My thoughts on quadratic voting and politics as education

That is the new paper by Lalley and Weyl.  Here is the abstract:

While the one-person-one-vote rule often leads to the tyranny of the majority, alternatives proposed by economists have been complex and fragile. By contrast, we argue that a simple mechanism, Quadratic Voting (QV), is robustly very efficient. Voters making a binary decision purchase votes from a clearinghouse paying the square of the number of votes purchased. If individuals take the chance of a marginal vote being pivotal as given, like a market price, QV is the unique pricing rule that is always efficient. In an independent private values environment, any type-symmetric Bayes-Nash equilibrium converges towards this efficient limiting outcome as the population grows large, with inefficiency decaying as 1/N. We use approximate calculations, which match our theorems in this case, to illustrate the robustness of QV, in contrast to existing mechanisms. We discuss applications in both (near-term) commercial and (long-term) social contexts.

Eric Posner has a good summary.  I would put it this way.  Simple vote trading won’t work, because buying a single vote is too cheap and thus a liquid buyer could accumulate too much political power.  No single vote seller internalizes the threshold effect which arises when a vote buyer approaches the purchase of an operative majority.  Paying the square of the number of votes purchased internalizes this externality by an externally imposed pricing rule, as is demonstrated by the authors.  This is a new idea, which is rare in economic theory, so it should be saluted as such, especially since it is accompanied by outstanding execution.

The authors give gay marriage as an example where a minority group with more intense preferences — to allow it — could buy up the votes to make it happen, paying quadratic prices along the way.

My reservation about this and other voting schemes (such as demand revelation mechanisms) is that our notions of formal efficiency are too narrow to make good judgments about political processes through social choice theory.  The actual goal is not to take current preferences and translate them into the the right outcomes in some Coasean or Arrovian sense.  Rather the goal is to encourage better and more reasonable preferences and also to shape a durable consensus for future belief in the polity.

(It is interesting to read the authors’ criticisms of Vickrey-Clarke-Grove mechanisms on p.30, which are real but I do not think represent the most significant problems of those mechanisms, namely that they perform poorly on generating enough social consensus for broadly democratic outcomes to proceed and to become accepted by most citizens.  One neat but also repugnant feature of democratic elections is how they can serve as forums for deciding, through the readily grasped medium of one vs. another personae, which social values will be elevated and which lowered.  “Who won?” and “why did he win?” have to be fairly simple for this to be accomplished.)

I would gladly have gay marriage legal throughout the United States.  But overall, like David Hume, I am more fearful of the intense preferences of minorities than not.  I do not wish to encourage such preferences, all things considered.  If minority groups know they have the possibility of buying up votes as a path to power, paying the quadratic price along the way, we are sending intense preference groups a message that they have a new way forward.  In the longer run I fear that will fray democracy by strengthening the hand of such groups, and boosting their recruiting and fundraising.  Was there any chance the authors would use the anti-abortion movement as their opening example?

If we look at the highly successful democracies of the Nordic countries, I see subtle social mechanisms which discourage extremism and encourage conformity.  The United States has more extremism, and more intense minority preferences, and arguably that makes us more innovative more generally and may even make us more innovative politically in a good way.  (Consider say environmentalism or the earlier and more correct versions of supply-side economics, both innovations with small starts.)  But extremism makes us more innovative in bad ways too, and I would not wish to inject more American nutty extremism into Nordic politics.  Perhaps the resulting innovativeness is worthwhile only in a small number of fairly large countries which can introduce new ideas using increasing returns to scale?

By elevating persuasion over trading in politics (at some margins, at least), we encourage centrist and majoritarian groups.  We encourage groups which think they can persuade others to accept their points of view.  This may not work well in every society but it does seem to work well in many.  It may require some sense of persuadibility, rather than all voting being based on ethnic politics, as it would have been in say a democratic Singapore in the early years of that country.

In any case the relevant question is what kinds of preference formation, and which kinds of groups, we should allow voting mechanisms to encourage.  Think of it as “politics as education.”  When it comes to that question, I don’t yet know if quadratic voting is a good idea, but I don’t see any particular reason why it should be.

Addendum: On Twitter Glenn Weyl cites this paper, with Posner, which discusses some of these issues more.


You could have quadratic marriage licenses as well. Something for Dr. Weyl to jump on.

"The authors give gay marriage as an example where a minority group with more intense preferences — to allow it — could buy up the votes to make it happen, paying quadratic prices along the way."

