ensure long term support.

I do think political systems that reguire building broad popular support are desirable in general because they encourage openness.


What if the status quo keeps moving in a direction that slowly makes things worse for a certain group of people?

You basically cannot get out of it unless you can convince most people that it's a good idea. With a 2-party system you can get someone who represents those people to rule for a while and maybe correct the course.

Also, with optional voting, we basically delegate decisions to those who really care about something. Having lived in a country with mandatory voting, I saw a few elections where people's views and the results of some elections were easily manipulated by false news close to the election day. People who are ambivalent I think are more likely to change their decision over such things.


That small minority might feel quite differently. Which is the point of the QV idea, I suppose.


> The one downside is it does make Australia a rather boring place to live :)

I don't know about boring, from my perspective it's more comical. Who's turn is it to be Prime Minister this week? and can she stack it in high heels on the grass again. We've had the same PM for nearly a year, must be time for another spill.


I would trade instability in PM's for stability in policy any day.

Your post did make me LOL remembering Julia trying to walk on grass in high heels and then faceplanting.


How is this a superior voting system? It just seems to be a way for those with more money to have more influence in the voting process. We've got enough problems with money in politics as it is, we don't need any more of them.


Your post is actually extremely important and spells out one of the primary weaknesses of such a system. As long as the budget obtained for the vote does not have an opportunity cost with the rest of a person's wealth/budget (and I can't think of any practical way to make that happen in reality), what the voting system will in effect create is increased voting power by the wealthy, as they suffer comparatively less marginal loss from expending their entire voting budget goals towards their agenda, irrespective of their strength of belief: the downside comes from their lack of any real real-world budgetary pain.

Unless one can come up with a way to inflict the same budgetary pain on each individual for each vote-expenditure, I don't really see how you would argue for its implementation/superiority in practice (against the other forms of voting out there I mean, not necessarily contrasted just against first past the post...).

Though this all depends on what one means by "optimal voting" or "efficient", since I don't believe there can be an objective definition of such.


As I understood it, "buy" does not have to be money. It could be hashing ability as in Bitcoin or maybe everyone gets X voting credits every few years which they "buy" votes in local and national elections.

I could be wrong, but I prefer the possibilities of such a system not directly involving money. The distribution of wealth is so imbalanced that I cannot see buying votes to have any kind of positive impact.


Yes. Perhaps the voting currency should be hours, not dollars. Make the first vote free. But N-1 more votes costs you N^2-1 hours from your "registered community service" account maintained by the government. No overdrafts allowed: the hours must be credited before they can be debited.


Otoh, if money already buys politics today, this system could be not worse than what we have now.


One-person-one-vote is a terrible system, with the only advantage of it being simple and easy to understand, which was important when votes could be counted only by hand.

CGP Grey has made an excellent and well known video series explaining this, so I don't think I need to debate it much further here.

CGP Grey Voting Series: http://www.youtube.com/playlist?list=PLej2SlXPEd37YwwEY7mm0W...


Do any of those CGP Grey videos actually address one-person-one-vote? Looking at the titles of the videos they seem to be mostly critiques of how votes are grouped rather than how much voting power a single individual has. For example, criticising the electoral college system in the US has nothing to do with one-person-one-vote, it's a criticism of how the winner is decided.


You didn't answer the question, you just said the current voting system is bad.


Isn't it a bit pedantic to want me to repeat arguments from the original post?

OK, here you go: "Weyl and Lalley prove that the collective decision rapidly approximates efficiency as the number of voters increases. By contrast, no extant voting procedure is efficient."


It's quadratic, do some quick math on how expensive it is to buy a victory.

It's actually more cost effective to buy people's votes the usual way.


The point is that Americans (me included) are going to put very little trust in a system which allows you to literally buy votes. Everyone should have the same amount of votes no matter the wealth and I don't see myself compromising on that issue.


The system where you buy votes is the current system, mind.

Somewhat true for elections of political representatives, but even more true for things like Senate Committees - these require party membership fees that get paid, which come via donations from lobbyists.

