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Quadratic Voting (2014) (ericposner.com)
210 points by evunveot 695 days ago | hide | past | web | 151 comments | favorite

The equity issues you all are raising are very important, but death with in detail here: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2343956. The simplest solution is just to use an artificial currency that everyone is given equal amounts of but can spread over the decisions most important to them. In this piece with Rory Sutherland we discuss this: http://www.spectator.co.uk/features/9512322/humans-are-doing...

There seem to be one big issue with this voting system. It allows variable number of votes per individual but how does an individual choose how much cost to take and exactly how much to vote? I think it is a fallacy to assume that individual would set the number of votes depending on how important they think is the issue. Instead they must speculate how others would vote and optimize their cost accordingly. For example, an individual may depend on wrong information to arrive at conclusion that everyone is in agreement with him/her sentiment and decide to spend less even though they deeply care about specific outcome. Mean while a small group might be secretly conspiring and spends huge sums to win their desired outcome. I would suspect that this voting system would promote speculation based market which can be easily manipulated by either asymmetric information or incorrect information by a small group.

Another thing to think about is too many small minority groups. So for instance, assume there are N questions to vote for and for each of these questions, we have a significant minority group that deeply cares about specific outcome. At some point, because of required increased expenditure, wouldn't votes for all questions favor minority sentiment?

I think we have to understand that while there is a dark side to "tyranny-of-majority", there is an important bright side too: It shields from scenarios where small group of radicals take over the system because they deeply care about their ideas that are not good for majority.

People in each minority group will also care about issues outside their group. Gun owners care about safety net levels. Gay people care about the environment. Family-values types care about crime. So people won't use all their credits or dollars for single issues. That is the logic of the quadratic function; marginal votes even for something you care a lot about will be too expensive unless used for something else.

They address this issue in the paper, "Voting Squared: Quadratic Voting in Democratic Politics", page 32:

> QV works best with a large number of voters: the more voters there are, the more accurately the system works. QV’s efficiency relies on all voters perceiving the chance of their changing the outcome with an additional vote as the same. When the number of voters is large, such a perception is (approximately) accurate. If it is small, it is less so. With a small population, it becomes possible for people to have different perceptions about the likelihood that an additional vote will change the outcome (that is, the likelihood that there would otherwise be a tie, in which case an additional vote is pivotal). For example, in a small group that consists of a number of moderate voters on one side of an issue, and an extreme voter on the other side, the extreme voter will believe that a tie is less likely than the moderate voters will believe. The moderate voters assume that all voters are (on average) moderate and so discount the possibility that anyone is extreme, while the extreme voter knows that this is not the case because she knows that she is an outlier. If the extreme voter cares more about the issue than the moderate voters in aggregate, she will buy fewer votes relative to her utility than is socially desirable and QV will suffer the same bias towards the majority that other democratic procedures entail, though in a less severe form. If the situation were reversed and the extreme voter cared less than the three others in total, a reversed failure could occur. The three voters are overconfident and expect to win easily, but the extremist knows that, because of her strong preferences and thus her willingness to buy many votes, a tie is more likely than it appears. In this case, QV could lead to dictatorship in the same manner as standard vote buying. Despite this, simulation evidence indicates that QV almost always outperforms majority rule.

You are absolutely right that QV can create speculative dynamics like a market place. Almost everything about QV is similar to the market mechanism. But do you really think that there are many cases where you would prefer rationing, effectively what one-person-one-vote does, to a marketplace? Marketplaces are imperfect in all sorts of ways, but few think communism worked better. Markets have natural self-correcting features that rationing does not. While speculation can occur, it creates natural incentives for those on the opposite side to offset it. I discuss this in some quantitative detail in this paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2571012

For people, who are new to HN, do not use downvotes to express your disagreement with author. Use them if the comment was off track, spam, bad mannered or in general not adding any value whatsoever.

That is what I thought as well, until this thread happened https://news.ycombinator.com/item?id=9237644 Apparently it is the official HN policy that up/down voting is for agreement/disagreement. :-(

And downvoted posts become impossible to read unless you use a custom CSS.


Then I wonder why HN sounds like a cult on some subjects...

@dang, if you're listening, I think this may be the majority perception (it was certainly mine). At the risk of a giant, raging debate, it may be worth starting a long-running discussion on this amongst the HN community. Possibly with real voting and everything. Dare I suggest - quadratic voting?

Hi Glen, I mentioned this in another comment, but copying here because I'd like to hear your thoughts on it:

> If enough people are participating in a vote, then the cost of voting (e.g., research + going to polling station) outweighs the benefit (possibility of changing the outcome). The cost of voting is roughly fixed, while the benefit decreases rapidly as the number of participants grows.

Does quadratic voting address this, or are there other ideas you've heard of that address that problem?

Fantastic question. QV does not really address this much; at a quantitative level you are right that it reduces the problem a bit, but you can't beat those asymptotic properties you highlight. The right solution is representative bodies (or random samples). Great work on this by Jerry Green and Jean-Jacques Laffont: http://link.springer.com/article/10.1007%2FBF01718517?LI=tru... If you make the set of deciders smaller this starts to go away. This is arguably the fundamental justification for representative rather than direct democracy. There is a nice property we believe QV has that we (myself and Richard Zeckhauser) are working to prove which is that if you have representatives elected via QV and then those representatives use QV to vote you get efficiency in a hierarchical fashion. So while I don't think QV directly solves this issue, I think it fits nicely into a broader system that does.

Thanks for answering my question! I hadn't thought of using random samples. So maybe a good solution is QV for representatives, with only a small random sample of the population being able to vote. The representatives should also use QV, of course.

I just read a big chunk of your paper "Voting Squared: Quadratic Voting in Democratic Politics", and I really enjoyed it. For a long time I've wanted to do an open source project related to characterizing an optimal government, or at least simulating the outcomes you could expect from different types of governments. If you know of a useful way to go about doing this I'd love to hear it.

By the way, I reside in a coliving space with 50+ people, and we've struggled with voting on certain issues that minority groups feel strongly about. I will definitely be suggesting QV!