Didn't that already more or less happen?

They didn't buy my vote (or if they did, I'm not aware of having gotten a good price). They persuaded me that they were correct.

Heh, yeah, my EEO compliance people persuaded me too.

Looks like they only had to persuade a few judges, and the votes didn't much matter.

It's a good thing that we don't have minority groups with intense, extreme positions who have concluded that convincing judges and other elites gives them a path forward towards which to allocate all their efforts and boosting their recruiting and fundraising. That might erode the the public's consensual belief in the legitimacy of the system. "Who won and why?" "That special interest and its sympathizers, and only because the judges said so, against the wishes of the majority, that's why."

Oh wait.

Still, judges make up good excuses that give them plausible deniability regarding domination and abuses of power. That's really valuable, because people grumble but still obey. Quadratic Voting doesn't have that useful fraud going for it.

How much did it cost Carlos Slim to bail out the New York Times? Surely that was more cost-effective for Mr. Slim than buying American votes outright? So why would he bother with the Posner-Weyl marketplace?

Indeed. Or why buy a vote retail when you can buy politicians wholesale?

The difference is that Sim is a lender and has no influence, but Rupert Murdoch is an owner, and through Fox, created the Tea Party. Post any evidence you have that Sim controls or influences the NYT, Do you want me to post any evidence that Murdoch controls Fox?

Are you merely playing stupid?

Take up the challenge if you really believe what you think. If you don't have support, what does that tell you about yourself.

created the Tea Party.

If fantasy pleases you, go ahead. Just quit pestering the sane.

Art, Go read the Wiki entry for the Tea Party, Glenn Becks contribution, coverage and support by Fox News and contributions by the Koch Brothers.

Here is the link:

Oh, and here is a more extensive piece by a news oversight organization, Media Matters, about the Fox sponsorship:

Art, do you live in the US? Do you or did you ever watch Glenn Beck?

I'd guess that Slim did not need any influence as the current leadership was just as bad.
But, did you just use Media Matters as a source, really?

TMC, What a statement: No influence shows that they influenced because they were happy. Ever take a physics course? What is the definition of power. (Hint: It isn't a body at rest.)

Bill, Murdoch paid to distribute a point of view. Slim did not need to fashion that point of view. The NYT already had that, they just needed the $$ to continue distributing it.

TMC, if they had gotten a loan from Citibank, your statement would also be true.

TMC, you are in the running for the poorest argument, unsupported by facts or logic, for 2015.

TMC, Now for the real world and the world of FACTS:

From Bloomberg:
"Billionaire Carlos Slim is poised to double his money after investing $250 million in a 2009 lending agreement with the New York Times, showing how dearly the newspaper’s owners paid for his help.

Slim, who controls mobile-phone carrier America Movil SAB (AMXL) and is the world’s second-richest person according to data compiled by Bloomberg, already has earned $122 million from his loan to the Times, based on an annual interest rate of 14 percent and a 12 percent premium charged to the company when its debt to Slim was redeemed in 2011. Under the terms of the loan, the Times still owes Slim additional shares worth as much as $141 million based on the Jan. 17 stock price, thanks to options he received to buy shares at what is now a deep discount."

Steve Sailer still hasn't posted evidence for his claim.

What makes you think creditors have no influence? Also, Slim does own a chunk of the NYT.

The claim is you don't need to buy votes--which is illegal in any event, only the government is allowed to buy votes--but you can buy media instead. Sounds plausible to me.

Anti, If Slim were doing this for love, and not money, he would make what type of return: slim or none. Go up and look at the facts, not your biases: Slim doubled his money for the investment. See the Bloomberg article above in my reply to TMC.

"If we look at the highly successful democracies of the Nordic countries, I see subtle social mechanisms which discourage extremism and encourage conformity."

This may be looking at it backward. Nordic countries are culturally homogenous, the conformity merely a manifestation of this homogeneity and the successful democracy part is an end result.

Now that Sweden has pursued a liberal immigtstion policy with large numbers of heterogenous cultures, this conformity is breaking down (Jews fleeing Malmö) and the democratic system is starting to show cracks, with all main parties for example agreeing to support open immigration despite mounting public opposition.

On the notion of voting practices and minority preferences, surely the easy first step is to reduce government responsibilities. If, for example, marriage isn't a govt decision, then little or no issue.