Not party political, both sides do it: http://www.definingthemachine.com/party_dues.html


But do you feel any better about the idea of being compensated for not getting your preference?


Not really. It seems sort of like selling some of my political power to the wealthy.


It's not necessary for a single wealthy individual to be able to buy a victory by themselves for the results to be skewed towards the will of the wealthy.

If 1000 votes cost £1 million, and 100 wealthy individuals all decide to spend that much in an election, that's 100,000 votes when these individuals would only usually have 100 votes. That's going to have an impact, especially on local elections.

As for it being more cost effective to buy votes the usual way, the "usual" way relies on voter fraud and massive advertising campaigns, one of which is illegal, and the other is very expensive and the voting decisions are not guaranteed. On the other hand, quadratic voting would be legal and guaranteed.


By the usual way, I was referring to large advertising campaigns that I'm sure yield more votes per dollar than a quadratic voting system.

One of the things you're missing is that people who can afford to buy that many votes for a single issue are very rare and could easily be out voted by a small organized group that buys multiple votes, but with a lower power multiple.

Assuming all votes cost $1, then 1,000 votes costs 1mil. That could easily be nullified by 100 voters buying 10 votes.

Consider also that the money would be rebated equally. So you might spend $100 and get back $250 and win the vote.


> "Assuming all votes cost $1, then 1,000 votes costs 1mil. That could easily be nullified by 100 voters buying 10 votes."

Do you not see the problem with that? With the situation you describe, it takes the coordination of 100 individuals to nullify the actions of 1 wealthy voter. Do you not see how much easier it is for the wealthy voter?


If merely 100 less-wealthy voters out of the whole population couldn't coordinate to buy a few extra votes—and they wouldn't even have to explicitly communicate, it would just take 100 people who individually hear about the issue and decide to vote more—then how important can the issue really have been to them?

I believe this is what is meant by "the collective decision rapidly approximates efficiency as the number of voters increases".


That's missing the point I was making. I'm attempting to highlight the difference in effort that is required. Do you accept that the rich voter makes less effort in the hypothetical 1 vs. 100 voter situation?


I'm not sure that is correct. Assume that you have only 101 people in the voting pool. The one person who is wealthy pays $1,000 for 100 votes. To match that voting power, you'll only need a handful of the other hundred to pay $4 for more votes. What I think you are overlooking the fact the wealthy person's $1,000 is going to get distributed to everyone which gives them more voting power. Everyone gets at least $10 at the end of the vote. If a few people are willing to invest the $10 back into their vote, they can easily overcome the rich persons' vote even though a vote was purchased for each person in the system.

How balanced this is, I'm not sure. Why use the square of the number of votes rather than the cube? But it isn't immediately clear that this gives a few rich people significantly more voting power in a situation where a larger number of poor people feel strongly about an issue.


> "I'm not sure that is correct. Assume that you have only 101 people in the voting pool. The one person who is wealthy pays $1,000 for 100 votes. To match that voting power, you'll only need a handful of the other hundred to pay $4 for more votes. What I think you are overlooking the fact the wealthy person's $1,000 is going to get distributed to everyone which gives them more voting power. Everyone gets at least $10 at the end of the vote. If a few people are willing to invest the $10 back into their vote, they can easily overcome the rich persons' vote even though a vote was purchased for each person in the system."

Two points:

1. You've chosen a value that's too small for the wealthy voter. $1000 is the cost of eating out at an expensive restaurant (e.g. https://financesonline.com/10-most-expensive-meals-from-mich... ), not the amount someone with money will spend to gain influence in an election.

2. There are cheaper ways to multiply the vote. Let's assume quadratic voting was in place in the 2016 US Presidential Election, and you're a wealthy person who wants to see the Democrats win. You have $1,000,000 you're willing to spend. What's the cheapest way to maximise your influence? Reach out to other Democratic voters to give them money to multiply their votes. On your own, the $1,000,000 may only net 1000 votes, but spreading the $1,000,000 around to people who were going to vote Democrat anyway could see that number skyrocket. Let's say you give $100 to 10,000 voters, now you're looking at 100,000 votes.