And in this moment, VoteCoin was born.

How do you mine it?

The "artificial currency" would ensure votes accurately reflect the importance an individual attaches to an issue relative to other votes, but in practice this gives significantly more "voting power" to groups which seldom participate in votes, even where it is difficult to believe the intensity of their preferences are stronger. Given a fixed budget to be used over a number of votes, an essentially apolitical person told by their community leader to use all their votes in opposing a particular issue they know little about will have more influence on the outcome than a highly-informed, politically-motivated and civic minded regular referendum participant, yet it's difficult to argue the absolute intensity of the preference of the regular voter is lower (this is of course related to the standard welfare economics criticism of cardinal utilities).

This isn't a problem if the individuals apportioning their vote budget are similarly-highly-motivated legislators prioritising from a known raft of policies whilst being well informed about which initiatives are most likely to meet with strong opposition (though it significantly advantages parties able to coordinate the efficient distribution of their votes). Probably they can handle the complexities of a voting budget that compensates the losers too.

But for a broader electorate that doesn't excel in performing stochastic optimisation problems, doesn't have good intelligence to help them vote tactically, doesn't know what future votes might be, the quadratic nature of the voting system doesn't deal with the problem of budgeted and secret voting being a game of iterated prisoners' dilemma; it might even intensify the problems.

It's not too difficult to devise a scenario in which it actually makes the "tyranny of the majority" problem worse: a minority of bigots wish very strongly to enact a law against a minority of regular targets. The disinterested majority wishes to avoid diluting their future voting power by participating, whilst the victimised minority wishes to hold back some of their voting power to avoid being disenfranchised when faced with conceivable future bullying initiatives[1]. In a secret ballot, the bigots can conceivably win if the groups are a similar size (even if they can subsequently reverse the decision)

[1]This is mitigated if the losers get their own votes back as compensation, but actually worsened if they get higher compensation, in which case optimum strategy in a iterated electoral battle is to win by the narrowest possible margin, whilst voting for something incredibly unpopular is a practical way to increase your future influence.

I cannot completely follow this scenario, but if you can write it up as an actual equilibrium analysis I would be fascinated to see this. I have worked very hard to come up with cases where QV does worse than one-person-one-vote and have never found a case where it occurred by a significant margin. But your basic point, that allowing exchange with a broader set of goods to make sure that if all voting is more valued by people they can have more overall voting influence, is something I very much agree with and why I think that while artificial currency is an improvement over one-person-one-vote eventually using cash will be better.

To be honest the premise of my argument is that a static equilibrium wouldn't be reached given uncertainty about others' preferences, risk aversion and a multi-stage game, but here's a simple edge case scenario

Imagine a scenario in which there are N Jews, N neoNazis (for simplicity: example works if the Jews simply believe the number of Nazis is approximately equal) and yN ordinary citizens. Each individual in those groups has an equal budget to distribute between initiatives V(1)...V(X), where X > 2.

neoNazis desire a "yes" vote for both initiatives V(1) and V(2) - let's call them "internment" and "pogroms" - so strongly that they are (or are believed to be) willing to forego all votes on initiatives V(3)...V(X) to pass them

Jews have similarly strong views on not being interned or the victim of pogroms, but in the absence of adequate information on how the neoNazis will use their votes cannot be assured of allocating their voting budget between V(1) and V(2) in a way sufficient to negate the votes of the neoNazis on both issues. (Note also that the existential threat posed by V(1) and V(2) sitting on the [future] referendum list also deters the Jews from using part of their budget to influence votes on V(3)...V(X) in ways which might improve their individual utilities)

If ordinary citizens have a preference for a "no" vote which would be sufficiently strong for them to vote against it in a regular referendum, but insufficiently strong for them to allocate voting budget that could otherwise purchase decisions on initiatives V(3)...V(X) the moderate majority will not provide the same bulwark against extremism as they do under a 1 person 1 vote system. If all or most Jews decide that pogroms are significantly worse than incarceration and are sufficiently risk averse to warrant allocating all their budget to eliminate the possibility of an equal number of Nazis enacting V(2), it's surprisingly easy and inexpensive in terms of voting budget for the Nazis to pass V(1). The only way I can see the Jews avoiding both initiatives being passed is to put the neoNazis on the defensive with an equally vicious anti-Nazi counter-proposal - assuming Nazis can be targeted as effectively as Jews - but I'm not convinced that mutually assured destruction is the ideal way of resolving voting conflicts.

Unfortunately, this also applies to less extreme examples where balloting is secret and intentions uncertain: in order to shift the Nash equilibrium of a particular proposal in your favour you simply raise the spectre of an [additional, and credible] proposal you anticipate your adversaries will like even less.

This is why there is a nominating procedure. I don't think this is a great forum for hashing this all out without a white board, but I would be happy to do it with a whiteboard. I think I could persuade you that there is no case where this can happen in an equilibrium of any model, including with uncertainty about preferences, risk-aversion, etc. to a significant extent and over a reasonable range of cases more than happens in 1p1v. One has to average over a reasonable range of cases to compare different systems. 1p1v can extremely easily lead to a nazi equilibrium as we have seen in practice: http://en.wikipedia.org/wiki/First_they_came_...

Glen good to see you around HN.

One question that comes to mind is whether quadratic voting is the best improvement. I look forward to giving this a read.

What Lalley and I (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2003531) prove is that QV is provably the only system of vote pricing that gives you efficiency always, so in some sense it is the best possible improvement, at least the best one that is robust. In more narrow circumstances in finite populations you can do better probably, but it requires a fair bit of detailed knowledge of the situation and a lot of complexity.

That Spectator piece is basically 100% false. Here's an explanation from a Princeton math PhD with expertise in voting system design.


With all due respect, it sounds like while it might fight flaws common to other voting systems, pay-back based voting will have its own gamesmanship.

Consider 1,000 voters upwind of a factory and 1,000 more voters downwind. Suppose the factory wants to stop scrubbing its exhaust for a savings of $1,000 (to itself) and cost of $10 to each down-wind voter (in health costs). All the factory has to do is propose the same initiative (to allow the removal of regulation) again and again and not vote that much. Each time the down-wind people try to protect their selves they transfer money to up-wind abstainers. After enough rounds of this the down-winders are impoverished and the factory buys the election cheaply.