My next two steps would be 1) sunset clauses on laws or removing one law for every one created, and 2) mandatory balanced budget over a 5 year period.

I think our founders had a better grasp of the problem of the "tyranny of the majority", as they devised a system of limited government. Now we are given a method for more efficient division of the spoils - rational brigandage.

I guess the U of C isn't what it used to be.

It isn't. Tragic, too.

"Nordic countries are culturally homogenous": 'were'.

iI would argue that our current system of super PACs and lobbyists already functions similarly. Due to the correlation between campaign spending and votes received a campaign donation amounts to vote-buying, just sloppier and not precisely quadratic.

Plus, lobbyists already are effective at creating tyrannies of the minority (eg too many subsidies to count), and often work on legislation directly, skipping that whole pesky voting issue entirely.

Not precisely quadratic? I think lobbying and politics prove that the pricing is something a lot less. You don't buy the votes of the people, you buy the votes of the legislators which is much cheaper (admittedly through campaign finance that's used to try to influence voters) - and it's amazing how little it costs (the ROI is amazing in some cases - like tax benefits). So my initial reaction is it's not even linear.

Gay marriage lost over 30 consecutive state referenda. But it was always pretty obvious that, whether by hook or by crook, it was going to win: while all voters are equal, some are more equal than others.

It's 2015, not 1975: do the rich really need more political power?

'I do not wish to encourage such preferences, all things considered.'

Prof. Cowen may sincerely believe that, but the chairman and general director of the Mercatus Center could never write that line and expect anyone to believe it.

'and I would not wish to inject more American nutty extremism into Nordic politics'

How is that project to correct all Mercatus Center work based on Reinhart's and Rogoff's flawed study going these days? After all, that is at least an area where the chairman and general director of the Mercatus Center can personally intervene to reduce at least a bit of American nutty extremism in American politics.

Psst PA; Google Wendy Gramm, Enron, and the Mercatus Center. Surprised? Rich get richer, as well they should, hehe. "CFTC chairwoman Wendy Gramm— wife of Enron-friendly Texas Republican U.S.senator Phil Gramm—was in a position to initiate the rule-making process, cut short the usual yearlong examination,and speed the decision through before Bill Clinton was inau-gurated and new appointees were named.This she did,and on January 14, 1993, the commission voted 2–1 to grant Enron’s request. A week later, Wendy Gramm resigned from the CFTC, and roughly a month afterward she was named to Enron’s board of directors. For this, her compensation between 1993 and 2001 was calculated by Public Citizen at between $915,000 and $1,853,000."

Eric A. Posner, Chicago Law School, any relation to Judge Richard Posner?

As for vote buying, they do that here in the Philippines, roughly $12 to $24 is the market rate. Of course the politicians intend to recoup their investment with bribes.

Eric is Richard's son.

It's another instance where the solution is worse than the problem, assuming such a problem really exists . If things are so corrupt where votes are being bought an sold you think the people in power would ever let this system be adopted?

"Tyranny of the majority"? The premise of this paper, and Cowen's comment, is that democracy is not "efficient". But political outcomes (and, hence, policy) in America are already determined primarily by the market, with only occasional (and short-lived) bouts of realism thrown in when the market produces horrible results. Moreover, these short-lived bouts of realism are becoming shorter: it took several generations for the electorate to get over the mess produced in the late 1920s and early 1930s but less than two years to get over the mess produced in the aughts. Voters, and votes, have always been subject to manipulation, it's just that today's version of the manipulation inures to the benefit of an enormous industry that didn't exist a generation ago. It's the market at work, with the help of the Supreme Court to make that market as opaque as possible. If the market is to determine political outcomes (and, hence, policy) anyway, I'd prefer transparency so we at least know who, or what, is determining them and our future. At least it would be "democratic".

>If we look at the highly successful democracies of the Nordic countries, I see subtle social mechanisms which discourage extremism and encourage conformity

Having lived in Sweden for about half a decade, I don't think there is anything subtle at all about these social mechanisms. Mediocrity is the ultimate ideal and it is promoted and reinforced in all tracts of life. It's a surprisingly anti-intellectual society, with a knee-jerk reaction against exceptionalism of any kind. And I was at one of the best universities in the country, presumably surrounded by smart people. Who even knows what goes on outside of Stockholm.

Yes, mediocrity is the great achievement of Sweden. Mediocre life expectancy. Mediocre vacation time. So many mediocre life outcomes. Glad you are there to shake them up with your exceptional values!