Even if those without the most money win, quadratic voting stacks the odds against them.


> You've chosen a value that's too small for the wealthy voter.

Yes to make it simple to intuitively see how rich people paying more gives more voting power to everyone else IF they choose to spend it that way. If you want to think about US presidential elections, you'd need to increase the total number of people by 3,000,000. Based on my math, this would just further amplify the effect I was trying to illustrate with my numbers.

> Even if those without the most money win, quadratic voting stacks the odds against them.

As I understand the math, it doesn't necessarily do this. The goal was a voting system that takes into consideration not just how many people want a particular outcome, but how badly they want a particular outcome. Today the way that is done is by donating money to be spent on advertising to sway votes or get people to go to the polls. Quadradic voting is designed to be more fair than the current way of allowing people to magnify the strength of their preferences for a particular outcome.

My initial reaction was the same as yours. After looking at how the math actually plays out and considered how money is currently spent on influencing votes I think it is probably a lot fairer than it looks at first for the goals it is trying to achieve. (Still could be a really bad idea for other reasons.)


> "Yes to make it simple to intuitively see how rich people paying more gives more voting power to everyone else IF they choose to spend it that way. If you want to think about US presidential elections, you'd need to increase the total number of people by 3,000,000. Based on my math, this would just further amplify the effect I was trying to illustrate with my numbers."

I respect that you had good intentions, but I think the approach was flawed.

In your example, $1000 vs. $400 ($4 * 100), what does it take for the rich person to gain the lead again? They can either spend more or split the money. For example, if they split the $1000 with a family member who was voting for the same party/candidate, that's all it would take to gain the lead.

Also, consider the difference in fundraising potential between the rich and the poor. For example, in the 2016 US Presidential Election, Bernie Sanders ran what I believe to be the most successful citizen-led fundraising campaign in US political history, raising approximately $228 million:

https://www.opensecrets.org/pres16/candidate?id=N00000528

In contrast, in the same election, just the top 23 super PAC donors alone spent a total of $468 million:

https://www.washingtonpost.com/graphics/politics/superpac-do...

So the most successful crowdfunded campaign in history was outspent by just 23 people.

I don't know if you were a Bernie supporter or not, but I hope you'd agree that he was a candidate that people were strongly behind. However, due to the income inequality in the US, the difference in spending power is massive. It's not a matter of the general public wanting something badly enough, $228 million is a clear message that the want was there.

The only caveat with all this is that not all the super PAC money would've been spent for a single party. However, the majority would've been spent supporting corporate-friendly candidates.


Spending a million dollars represents a lot of effort. Even if you're rich.


Represents a lot of effort in what way? Certainly not in terms of time to spend or earn it, both of which can be achieved in less than a day. Also consider that wealthy individuals are already spending a lot of money in elections. For example...

http://www.huffingtonpost.com/entry/super-pac-donors-2016_us...

"An analysis of 2016 super PAC filings shows that the 257 donors giving $500,000 or more have contributed a total $709 million."


It's not, anybody can write a bullshit paper today. There is a reason this hard won democracy exist and why we dealt away with lesser systems where less people are in power.

The author of the papern should go visit North Korea or Saudin Arabia and perhaps live there if he thinks the majority is tyranising him with their voting rights.


Wait, this argument makes no sense. It wasn't until 1950 that we had game theory to analyze voting systems directly, and it wasn't really until much later that people looked at more efficient systems. It's not hard to show that the 1-1 voting scheme is pretty useless in that its Nash equilibrium isn't guaranteed to be reflective of the population's general desires.

So, fine, while the current form of democracy may have somewhat worked until now, that definitely does not imply that we reached an optimal voting system. If we can make the world a little bit better, why not?

(This paper looks interesting, but, of course the devil is in the details of implementation; would I personally want this system? No idea.)


Well, why wouldn't it make sense?