Edit: and instead of voting large the factory could try to bribe the up-wind voters or a faction of the down-wind voters.

This is not an equilibrium; the down-winders would not vote unless they thought that vote mattered. In any case we have a nominating process to avoid this sort of manipulation; see http://ssrn.com/abstract=2321904 or http://ssrn.com/abstract=2343956.

My point is: it is a bad situation, equilibrium or not. And some down-winders have to vote if the factory votes a little bit each time. Or even if the factory threatens to vote (and then doesn't). If all the magic is in the nominating process- then we really don't need the voting mechanism.

Agreed, but what I mean is it can't happen.

If it's not an equilibrium then it can't happen! That doesn't make the claim foolproof or anything-- maybe it's not actually an equilibrium for one reason or another we didn't foresee, but the phrase "it is a bad situation, equilibrium or not" is nonsensical.

Assuming that the proofs make perfect assumptions that exactly match real life, sure.

"the down-winders would not vote unless they thought that vote mattered." - this decision requires mental resources to make, and if the rational choice is too complex then many people wouldn't make it, breaking your assumptions.

Is there any research that tries to model the economic cost of coming to a "rational" decision (as defined by the voting game)?

Yes, in this paper (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2571012) I also consider the case where people make mistakes. You can study equilibrium even in models where people are not perfectly rational.

The paper covers this. The solution is to force a commitment of votes before you can propose a vote on an issue.

So factory votes $1 each time (small commitment, forcing some fraction of the down-winders in unless they can form a coalition).

...as in an actual financially significant amount

Setting that amount to something that's actually a barrier and allows for grassroots movements to actually participate could be quite difficult.

Possibly, but it's an alternative that could have promise and is worth experimenting with in more contexts as the paper suggests. Such experimenting could disprove its utility and we on with the systems we currently have, or it could show promise and we keep experimenting with it in more and more contexts.

Just because it could be gamed is not a reason to wholly dismiss.

Yes, but every time the factory proposes that initiative the 1,000 downwind voters can also counter-propose that the factory continue to scrub the exhaust AND for the factory to pay $1,000 to some initiative they do support.

The 1,000 downwind voters collect 1,000 votes of the counter-proposal and the factory has to either make up the cash for 1,001 votes or implement the counter-proposal. Whichever is more economically viable for the factory.

I would expect the formation of a "union" of down-wind voters. They pool their money, and one person votes with it all.

It seems important to distinguish between actually voting, where everyone votes or has a chance to vote (at near-zero cost), and lobbying for individual legislation, where only the very highly-motivated "vote", at high cost.

In the latter case (lobbying), most people seem to believe that small groups exert too much power over the process. But that's entirely because the majority have essentially zero influence. If some small industry has an intense preference for a special tax break, they would easily be defeated if everyone else expressed their mild disapproval. The problem is not that the rich get too many votes, but that the first vote is too costly.

In ordinary voting, the opposite situation is more likely. A small group of people are very passionate about some issue (gay marriage, drug liberalization, environmental protection), while the majority doesn't know or care very much, but is slightly negative on average. In that case, the weak preferences of the majority win out, giving an inefficient outcome. This is where Quadratic Voting could help.

People will be more likely to vote in the first place because they can exert greater influence over the outcomes they care about (say, gay marriage). Once in the voting booth, they can use marginal votes against things they oppose but less passionately (say, farm subsidies). Of course, there are complex design issues--just how much should people vote about, and should a representative system be used instead. But on balance QV should motivate people to vote more not less.

Their startup: http://collectivedecisionengines.com/ seems to give decision makers X units of currency and then refund them the average outlay.

It seems like it would have failure modes in communities w/ transient populations. As in, if you give me 100 units, I'll buy 10 votes and know that I at least voted as much as I could. But in conditions where you have a fixed community it could work well.

Clearly in the real world if you have 100 credits, a Koch brother would have ~100 million credits... Bill Gates ~200 million credits... (based on US median net worth of $44,000 vs their respective 42billion and ~80billion)

But there are plenty of decisions to be made that could be done with fake credits in a controlled environment.

If a Koch brother really wants to use up $40 billion on voting, he could put 200,000 votes on a single issue. If everyone opposes his position, he could be easily outvoted by a small town of low-income people casting a couple votes each for a few dollars. They would also get nearly all his money.

That is quite true, the redistribution on the backend after the vote would be amazing. :D

People in North Africa have been doing this for a while now.

When I was kid we had a congressman where I lived in Morocco who win a election with a strategy similar to a quadratic voting. His team went to the poorest neighborhoods of the district and they distribute half (literally half the bill) of today equivalent of 20$ and you get the rest after the election, it had cost him roughly around 100k$ and he won. From the power he got he had made a lot more and been able to invest again in his own district and get two more districts for his son and brother in law in the next election... this is a bad idea at least for the poor.

The point is you need an independent third party to establish a fair market value for the votes otherwise the poor will be ripped of...

I still prefer approval voting over it:


1) elimintes the spoiler effect problem

2) most "approved"/liked candidate can win, not necessarily the most "popular" within a certain group

3) gives lesser known candidates/parties a much better chance to compete and rise up against the incumbents

4) statistically proven to be one of the voting systems with the least remorse

5) very simple (essentially HN style voting)

Range voting could also work, but it's debatable whether the extra "scores" are worth the loss of simplicity. Range voting also seems to have a bigger degree of regret, although it does seem to do slightly better with electing the "ideal" candidate.

The non-garbled link is www.electology.org/approval-voting

> Range voting also seems to have a bigger degree of regret

No. It has the lowest regret of any commonly discussed system. http://ScoreVoting.net/BayRegsFig.html

> although it does seem to do slightly better with electing the "ideal" candidate.

Lower regret = more ideal candidate. So you just said a contradiction.

I'm interested to know what the authors think about the problem that could be called vote splitting or support buying, which would be akin to vote buying in one-person-one-vote system. This seems particularly relevant because, unlike most systems, buying the support of small numbers of voters could be useful.