Can't be wholly true. They do give out the Nobel prize. Unless you feel that's a celebration of mediocrity.

Thirty-one Swedes have won the Nobel prize out of a total of 860 different individuals that have received it.

Yes, but the Swedes are handing out the prizes, which suggests they (at least, the prize-giver-outers) care about rewarding excellence. It doesn't matter that few Swedes have actually won the award. My isn't that Swedes are themselves excellent, but that they, or, at least, some subset of them, do care about excellence in the general sense.

Editing mistake. Should read: "My point isn't that…."

A society that discourages the pursuit of excellence in its internal arrangements isn't necessarily going to discourage national chest thumping on the international scene. Indeed, it might even be a wise decision for a mediocrity-seeking culture to hand out international "excellence awards" if that allows the nation to maintain some of the international prestige that might be lost from a culture that is somewhat stagnant.

It's weird how the entire time I lived in Belgium quite a few people despised me purely for my being American but never did any imply Belgium was a "better" country than the US. On the other hand Sweden's superiority to the US is just about the first thing any Swede I encounter wants to mention. Followed by Sweden's superiority to its neighbors. Sweden obviously cares desperate about international status so even if they were devoted to limiting status competitions internally they would never abandon the one thing around which their international status is based.

Nevermind that the Nobels are a legacy of a period when Sweden was likely less self-consciously devoted to promoting homogeneity though discouraging "stand out/ status seeking" behavior. It's a mistake to gauge a nations current culture by cultural legacies like the Nobel Prize.

There must be a national vote among the Swedes, and maybe their emigrants to the Midwest USA, that results in the selection of the award recipients. I was under the impression that it was given by various committees, like the Swedish Academy, but I must be in error.

"Yes, but the Swedes are handing out the prizes," So ONE Swede decides to...

By the way:

Talking extremism in the Nordics, a new pact by mainstream parties in Sweden effectively sidelines the surging anti-immigration party....for the next eight years. There was going to be gridlock and pressure to bow to far right extremists. Other countries in Europe are falling victim to this and getting into bed with the far right. But Sweden has put together a drastic, crafty solution that fights both governing paralysis and nationalism. Other countries should know about this.

I do not perceive this solution as crafty, only drastic. Pure "brute force". As a side effect, SD will be seen as the only authentic opposition and will probably gain some support within electorate. In the neighboring Denmark, nationalist parties were accepted as a part of the political scene and subsequently tamed a bit. The Swedish way will radicalize them more and potentially pave way for a coup d'etat. 20 years ago, that would be unthinkable. Now I look around Europe and it is no longer so.

Watch the Supreme Court rule that, since each vote is bought from a single voter, each is a separate transaction with N=1, and the resulting price is also 1.

Funny, I thought tyranny of the majority was where the 51 voted the 49 their slaves, or 99 vs 1. But Eric Posner says:

"...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."

It's called "tyranny" not "mild inefficiency" for a reason Eric.

Though I have to think about QVB more. Now I have a prior as Eric Posner is almost always wrong, for instance he hates our Constitution, but that's "almost."

I love pricing mechanisms but looking at this for literally 15 seconds I think Eric likes it as price goes up so fast it's not about resources but motivated coalitions, ie, potential tyranny of the MINORITY and tyranny by organization/motivation not resources, instead of majority. This fits my Eric Posner prior but again is after 15 seconds of thought.

I despise and fear tyranny of the majority but think enforcing the Constitution Eric P despises, designed precisely for this purpose but destroyed by 100 years of Eric Posners, is the way to go.

Put differently:

Tyranny of the majority is about the majority imposing its utility function on the minority not the failure to maximize social utility.

Posner is a totalitarian in all things.

Voting under the constitution is fairly flexible and has been modified several times. States could choose to allocate electors under a system that in part used the proposed system.

We need to admit that we have come to a 'near end' for creating a functioning but pleasant (not so polarized) political system based on party electoral democracy. Perhaps we need to vote for policies rather than parties or individuals - perhaps political corporations who would undertake a policy as their sole objective. Say a $1B immigration policy put forth by a consultant's report - followed by a tender process of political corporations who would just survive long enough to enact the scope of work. No politicians per se, just recommendations followed by a marketplace of contractors to enact it subject to a cost, schedule, and performance criteria.