People were governed and had different levels of say through the history.

Perhaps the most extreme example would be the French Revolution where the aristocracy had more votes per person than the common peasant, and we know whose heads rolled afterwards.

The problem isn't game theory. The problem is that power attracts certain personalities that are not altruistic. The current iteration of having say in common decisions is explicitly trying to curb the maniacs from reaching/staying in power.

> If we can make the world a little bit better, why not?

Sure. But right now, will Trump sing Kumbaya, or is USA regretting the decision? If it was 40-40, imagine him buying 20% of the votes.

"Many forms of Gov­ern­ment have been tried, and will be tried in this world of sin and woe. No one pre­tends that democ­ra­cy is per­fect or all-wise. Indeed it has been said that democ­ra­cy is the worst form of Gov­ern­ment except for all those oth­er forms that have been tried from time to time.…" - Churchill


> I don't believe we are close to having a voter base that is capable of understanding, and hence accepting an outcome of such a voting system.

Completely on point. Especially true of the American public.

Getting people to migrate to this scheme is a huge problem. Today in America, voting is a right. However, to many, it appears to be a financially free activity as well. Or some may tie it in with "you get to vote if you pay taxes". Regardless, this "pay into a fund in order to vote" won't really go well -- we already pay a fund (taxes), and it's distribution is mishandled / non-optimally allocated / gamed by people in the system.


But the poor will (most likely) receive money in this scheme. This can be an incentive for them.


But that's where it all falls down - the poor in america are most likely not to understand why they need to "pay more" to vote when it's already "free"!


Well very few understand the the current US system so complexity is hardly an argument.


It doesn't matter how many people understand it, but how many people think they understand it - from what I've seen, a lot of people think they understand the US system (at least they did, until Trump won with a minority of votes :P )


I don't think you have anything that backs up whether most people think they understand the US system. And even if they did they would agree it was complex (which was the claim I was responding to)

It's the change that make it hard to implement and it's not just in politics but in most things humans are involved with.

We accept what is as the norm because we grew up with it.


Would you trust a voting system you don't understand? More people think they understand the current system then a new more complex one.


Thats a different discussion. The claim was the complexity alone was the issue which its clearly not. A much bigger issue is the change itself. Even if we did a simpler system that everybody understood it would be hard to convince people to switch to it.


Is this a fair system? It looks to me like the very wealthy get there own way.

Let's say I'm a very wealthy person, and I have $4M to spend. It looks like I can buy 2000 votes. However, money is very fluid. So I decide I'm going to find 10,000 "budget-constrained" voters and give them each $400. I'll say, "Here's $100 for buying 10 votes, and keep the remaining $300 for yourself." Now I've just purchased 100,000 votes.

Ah! ZenoArrow (https://news.ycombinator.com/item?id=15206589) beat me to it. Well done.


If we have a system that allows you to buy votes from other people, how is that any more of a flaw than simply using our current method of voting and allowing the same type of vote buying?

It sounds like you are saying that a system that allows you to buy other people's votes skews toward rich people. We don't outright allow that today unless you count advertising. With the quadratic system proposed, rich would have to choose between advertising or putting more money into the voter pool (is distributed to everyone and thus increases the voting power of the poorer majority).


In this system rich people have the opportunity to buy a couple of extra votes for (e.g.) everyone who has been a member of Party X for four or more years. Unlike the present one-man, one-vote system, they can swing the election in favour of their cause without changing a single person's mind.


That's such a super obvious flaw. I felt I must be missing something because nobody else was talking about it.


Noone is talking about it because the fix is obvious: If you have secret votes then you can just take the money and vote the other way.

Which is what prevents this today.


The only way I can see QV might work is if each voter was given the same amount of voting credits, which could only be used for voting. On the surface, it seems to me that this degenerates into the one-person, one-vote system.

If real money is allowed, then the very poor are completely disenfranchised. Many don't have enough money to put food on the table, never mind spending it to vote. That gives the wealthy a huge advantage - more so than they have today.