Consider the case given elsewhere in this thread of 10,000 voters willing to pay only $1 against a proposal, and a single supporter. That supporter would need to pay over $100m for the measure to pass, giving each person against it at least $10,000.

Now suppose that person takes their $100m, and only purchases $25m worth of votes. They find someone else, and transfer $35m to them with the agreement that the person will buy $25m in votes, and keep the remaining $10m. A person who is only willing to vote $1 against a measure is unlikely to turn down such a deal, but it saves the lone supporter $40m.

It seems like it would be very difficult to police this, as the transfers would not necessarily need to be direct. For example, verbal agreements between the one wealthy, lone supporter and nine opponents that those opponents would get contracts in the future worth $1m each would be hard to notice, but would save the supporter $90m. An employer could give bonuses vaguely tied to the success or failure of a measure, and so on. And in all of these cases, the savings are so extreme that vast amounts could be spent hiding the fraud.

Even without buying the votes of opponents, it can be very beneficial for wealthy, motivated supporters to transfer money for voting to poorer or less motivated supporters, to move closer to the optimal funds arrangement (all amounts equal). In some cases, this could be almost indistinguishable from legitimate behavior, and would lead to all sorts of claims: is a philanthropist giving money to the poor to help them live, or to support her social agenda?

In a one-person-one-vote system, buying the votes of individuals requires mass fraud to have an impact. In QV, however, every doubling in size of a group that votes optimally doubles the number of votes they can buy at the same total cost. Thus it seems like small, motivated groups have a very, very large motivation toward fraud, while that fraud could take place at an extremely small level that would be difficult to detect. This doesn't even need to be organized: it makes sense for even a single motivated supporter to go out on their own and split their vote with one other person, perhaps a close friend of theirs.

This is a great question and one of the central ones my analysis addresses (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264245). You can read the results in details for the general guarantees, but a few observations about the scenario you describe. First, doubling group size at worst increases by a factor of the square root of two the number of votes you can buy with the same amount of money. To double the votes you buy you would have to increase aggregate expenditures by the square root of two as well. Second, I disagree that these coalitions would be stable. If you gave someone $35 million, why wouldn't they just keep the full $35 million? Under 1p1v there is no incentive to cheat on the coalition...you get to keep your money regardless. Under QV there is a huge incentive to cheat on the coalition and it could be made even larger by giving bounties for ratting out to the police, which has been extremely effective in antitrust in breaking cartels. In fact the situation is extremely analogous to antitrust. Cartels do harm market performance, but I think few of us would, as a result of them, prefer rationing over markets.

> In a one-person-one-vote system, buying the votes of individuals requires mass fraud to have an impact.

More specifically, even if you do go to the trouble of outright buying people's votes, since secret ballots are generally considered the way to go (though they haven't always been, even relatively recently), it's extraordinarily difficult to have confidence in the value of your 'purchase' because you have no way of knowing if the person you paid off did it.

In this system, the scaling may make it a lot easier to identify that a person followed your directions and spent a particular amount on the vote...

We are actively working on the identifiability issue; Ron Rivest (of RSA encryption) is writing a paper for a conference on the topic trying to solve this: http://bfi.uchicago.edu/events/quadratic-voting-and-public-g...

Exactly, if we've already created a system where buying votes is accepted, why would I buy 1000 votes for 1000^2 money, if I might as well pay 1000 uninterested people 2 money each to vote the same way as I?

Buying votes is not accepted. Using the system would be accepted, but not buying separately. Why couldn't we create a norm where buying outside the system is just as punished then as buying outside the system is now?

I'm not saying we couldn't, just that it would be harder. Right now votes are thought of as something inherent to a person, similar to a soul. If votes becomes something people speculate in buying, isn't it likely that they'd start to speculate more than that?

Then again, it does sound like an interesting system to try, but maybe to be used for smaller decisions and groups first.

I couldn't agree more. Lots of social institutions would have to be built up around it to make it work. That is why we are starting on a small scale with market research.

> 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.

Notoriously? In actual practice, U.S. democracy and many others function the exact opposite of what is described (passionate minorities such as Iowa corn farmers and F-35 plane builders and M1A1 tank builders and various intellectual property advocates routinely beat unpassionate majorities, resulting in laws that are bad for most and good for a very few, decreasing overall welfare). The idea that the masses are voting themselves loot from the treasury over the objections of the noble elites is a fantasy that exists only in some libertarian heads, and never in the real world. I can't really read any further in this article. This is basic stuff.

How does this system deal with the logarithmic value of dollars, and the asymmetry in who has them?

When you get ln(X) happiness from X dollars, you are sacrificing 1/X happiness per dollar spent. A billionaire buying a thousand votes is paying ln(10^9 - (10^3)^2) - ln(10^9) ~= 1 milli-utilon, but a thousandaire buying ten votes is paying ln(10^3 - 10^2) - ln(10^3) ~= 100 milli-utilons.

It seems like billionaires, who easily get a factor of a thousand advantage in marginal votes-per-happiness cost over 99% of the population, will massively distort a quadratic voting market.

Uniformly redistributing the voting cost makes that effect smaller, but I don't think it overcomes the logarithmic effect.

Billionares are vastly outnumbered by thousandaires. For example, in an FPTP election their ability to buy 31600 votes would, nationally, let them move the 50 yard line, towards which politics converges, 0.001% to the left or right.

> Billionares are vastly outnumbered by thousandaires.

While true, the billionaires' liquid and un-accounted-for dollars vastly outnumber the thousandaires'. If Joe Average has to choose between voting on something and paying his mortgage, while Jim Squillionaire is choosing between voting and buying another jet (yes, hyperbole; my point still obtains), guess whose votes you're more likely to see...

I just explained why spending $1 billion on votes won't affect the outcome of politics, in the other sentence of my post, that you didn't quote. That's part of the reason the cost of votes is nonlinear in this scheme.

You didn't explain anything, you only provided a cryptic analogy.

Don't you have your square roots memorized? 31600 is approximately the square root of a billion. The U.S. population is about 316 million.