I'm not sure what the proposed "fix" fixes.
1. Passionate minorities already buy votes from politicians, even write our laws
2. Why would it be more welfare-enhancing for all for passionate minorities to get their way?
3. In the current system, most people don't know the positions of the politicians they're voting for or against and use tribalism as a proxy for information. Wasn't there an economics book written in the fifties or sixties that showed that the political value of being an informed voter was ZERO? Why would enhancing that feature result in a better system?

If you really want better outcome, asking voters to rank their policy preferences without any emphasis on which politician/party is supporting the policy, and then selecting the politicians whose policies have the highest aggregate score would be more efficient.

You could put the money used to buy votes into the federal treasury, where it could be used to either provide additional services or lower taxes. I'm kind of searching here.

"If you really want better outcome"

What defines a "better outcome"?

Whatever it is that QV is supposed to fix. What I would want is to get tribalism out of our voting decisions and a more data driven approach to the selection of representatives. I don't know what the QV system is supposed to improve.

What I would want is to get tribalism out of our voting decisions...

Yeah, if only we could remove the humanity from humans. We should work on creating the New Democratic Man.

Not sure I follow your logic. Every political system goes against human nature in some way. We accept that because we think of our representatives are legitimate so we submit to the laws they enact.. The goal of reforming the electoral system isn't to change human nature, it's to ensure that the elected officials more accurately represent the will of the people than they do now.

If you think the rich buy elections anyway, then formalizing and regulating (in the literal sense of making regular) the process has obvious benefits from an efficiency and transparency standpoints if nothing else.

Or, if the rich run the place anyway, then just give them the keys and let them compete with each other for human and financial capital.

I think that only follows if the case can be made that voting, governing and politics are all essentially private goods. If that's the case then the voting system is not the solution as it's merely perpetuating an unnecessary bureaucracy -- government should be privatized entirely and voting is not a factor at all, only prices like milk, soup and any other good produced.

If it's not the case that voting, governing and politics are just other forms of private goods then it's not at all clear that the pricing solution that might work in a private-good setting would be the correct solution outside that setting.

Interesting and clever, although there's a lot of work indicating that people won't change their minds on the values you're talking about.

A deeper problem with these mechanisms is that you still have to generate a binary choice to allow for stable outcomes, which is where the issues tend to arise. I'm all for more efficient aggregation of preferences, but deciding on the right question to ask still determines most of the choices. E.g. we could ask either: gay marriage - legal / illegal? Or: civil unions for gay couples / legal marriage for gay couples? The second question will be more expensive to buy the votes for (I think). There are probably many better examples. In other words: the real issue with the political process is agenda setting and the institutional configuration of choice structures, not preference aggregation efficiency.

"The authors give gay marriage as an example where a minority group with more intense preferences — to allow it — could buy up the votes to make it happen, paying quadratic prices along the way."

Without reading the rest of the comments this may have already been mentioned, but…I observe there's an equally passionate minority that strongly opposes the legal recognition of gay marriages.

Yes, but we're declasse and do not have positions in law or economics faculties.

I think this is fundamentally a horrible idea.

It's all very rational and efficient and my inner economist like sit quite a lot.

But it utterly violates some of my deeply held political foundations. For example - equality before the law, equal human dignity, a democratic contract between the state and the individual. One man one vote is about far more than efficiency, it is a statement that at a deep level we are all equal - rich and poor, smart and stupid, all of us have an equal say in the final determination of how we are governed. Sure the rich can buy more press or advertising, the clever can write more convincing ads and celebrities get more attention paid to their views. But in the end we go into the voting booths where each of us has an equal say in who will govern us. Sure you can argue that this equality in the voting booth is an illusion, but it is one that has, when necessary, motivated Americans to sacrifice everything to defend. The idea that quadratic voting would generate this seems far fetched, it would quickly be seen by an ever more cynical populace as a plutocracy run for the benefit of Wall Street bankers and other insiders.

Alas your instinctively lefty reaction is also wrong.

It goes up too fast for the rich to dominate, it would be a tyranny of the radicalized minority, which is what Posner wants.

You should love it, would be more "equality" of the kind u really want, socialist type, not a plutocracy. But besides being a leftist you don't even understand the leftist plan. Next time get the memo.

Oh and whine about one person one vote when we are all paying even a dollar into the pot.

Lefty and clueless, nice combo.

Kevin makes more sense than you think, especially as regards his point that the proposed system would just be gamed by Wall Street & other vested interests, such as a Wichita based billionaire who indirectly subsidises this site.