Besides it being illegal to buy votes...


Yeah. People can talk about the influence of campaign spending on elections all they like, but campaign spending only works if have arguments (good ones or otherwise) that persuade people to change their voting intention.

Here, you just buy extra votes for a block of people you have good reason to believe already intend to vote your way, and the net result is very much in your favour.

The only way this works is if you're giving everyone credits to spread between multiple known issues according to their priorities (and even then interested parties can theoretically trade votes on the side)


For what its worth, I thought your explanation was helpful in highlighting how organised voting blocks could game the system even more effectively. :-)


> Majority rule based on one-person-one-vote notoriously results in tyranny of the majority–a large number of people who care only a little about an outcome prevail over a minority that cares passionately, resulting in a reduction of aggregate welfare.

Calling the majority tyrannous and assuming fringe interests to be naturally benevolent reeks of an agenda.


That’s a phrase, well-accepted and very famous in this domain. https://en.m.wikipedia.org/wiki/Tyranny_of_the_majority

Please don’t insinuate bad intent where there needn’t be any.


The suggestion being made is that the unwashed masses don't know what's best for them, and need to be guided by the enlightened minority. The problem with this is that there isn't a minority that's fit to lead. No one group fully understands the needs and wants of a society. That's why, as imperfect as it is, it makes sense for every citizen (of voting age) to have an equal say in how a society is run.


The phrase "tyranny of the majority" does not usually refer to an unenlightened majority making suboptimal decisions for itself (and therefore requiring the rule of a more enlightened minority).

It more often refers to settings where a majority and a minority have conflicting interests, and in which the majority is inclined exploit the minority in ways where the damage endured by the exploited far outweighs the benefit to the beneficiaries. The phrase has been uttered: "Democracy can be like two wolves and a sheep deciding what to have for dinner."

  EG:

 - A majority of city-dwellers will vote to destroy the homes of the forest people to improve the development of their cities, however slightly.

 - A majority of old people will vote to tax the young more heavily to achieve a transfer of wealth, even though the gains of each beneficiary is smaller than the loss of each loser

 - That same majority of old people, finding that their preferences in nearly every domain are different from those of the young, might vote to raise the voting age.

 - ...


> "It more often refers to settings where a majority and a minority have conflicting interests"

Look beyond the surface level. If you can't trust the majority to make the right decisions, who do you trust to do so? The only reason to bring up the tyranny of the majority is to imply that another (smaller) group could do it better.


Good question, but although I'm too stupid to come up with an answer, I hope there is one, because the whole majority-exploiting-the-minority scenario sounds awful.


>The suggestion being made is that the unwashed masses don't know what's best for them, and need to be guided by the enlightened minority.

An enlightened millionaire minority, by the looks of it.


I also thought that it was ironic. He does mention a valid flaw in the one-to-one voting system. I wonder if quadratic voting, in practice, encourages extremism. It also offers more choices, so more time spent thinking, and less easy to make a choice. Perhaps it discourages voting for those who care just a little.


I thought that the article did a good job of explaining that the goal was to allow people to weight their votes based on how important it was to them. In other words it would give people the ability to decide how much they wanted to invest in the outcome. With that money distributed to the voting pool, not investing in a particular decision because they don't have strong preference results in acquiring resources that can be used to invest in other decisions where they do have a strong preference.

I'm not saying it is a good idea overall. Just that while it looks unfair when just consider how the votes are purchased, things look much fairer when you consider that the money used to purchase votes is distributed evenly back into the system.

I'm not sure it would work well for the US government, but it seems like it might work very well for other organizations--for example stockholders in corporations.




Why would you ever pay for an additional vote yourself, instead of giving the money to someone likely to vote in your favor? If you want 50 votes, just give 3$ to 1/p * 50 people with a p probability of voting for the thing you want. 1/p * 150$ is almost certainly massively cheaper than 2500$.


Because the people you pay could just take the money and then cast the (secret) vote the other way. Secret voting is what prevents buying votes today.