That is the point of the software!

That's easy to fix with a social security-like scheme that forces everyone to spend at least $1000 on voting.

I have never seen this log model for the value of model. In the plots I've seen, it always appears that the happiness peaks when you have around twice the money of your peers.

Do you have any references?

How would you feel about "exponential voting", which would be like quadratic voting but the cost is 2^N instead of N^2?

Exponential voting would be too close to 1p1v in effect, as we argue in the paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2003531

Most of the time, it's not the voting system that's the problem, it's the set of things you can vote for. Sometimes, you can vote A or B but you like neither alternative. Maybe you should be able to express your dislike too. A vote like "I don't care who gets elected, as long as it is not this specific person".

The ability to "negative vote", really should be a thing. Since the US system, in particular, is set up in a way that makes change unrealistic for the "common folk" it would be the only way I can think of for poor people to really get any disapproval across.

I completely agree. This is a crucial feature of QV with multiple alternatives. QV also has a nominating process to ensure the right things are on the ballot.

> 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.

Except in voluntary voting systems, where highly motivated voters dominate the apathetic majority.

Mandatory voting won't help as apathetic votes would be either distributed randomly or given according to preference having nothing to do with the issues, such as which candidate is better looking or which one appears more on a popular comedy shows.

You're speaking hypothetically, but the experience of countries with mandatory voting bears out that mandatory voting drives parties towards the median voter, not the fringes. It's called Hotelling's Law.

America and Australia have a lot in common, including that of people of eligible to vote, those who have religious aims are in the minority.

One of these countries is dominated by the politics of trying to enforce the laws of herders from thousands of years ago. And the other is not.

Motivated voters -- such as folk with a religious bee in their bonnet -- are highly over-represented in voluntary systems. In a mandatory system, the median voter dominates. That's generally a better outcome, because the median voter is more interested in Shit Just Sorta Approximately Working, rather than ultra-serious micromotives.

USA and Australia are very different politically. I have no idea what you mean by "the laws of herders from thousands of years ago", but if I venture a guess I'd assume you refer to the Judeo-Christian principles. That ye olde "do not murder", "do not steal", "do not perjury" stuff. If so, I'm pretty sure, unless I missed some recent developments, that both USA and Australia are still on board with enforcing those. As USA is about 15 times bigger than Australia, fringes are bigger too - on bigger sample, you get more place for exceptional outcomes to manifest.

> because the median voter is more interested in Shit Just Sorta Approximately Working,

Why this is a good thing? It is known that every hard problem has easy, cheap, understandable and incorrect solution. Or, as you call it, "Shit Just Sorta Approximately Working" but not actually working because of complicated reasons that median voter wouldn't bother to comprehend. So you get a lot of voting for shit that sounds good but doesn't work. How that's good for anything?

> the Judeo-Christian principles

It may shock you to learn that legal systems other than the Mosaic law have that "don't kill or steal" stuff. I was thinking of the more tasteless parts of Leviticus. In fact it was worked out and written down thousands of years before anyone was thinking about leaving Egypt.

Another name for it is "Judeo-Greco-Persian-Roman-Christian-Celtic principles", given the roots of the western culture which Britain transmitted to the colonies.

> Why this is a good thing?

Because it leads to a Benthamite political culture. Australian politics is either boring or depressing, American politics is either exciting or depressing. But the boring-or-depressing option leads to occasional outbreaks of good policy. Australia is one of the less-worse governed countries in the world over the past 30 years.

Neither side of politics needs to pander to a narrow base, except as mild lip service. So they tend to be centrist managerialists. Boring but sometimes effective.

> legal systems other than the Mosaic law have that "don't kill or steal" stuff.

It wouldn't shock me, but it so happened one that is in force in US and Australia draws largely from Christian law and moral traditions, which borrows a lot from Judaic tradition (not only, Roman too, some Celtic, very little Persian as far as I know). In other countries, it is different, but in those two specific ones that's where the roots are, that's just history.

> Australia is one of the less-worse governed countries in the world over the past 30 years.

How do you know that? Australia doesn't have the same problems the US has, by many dimensions, and is very different geographically, population-wise, traditionally and so on. How you would even compare the governance, on which basis?

> Boring but sometimes effective.

Effective doing what? I don't know much about Australian politics, I admit, but I know Australia has no freedom of speech - people were imprisoned or otherwise sanctioned by government for merely expressing various political positions. Or this one: https://wikileaks.org/aus-suppression-order/. But maybe the government is efficient doing something else than protecting basic rights - but what?

> one that is in force in US and Australia draws largely from Christian law and moral traditions

Nonsense. The Common Law doesn't take the Torah as a source of precedent, neither does it look to the continental law for precedent. The bible is useless as a source of anything other than motherhood statements.

It spends less than a page listing the "ten commandments", of which only 4 (killing, theft, adultery and false witnessing) are actually enforceable laws of social consequence.

It then goes on to spend pages and pages and pages listing interior decoration instructions for the Holy Tabernacle. Even a few scribbled pages of notes about common moral questions ("is killing in self-defence murder?", "do Moses's instructions to commit genocide override the commandments?") would have been helpful. Not a peep. It was left to Rabbis and Churchmen to make any sense of.

What does the Bible say about the common defences to a murder charge? Nothing. About the intricacies of trial law? Not a peep. The bread-and-butter legal issues -- property, trusts, estates, torts, duties, equity -- that occupy 99% of the daily life of the law and most of its positive value to society? Nowhere to be seen.

Any major actually-used legal system utterly ignores the Bible as a source of law. Probably because it was not written by lawyers.

> How you would even compare the governance, on which basis?

Very much a matter of opinion. But if I had to gamble on which country will be bankrupt in 100 years, I'd be asking to settle the bet in Australian dollars.

> Effective doing what? I don't know much about Australian politics, I admit, but I know Australia has no freedom of speech - people were imprisoned or otherwise sanctioned by government for merely expressing various political positions.

Actually, the High Court has consistently found that the Australian Constitution provides freedom of communication on political matters, starting with ACTV v The Commonwealth, proportionate to public safety.

