Quadratic Voting (2014)
ericposner.com
ericposner.com
One question that comes to mind is whether quadratic voting is the best improvement. I look forward to giving this a read.
> 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?
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!
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.
Nice.
Then I wonder why HN sounds like a cult on some subjects...
> 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.
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.
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.
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.
"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)?
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.
Just because it could be gamed is not a reason to wholly dismiss.
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.
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 $44,000 vs their respective 42billion and ~80billion)
But there are plenty of decisions to be made that could be done with fake credits in a controlled environment.
http://www.electology.org/#!approval-voting/cc04
1) elimintes the spoiler effect problem
2) most "approved"/liked candidate can win, not necessarily the most "popular" within a certain group
3) gives lesser known candidates/parties a much better chance to compete and rise up against the incumbents
4) statistically proven to be one of the voting systems with the least remorse
5) very simple (essentially HN style voting)
Range voting could also work, but it's debatable whether the extra "scores" are worth the loss of simplicity. Range voting also seems to have a bigger degree of regret, although it does seem to do slightly better with electing the "ideal" candidate.
> Range voting also seems to have a bigger degree of regret
No. It has the lowest regret of any commonly discussed system. http://ScoreVoting.net/BayRegsFig.html
> although it does seem to do slightly better with electing the "ideal" candidate.
Lower regret = more ideal candidate. So you just said a contradiction.
When I was kid we had a congressman where I lived in Morocco who win a election with a strategy similar to a quadratic voting. His team went to the poorest neighborhoods of the district and they distribute half (literally half the bill) of today equivalent of 20$ 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...
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.
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.
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...
Then again, it does sound like an interesting system to try, but maybe to be used for smaller decisions and groups first.
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.
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...
Do you have any references?
Except in voluntary voting systems, where highly motivated voters dominate the apathetic majority.
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.
> 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?
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.
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?
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.
Rethorical devices would still maintain the greatest power. You don't need information just conviction and resources.
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.
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.
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.
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).
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.
It would be extremely difficult to buy massive numbers of votes without paying hugely to the rest of the electorate.
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.
Has QV been used in any practical context? If so, I'd welcome replies as I didn't pick up on this.
The interesting thing about this is that the more votes you buy, the more you fund your political enemies.
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.
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?
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?)
https://en.wikipedia.org/wiki/Tullock_paradox
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.
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.
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.
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.
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.
In a QV system one can bypass the quadratic penalty by buying people's votes directly for a small premium.
Am I missing something?
are we 5, sir?
for you.