Could. With a better choice you can get a better chance: 1. Take an organization working for your cause, 2. identify a subset of org members you assume to be zealous enough for your taste 3. give all of them some money

Now: Your vote can be bought once Then: Your vote can be bought arbitrarily often with diminishing returns.


On the other hand, advertising is something like a means of buying votes. But the authors have assumed the possibility of influencing other voters away.


Hmm, but what if "a minority that cares passionately" are nazis or religious fanatics or some other extremist group? They fit the description pretty well, and just being a minority doesn't validate your ideas or views automatically. This system would, as a side-effect, effectively give more political leverage to all extremist groups out there, too.

In many European countries ethnical minorities are given a few guaranteed seats in the parliament to ensure that their voices are heard. The same could be done for a wider spectrum of minority groups that are of interest to society, selectively boosting their political influence, but still filtering out the crazy ones. Problem with this is that it's not as stable as giving everyone the same rights unconditionally, as it's much more prone to manipulations, like cutting deals with minority representatives who got elected without voting and making wide coalitions with them in order to take over the power, against the will of the majority.


I think you actually have it back to front at least in the most extreme example. Suppose group A strongly wish to do horrible things to group B, expel/exterminate/incarcerate, whatever. A might care passionately, but B's lives are at stake, they care even more about the issue. A wouldn't actually get their way unless they are the majority.

As long as one group's actions are considerably detrimental to another, that other group will care.


A could be a big enough threat that B will buy a lot of votes.

In a way, A can blackmail B, because the money gets distributed later (A will get a lot more back than they put in, because B bought an unnecessarily high amount of votes).

Is this scenario acceptable?


The real problem is that there is a tyranny of sorts involved, whether by the majority or the minority is not really all that important. Consensus building should be the norm, not to ram your view down other people's throats because you can.


We can't have genuine consensus until people reason with arguments and facts, instead of emotions. And emotions are currently extremely manipulatable. The entire media ecosystem is built around doing just that.


That's why school subjects like media studies and civics aren't bullshit wishy-washy ones, they're essential for getting us out of this rut. We should teach the young how to be better citizens than we are by equipping them with the tools to see through propaganda and to help them set the direction they see as best for their country.

Also, there should be room for both rationality and emotion in public debate. Emotion is a key part of the human experience, making decisions based on rationality alone will stop us seeing why certain rational decisions should not be followed.


I'm fine with that as long as they're not used for indoctrination. I.e. Every single issue and previous decision by society needs to be "re-decided" by the children in the civics class, without influence by the teachers. If you're not doing that, you're reinforcing previous generations' biases in the form of indoctrination. It's a very precarious line to walk, and a very important one because you're dealing with innocent and impressionable minds.


Yes, it would be best to let the students explore the subjects with only a minimum of guidance. I'd suggest that for this reason it'd make sense if these subjects were not graded.


I didn't read the whole article, so maybe they address this, but instead of letting people buy votes with money, which favors the rich, why not allocate an equal number of special credits to everyone that they can apportion among different issues (still using the quadratic system, if that there are reasons to think that is optimal)?


Interesting idea. The difference I see is that with the payments, the money goes back to the voting pool. So a rich person buying lots of votes for something they care about, gives money to everyone else which increases everyone's ability to vote with more weight on things they care about.


I suppose, although with the money system it seem like there is this crazy hyperparameter of how much a single vote costs. Plus, if you want to make things more economically equal (which is something we should want), you can do that with redistributive taxation. There are pragmatic considerations of what can get passed, but the same is true of voting reform. (Many people will make their decisions based on whether it will benefit their causes. This is why, for example, we have gerrymandering and left-right polarization on issues like making voter registration easy or allowing felons to vote or electoral college reform. General principles take a backseat, perhaps even rightly to some extent, to what one believes will lead to good outcomes.)


Vote cost is not a crazy hyperparameter: it's only an arbitrary unit of measure. If votes "cost twice as much" everyone buys sqrt(Xi/2) votes rather than sqrt(Xi), by spending a fixed sum Xi that depends on the utility of winning the vote. Results are unchanged.