I may be missing something, but it seems as though QV is associating how passionate a party (specifically a minority) is about a topic with the importance that their view be equally represented against an apathetic opposition. The problem inherent to this is lack of education of topics that will be well know to a minority party but unknown to a majority. The majorities ignorance is not the same as not caring, and the impetus to gain knowledge may not always be clear. Beyond this its seems like minority opinions no matter how impassioned should not become the center of debate merely because they have spent more money. The act of voting involves far more than the act itself as evidenced by the prolonged campaign periods in the US. The national attention span is short and is already dominated by the extreme and the rich.

As Marty Gillens argues in his book Affluence and Influence (http://press.princeton.edu/titles/9836.html), on almost every issue there is a sub group within those who feel a particular way on an issue that is highly informed about that issue and a subgroup that is less informed. 1p1v gives both groups equal weight while QV gives much more weight to the informed. This is much fairer, because the uniformed group will typically be easily swayed by advertising and manipulation to vote the other way, making groups with more uniformed people easily undermined even if there are some members that are informed and who could speak for this group's interests. This is a major problem in American politics: the poor often favor less redistribution than the rich do (again see Gillens)! So I actually think QV would improve the situation precisely along the dimensions you are highlighting.

Part of the real issue is identity politics and the black box thinking it generated.

Rethorical devices would still maintain the greatest power. You don't need information just conviction and resources.

Tyranny by majority is important, but I wonder if quadratic voting would address another important issue: if enough people are participating, then the cost of voting (research + going to polling station) outweighs the benefit (changing the outcome). The cost of voting is roughly fixed, while the benefit decreases rapidly as the number of participants grows.

Maybe if quadratic voting was used, then only people that truly care about an issue would vote, giving the individuals that do care enough influence to make voting worthwhile.

I feel like this could potentially work with "voting tokens" or something else that's not money. Maybe with some sort of crypto verification. You'd still have the scarcity that the system demands, but without the "inequality baggage" you'd start out with if the system were implemented with actual money.

If you implemented this system using money to buy votes, then you'd end up... well probably with something like the inequality situation we have today.

I think one feature of the system is that the accumulated funds are then distributed equally after the vote. With tokens, this would not be very useful, as if everybody gets the same amount tokens, there's no difference between getting one token and getting one million, tokens themselves have no value.

They have value when it's time to vote for something.

If voting tokens do not perish between votes, that leads to the similar inequalities if I abstain from voting for a number of cycles. If old tokens do expire, then it doesn't matter when everybody else gets the same - up to the limit of the quantization of tokens, how many tokens you have is less important than how much more tokens than your opponents you have . I.e. if there is a yes/no question, the important thing for you, if you favor "yes", it to have more tokens for "yes" than for "no", but how many tokens for each does not matter. In multilateral choice it's more complex but I think if you have enough tokens to not be limited to voting for one thing because you only have one token, it is again the same situation.

> if I abstain from voting for a number of cycles

The whole point of the system is to railroad people into only voting for what really matters to them, by "saving up" their votes. I think this isn't a flaw but a feature.

I'd expect that there'd be a fairly large number of tokens so that quantization wouldn't come into play too much.

Since QV appears, on the face of it at least, to be a single-round blind auction, why would it not be vulnerable to bad signalling and consequent price distortion? As another poster commented below, all players are blindly speculating on the real price of a win.

Take any vote as an example. One side announces they will pay a mighty sum (or have already marshalled a sufficiency) towards a vote Con to scare off those supporting an opposing vote Pro.

Pro voters may react either by believing this signal (and not voting/ buying in at all) or issuing their own claims - all are strongly incentivised to exaggerate their own preferences and strength of support prior to the vote.

Bad signalling is bound to occur AFAICT

1. To win the vote cheaply with FUD by scaring off both the apathetic (apathetes, let's call them that) and some percentage of the previously committed.

2. To punish the winning side financially (maximising Winner's Curse) in case of my side losing. This benefits the losers by weakening the winners as a precautionary measure for the next round of voting on some other issue too. That is, I may be likely to oppose the opponents of gay marriage on other issues too, for example. So it's 'worth it' to hurt them.

As an aside, QV appears to have a limited concept of time and the irrational (pre-vote FUD, post-vote revenge) alike. There is a distinct taste of 'rational actors' acting rationally (when will they learn?) underpinning the scheme generally.

3. To benefit from maximising pro-rata payout if you are a canny apathete.

I must be missing something very obvious here and would be delighted to be corrected. Otherwise QV looks like a fascinating, useful and interesting probe for tabletop scenarios (using virtual currencies for expressing trivial preferences, say).

As we prove in this paper (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264245), a small group can never beat out a large population with an overall preference in the opposite direction in equilibrium, regardless of what they announce. The reason is that any small individual or group can never really buy very many votes. $10 billion buys only 100,000 votes. Do you think this could really deter others from voting? Now a large group could deter other from voting, but of course this can happen under one-person-one vote as well. If you think Obama is the overwhelming favorite you do not show up. But that is not really how things work out in practice and I doubt they would under QV. To begin with, the members of the large group would have no incentive to show up either. It requires assuming a very strong asymmetry across groups which will mess up any system.

If this was implemented, it seems like the best strategy for an interest group would be to spread their funds over as many voters as possible. I wonder what kind of complications that would cause?

Existing laws that prohibit people from bribing others to vote their way would be sufficient to block this behavior. So would the secret ballot.

QV would work better than HN's mysterious points system. Give everyone who signs up 100 credits, replenished periodically, to allocate among posts in quadratic fashion.

Just reading the linked summary (and not the paper itself), it seems like this doesn't take wealth disparity into account. If the cost for your votes is the square of the votes you want to cast, then that means people with a lot of money can trivially buy significantly more votes than people with very little money, even if they don't necessarily care more about the issue than the people with very little money. It seems like this would change tyranny of the majority into tyranny of the wealthy.

The thing is, we already have the tyranny of the wealthy. The Tullock paradox is basically that the cost of lobbying is dwarfed by the returns.


I'm still getting my head around it, but it seems that Quadratic Voting would actually increase what wealthy people pay to influence public policy.

Edit: Just as an example, the largest "outside money" spender in the 2012 election was Crossroads, which spent about $57M. I have no idea how many votes they were able to get for that money. With Quadratic Voting, they'd get 7,550. That doesn't seem unreasonable to me.

> spent about $57M. I have no idea how many votes they were able to get for that money. With Quadratic Voting, they'd get 7,550.

Doesn't that make it seem likely that they would prefer to continue with their current strategy rather than use the money to buy votes then? It seems likely that they ended up with more than 7550 votes for their 57M, especially considering that 7550 votes would be a smaller proportion of total votes in a system where people could get more than one vote.

While very interesting, I don't think a system like this really addresses the main problems which are more to do with the need for an educated and informed populace than anything else.

This is a great point. We address it in great depth in the paper with Posner, Voting Squared (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2343956). QV helps here, a lot we hope, because most current expenditure on advertising is useful because it targets very indifferent swing voters who feel a duty to vote but do not care one way or the other. They can easily be swayed by noisy and wasteful advertising. But under QV they would not matter much as they would never cast more than a very small vote in either direction. On the other hand persuading those who really know an issue to feel a bit more strongly or less strongly would have a lot of value. This would make the sort of public discourse that was encouraged much more intelligent and mature, like investigative reports rather than slanderous or vacuous ad copy.

Here's another interesting thought: QV might reduce the influence of PACs by solving the principal-agent problem. PACs like Crossroads are not, in fact, wealthy people. They're pools of donations from many politically sympathetic individuals. People donate to PACs because they want to do more than cast their one vote on a particular issue.

But donating to a PAC is a really inefficient way to have a political effect. The rules governing PACs are so loose that the people controlling them can do anything they want with the money, including flying a private jet to Tahiti and drinking MaiTais during the election. Even more responsible PACs will probably not spend the money exactly the way the donor would. They might, for example, concentrate their spending on certain "key" elections and ignore the donor's favourite candidate. Or they might support all the candidates from a given party, when the donor only really cares about one of them.

With QV, the donor can put his money to work in exactly the way he wants. That might leave PACs with much less money to spend.

> With QV, the donor can put his money to work in exactly the way he wants. That might leave PACs with much less money to spend.

We can hope. I expect though that in general having your dollars have - by design - a quadratically decreasing power in vote purchasing is quickly going to give you less bang for your buck than spending it on manipulating the perceptions of others. There'll be some cross over position in value, and people will spend $x on votes and the rest on manipulating/persuading others which is what PACs are for.

To reiterate kybernetikos's point:

if Crossroads can get more than 7,550 votes today for their $57M, they can get more than 7,550 votes tomorrow for the same $57M without skipping a beat, by pre-bribing the electorate to make 1 vote each.

So this doesn't seem to change much from Crossroads' point of view.

It doesn't look as though Quadratic Voting should have any effect on lobbying.

The paper has examples with dollar amounts starting around page 30.

If ten thousand poor people buy one vote each for $1, the wealthy would-be tyrant needs to buy 10,001 votes to win, at a cost of $100,020,001. If the tyrant goes ahead and does this, after the election all the poor people will receive $10,001 each.

It would probably be cheaper for the would-be tyrant to just promise $5000 to each of the poor people (not necessarily in cash - i.e. "if I am elected I will institute a new support program for the people with the budget of $5000 per capita", etc.) - that's how it is done nowdays and works quite frequently.

Additionally, the $5000 per capita program can be financed with budget income and not private cash, making it virtually free for the would-be tyrant once he's elected. Of course, the budget is limited so you have a cup on how much you can offer, and people more adept in economics would figure out it's ultimately their own money that they are being promised, but usually the margin between competing politicians is small enough that people who would vote on the promise of getting "free money" have a good chance to tip it over.

Two wealthy would-be tyrants taking the same position on a view would only require a combination of 10,001 votes, at a combined cost of $50,010,001. And it only goes down as more wealthy people decide to vote in the same way.

It also seems really quite repugnant to tell people "your vote was overruled by one wealthy person, but it's ok because here's some money!" Why should being given some money automatically be assumed to make up for the fact that someone else was able to overrule your vote?

But it only grows with the square root of the number of wealthy individuals. See the paper with Posner; we go through many such calculations: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2343956

A bit offtopic, but what's your (or the field's) take on buying/bribing/bullying voters?

Even if 10 000 poor person just needs to amass 10K USD, a sufficiently brazen party can just organize for 10 000 other easily mobilized people to vote against the other poor folk. (A common theme around the smaller villages here is the election day free meals, or course the place in full party colors to remind the people who to thank for.) Or is this not so common/significant in practice?)

And so? My $100m made me lord tyrant ruler of the universe. Is existing inequality enough that quadratic voting realistically dismantles rather than reinforces existing power structures?

Has QV been used in any practical context? If so, I'd welcome replies as I didn't pick up on this.

Your $100M got you 4 years in Congress. Let's say you can pass a key bill that'll make you more than $100M. It had better not piss people off very much, because in the next election they'll buy TWO votes each and you'll have to spend $400M to keep your law in place. In the meantime, all those poor people you outvoted are $50,000 richer.

The interesting thing about this is that the more votes you buy, the more you fund your political enemies.

No, you miss the point.

Being $X richer is now meaningless. Whoever is in power controls the currency and the time value of money sufficiently that they can manipulate the next round of voting.

Right, but the money paid into the system gets redistributed equally. So the poor get paid for their troubles, and under some probably hefty assumptions they show this leading to equilibrium.

The cost per vote increases quadratically. If the first vote costs $1, then buying one million votes would cost one trillion dollars. If there are 50 million voters, then this trillion dollars would be distributed among them: $200,000 each.

It would be extremely difficult to buy massive numbers of votes without paying hugely to the rest of the electorate.

It would be extremely difficult for one single person to do this. But we're talking about a wealthy minority, not a wealthy individual. If 25% of the population is significantly wealthier than the other 75%, does that mean the 25% should be able to pay on average 9x more than the 75% in order to get their way on an issue?

it increases quadratically not exponentially

Yeah, obviously. Thanks.