Take note if you're thinking:

> Hmm, but what if "a minority that cares passionately" are nazis or religious fanatics or some other extremist group?

Then they cause an outcome by paying all the people that are not in the minority lots of money, and then next election the majority uses that money, more effectively per voter, to reverse the outcome.

If you think the median individual is rational enough to be allowed to vote at all (I don't), then the passionate minority still has to keep the majority happy or else they transfer large sums of money and therefore a larger sum of distributed-voting-power onto that group for future elections.

Understanding the quadratic effects and that the money is returned per capita is absolutely key to the beauty of it. Imagine 10 rich voters buying an election out of 1000 voters. They spend $10 million to do so. The next election, those 990 (now unhappy) voters, with the proceeds of the $10m money they received, can all buy many more distributed votes than the 10 voters were able to buy, and reverse the decision overwhelmingly.

So if you're really worried about this (and think voters are rational), just allow snap elections or votes of no confidence if there's enough protest, and the majority with their new dollars can right the ship very quickly.


I'm not sure the tyranny of the minority that we have now is any better.


Yeah, the minority of elected officials and bureaucrats. It's kind of sad seeing how little say the voting-populace actually has. Not only are they fragmented per-issue, but the entire establishment is built around not actually getting things done. E.g. Look at how Trump is not actually able to do any of the things he was voted in by the voting populace to do. What is the point of voting him in then? Either you want all of what he platformed on, or you want some of it and you're hoping that that "some" thing that he manages to do is the thing you actually want?

It's all bread and circuses, with the media running the circus. Just spend 10 minutes watching one of the big networks and you quickly realize it's all just rhetoric and bias, sprinkled with facts. No one reasons or argues, it's all just emotions and word-juggling. E.g. the recent "undocumented citizens" and "dreamers" double-speak when referring to illegal alien children under DACA. They're children, they're illegal aliens, it's not that hard.

Edit. Grammar.


If you think of the market as another democratic institution (albeit with another set of principles for what's considered fair), could this be a step towards addressing both? (A market is afer all just another way to try and select preferences fairly and effective)

I've long found it an interesting idea to allocate limited capital assets (aka land) in a similar manner, select best use (aka owner) through highest bid (aka vote), but offset the opportunity cost, and rent extraction, by expressing said bid in a rent paid as a public dividend.

Perhaps when discussin public policy decision by means of voting with your wallet it opens the door to also discuss market decisions as a democracy implementation.

(Oh well, I have a 58-page paper to read to see if this comment was entirely of topic)


The real problem is the winners take small American electoral system and the lack of mandatory voting.

Fix either one, preferably fix both, and I suspect people will stop proposing brain dead ideas like this.


> Weyl and Lalley prove that the collective decision rapidly approximates efficiency as the number of voters increases. By contrast, no extant voting procedure is efficient.

I'm assuming they're working within some mathematical formalism where efficiency is defined in some manner, but I can't access the linked paper. Can anyone explain what efficiency means in this context or provide some links to the mathematical framework for this stuff?


Efficient usually refers to Pareto efficiency. Sometimes (rarely) Kaldor-Hicks efficiency or "no deadweight loss" efficiency


At a cursory read, this is similar to Demand-Revealing Referenda / Revealed Preferences, I think? http://stumblingandmumbling.typepad.com/stumbling_and_mumbli... https://rwmj.wordpress.com/2014/03/27/half-baked-ideas-deman...

I love that there are so many better ways to vote, and I hate that we still use FPTP.


Does anyone know whether this has any effect on Arrow's Impossibility Theorem? Or does it violate some assumption, making it a separate (but related) issue? (Of course a theorem is a theorem, so it's not going to invalidate it...)

I'd assume that this paper is written by someone who has intimate knowledge of AIT, just looking for some perspective.


AIT applies to:

- Votes with at least three options. A simple majority vote between two options does in fact satisfy all of Arrow's fairness criteria (if only vacuously).