That's why the cost is the square of the number of votes. Then someone with 100x the wealth would be able to only buy 10x the votes. If you consider the act of lobbying for policy to be equivalent to purchasing votes then currently the cost is linear. Of course by that analogy there's no real way to enforce quadratic cost on lobbyists, but perhaps if there was an alternate "legitimate" means for individuals to purchase voting power then they might follow such a scheme if the alternative were illegal and strictly policed.

Theoretically, this could be fixed by making the cost of votes expressed as a percentage of your income and/or wealth.

Some european countries like Switzerland are applying this principle to traffic tickets. It's not uncommon for rich people in fast cars paying few hundred thousand dollars for a speeding ticket.

Really? I'd argue 1% of my income making minimum wage is far less disposable and than a 1% of the one percents salary. And so I would be far less inclined to buy more votes. Then taking your Euro analog, is it right/fair to make someone pay more (even say in proportion to their salary) than any other person for a vote? Who decides how much I should pay for my vote? Is it based on current salary? Because if it is there are a whole load of very rich people who technically have a very small salary. Is it based on net worth? Sounds like a nightmare to me.

Approximate solutions are better than clearly wrong solutions.


As paper describes, quadratic is the unique function with linear derivative and thus the only one that reveals true preferences.

Distributing the money to other electors gives them a lot more voting power in the subsequent election. Edit: unless that makes wage-earners negotiate to less income.

I suppose it seems cool, since the fund pays back to the voters -- so it's effectively a tax on political influence against those who would spend a lot on a campaign. But I have to naively ask if this will really change anything. How will this divert money in politics away from directly buying off people in power. It seems like a new, parallel avenue to assault with big bucks.

Read to the bottom -- it looks like the general idea here is to empower direct democracy. Less institutional power in the form of representational voting and beauraucratic/constitutional checks on each other means less attack surface for corruption.

Direct democracy is a very dangerous thing and unchecked can very quickly lead to oppression of minority contingents and minority opinions. And, of course, direct democracy is vulnerable to the base form of corruption in the form of "vote for us and we'll take money from the other guys and give it to you".

The whole point of this seems to be to avoid oppression of minority opinions by weighing in how much you care.

Idea: Sow discord between [group a] and [group b]. Profit as they fight.

What experiments could be (or have been) run to test this?

Two sets, in very controlled laboratory settings, have turned out well: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&c... and http://rangevoting.org/GoereeZhangMar2013.pdf

I don't get it. So I can randomly vote with my single vote for all the causes and get increased votes back (since somebody else may buy additional votes and the total sum for redistribution will be larger than individuals count). Or not?

pas on vote buying, linear vote buying is bad according to the same theory that predicts QV is good. The only equilibrium under linear vote buying is that the single most intense (or wealthiest) individual has her way at everyone else's expense. This intuition seems to underly much of the discussion here, but only applies when vote buying is linear. The logic, as cwp pointed out, is Tullock's. So while QV is much better than 1-person-1-vote, linear vote buying is worse than either.

This is assuming that quadratic voting isn't really linear voting. Participants in a process like this aren't "honest" they can't be counted on to follow the rules.

In a QV system one can bypass the quadratic penalty by buying people's votes directly for a small premium.

Think how hard this would be in real life, plus it's illegal to buy votes, and impossible given the secret ballot.

Look above; I address this extensively in the paper.

If this is really a good thing (tm) then perhaps the best incubator to test the theory in a 'crucible of experiment' would be in corporate governance. As more corporations move towards QV (with, hopefully, good results) it may find its way into political public policy.

We decided to follow the advice of a leader in the field, Rory Sutherland, and pursue the application to market research surveys first: http://www.research-live.com/impact-magazine/the-shape-of-th.... My start-up, Collective Decision Engines, is actively working on this.

FYI: Quadratic Vote Buying as Efficient Corporate Governance http://chicagounbound.uchicago.edu/law_and_economics/643/

The paper mentions that efficiency of quadratic voting only kicks in with larger numbers of participants (> 50).

I don't think "the tyranny of the majority" is really the problem.

I don't understand, so basically if you're homeless or don't have a bank account, or if you're not in the workforce for one of a million reasons, you don't get a say at all?

Am I missing something?

Votes are cheap when you just want a few of them. Perhaps the first one is free? Then you get a windfall for being a voter, because all the money spent is redistributed per capita among the voters.

This is a terrible, terrible idea. What kind of idiot would pay n^2 dollars for their own votes when they can pay 2n dollars for other people's votes?

How does quadratic voting get around Arrow's Theorem?

Arrow's Theorem applies only for voting on ordinal scale. QV allows degrees of preferences in voting so Arrow should not apply. (This actually is why I do not understand all the fuss about Arrow)

For a long time I thought this too. But then Ken Arrow started working on QV and while he agrees that in spirit QV gets around the theorem, it does not to the letter. The reason is that there can be multiple equilibria given income effects if you had a whole society governed by QV. All equilibria would be pareto-efficient and any pareto-efficient outcome could be implemented by QV, just as in the market economy, but in the market economy as well there may be multiple equilibria with income effects. This has little impact in a small vote in the short-term, but in the long-term taking everything into account, prices changing can impact effective budgets and lead to multiple equilibria. As soon as there are multiple equilibria effectively the system is not transitive because different equilibria are simultaneously preferred and dispreffered by the social ranking to one another. But this does not stop us thinking that the market is a good system because of its efficiency properties. So I think Arrow's theorem has been misunderstood.

Quadratic, exponential, or Ackermann - it's a terrible idea to exchange votes for money.

'Money' does not necessarily mean the same thing you're currently using daily. You could also simply be dealt a finite amount of 'voting tokens' per time unit.

Can you expound on what this would look like? (I don't think that is what the paper is recommending.)

Thanks for a thoughtful and well written comment, it opened my eyes.

Your sarcasm aside, here is a more in depth commentary: https://news.ycombinator.com/item?id=8831688

Is there a short sketch of an intuition for why quadratic works better than linear?

Key phrase is.... Collective good. How do they figure what will accomplish that?



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