- Ranked voting systems, i.e. ones where voters only give a rank ordering of their options, not any more information.

Quadratic voting is neither of those: It applies only to binary decisions, but for those decisions, it tries to be more fair than Arrow's criteria call for, by getting out not only information about which option voters prefer, but how strongly they prefer it. Whether it could be extended to more complex votes than binary ones, I don't know.


One question that remains for me other than whether this is fair to groups with income <x>, is: how do you decide which proposals to vote on? Otherwise, there'd be incentive to submit ridiculous proposals that greatly disadvantage the wealthy, who would then have to pony up to keep those proposals from being implemented.


Allow me to shine some light on the title:

What does the general population think if aristocracy is about to buy back it's way to power?


HN thread from two years ago, featuring participation from the paper's authors:

https://news.ycombinator.com/item?id=9477747


It only favors extremists and extremely rich over the normal democratic process. But since the US is already an oligarchy, it makes sense for them.

And it's of course a cheap take on the tragedy of the commons.


How does it work?

If there is say - Aerith and Bob running for president, say there are Charlie and Drako that want to buy two votes each for Aerith.

Do they each pay 4 or do they pay 16?


They each pay 4.

Otherwise, a marginal vote purchased by a different voter would change the total price of prior purchased votes. If votes were tallied per candidate, voters would bid without knowing how much they owe until after the election.


Can't this be used for a direct democracy where all the population can vote directly on issues instead of voting representatives? This essentially makes the people the legislative branch of government. Now scale this decentralized system globally and we've got ourselves a planetary civilization.


So basically a basic income scheme financed by people with financial interest for the law to be one way or another.


I would like to see how this compares to exponential voting.


This is certainly an intriguing and creative proposal.

But as the paper notes, it is mainly around referendum voting. And referendum voting can be viewed as opposed to representative democracy. Voters will happily vote yes on one referendum for higher benefits, and yes on another referendum on lower taxes, and the end result is laws that don't make sense. This can be seen as an example of the Condorcet Paradox [1]. But the point is, referendums are generally a terrible way to make decisions.

So on page 45 of the paper [2], the authors discuss that democracies are generally run according to representation, not referendums. So first they suggest using QV to elect candidates. Yet when given a choice between 2 (or even a handful) of candidates, do we really expect QV to make a difference? Republicans and Democrats are both extremely passionate, so I'd call it a wash. There's such a mix of social and economic issues large and small, QV doesn't seem to help untangle that.

The second thing the authors suggest is for representatives to "put their constituents' money at stake" when voting on laws. The authors wisely don't go too deeply into this, because it's clearly nonsensical when representatives are from a district which contains significant members of both sides. They actually admit as much ("QV in representative assemblies would probably make more sense in a parliamentary system than in a presidential system") but actually get their terminology wrong -- it would make more sense in a proportional representation system than in a first-past-the-post system. (Presidential/parliamentary refers to the relationship between the legislature and the executive, which this proposal has nothing to do with -- which reveals their amatueur-ish level of analysis in this case.) At least they're honest in saying "many details clearly need to be worked out".

But I have an even more basic question, even for deciding referendums: who determines the base price of a vote? If a single vote cost $0.10 or $100, I imagine that could drastically affect outcomes, and I don't see them address this question anywhere.

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

[2] https://poseidon01.ssrn.com/delivery.php?ID=2871141120741160...


What's the reasoning behind choosing the power of 2 for this?

It could be tuned to a power of 1.9 or 2.1 or 3 or 1.5.

Aside from being a round number, how do we know 2 is best? What would be the pro/con of a higher exponent? What about the pro/con of a lower exponent?


As the paper's abstract states, "Quadratic cost uniquely makes the marginal cost proportional to votes purchased". The full paper shows their proof and the assumptions behind it, such as "an individuals’ value for votes is likely to be approximately linear in the number of votes she casts so long as her utility is driven by the impact she has on the vote total, as argued by Mueller (1973, 1977) and Laine (1977)".




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