People like you chastise Putin and Chavez for nationalizing oil companies, but you're too clueless to comprehend the nationalising of trillions of Wall Street bad debt in 2008.

Addison's Disease, must be a bitch when your symptoms flare up: Mental confusion, mood swings, paranoia.

Crawl back into that slimy, dark hole from whence you came, you moron.

Do they offer any documentation of any actual "yranny of the majority" in modern times? My sense is that none of the modern democratic polities truly represent any majority. That's clearly not the case in the USA where policies are driven by blocks representing less than 30% of the eligible voters. For the representative multiparty system I get the sense what occurs is similar to the political horse trading that we see in the USA so they end up with policies that don't actually have any majority support from the population but is the result of a compromise by the various factions that formed the government. A case of "we'll let you get X if we can have Y" where neither X or Y are generally supported by the people.

Looking at the article (and if I could edit I'd just update the edit to the original post) it seems that the claim is at best an assumption as I suspect that historically the majority of people have cared less about other people's sexual preferences but the established political system (likely dominated by a minority, or several minorities at least one of which was homophobic) was anti gay marriage. A case of valid argument but false premise I suspect.

"The actual goal is not to take current preferences and translate them into the the right outcomes in some Coasean or Arrovian sense. Rather the goal is to encourage better and more reasonable preferences and also to shape a durable consensus for future belief in the polity."

Seems like this deserves a lot more attention. In one sense I think I understand where Cowen's going and possible have some agreement. However there's some orwellian aspects to the last sentence that are a bit disturbing. What would be the appropriate preferences that are deserving of our political processes? In what sense should we have a consensus for that "future belief in the polity"?

I certainly agree that we're not going to find solutions to our political problems in the suggested voting scheme (as I understand it from this post).

"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." Eirc Posner

Seems like there's something fundamentally wrong here. A large number of people care very little about the color of the siding on my house or the type (or color) of the car I drive. This of course doesn't matter as it's not a political issue so seems like the question here is what situation would meet Posner's setting. Perhaps I'm missing something but all I can think of are cases where the government is already doing the wrong things. In such cases a vote buying system would not help resolve the situation but would actually make it worse.

Let's think about it. Would quadratic voting have help the anti-bellium political situation vis-a-vis slavery? I'm not sure at all and it's certainly the case that the slaves would not have been able to buy enough votes in the south to overturn the legal status. How about 1950's and segregation? Anyone really think a vote selling polity would made Rosa Parks historically irrelevant?

I read that sentence and thought: this is the most interesting and insightful thing I can remember ever reading from Tyler Cowen. I'm not 100% sure it's true, but I think it probably has the right idea and at the very least it raises some very important issues. I was actually pretty disappointed to read the comments and see that nearly everyone seems to have skipped that part. There is a lot loaded into that second sentence related to why some societies work and others don't. You could spend a lot of time expanding on those points, but what I'd add very briefly is that if people are willing to cooperate and try to make things work even when they don't get their way in policy making, that makes things a lot better for everyone. In fact, this might be more important than just getting the formal policy right. But in order for that cooperation to happen, people have to have a certain amount of faith in the whole process. The opposite result is ceaseless factional civil war.

Un-bundling Government would be better and more plausible.I.e. you elect an executive of benovolence with his tax a president of healtcare etc.

The main problem with the research is that no political decisions are binary. Choosing candidates is a pick one of many problem. Overall, the total resultant set of policy matters. Taking abortion for example, society must chose how long abortion is permissible, what methods and personnel are required, any circumstances such as rape/or health of the mother, who determines how such health is assessed, and what the penalties are and resources used for enforcement. Any two people rarely agree on those issues.

This kind of problem is where future research should be focused.

The paper kinda fails at noting a much more uncontrocersial application: Getting "senate-style" voting power right. For the US, this would mean: How does (should) #{senators} scale with #{voters in state}? Obviously the naive answer "two senators per state" is braindead stupid if the states have widely differing population (marginalizes large states). Slightly less obviously, the naive #{senators}~#{voters in state} also fails (marginalizes small states).

See This is the exact problem for determining the number of seats in the EU-council, depending on the number of cititzen. In fact, something like quadratic votingwas widely discussed in the EU a couple of years ago, pushed by Poland. Unsurprisingly, the public did not get it and Germany blocked it.

That is to say, I am pretty sure that Poland pushed the square-root allocation because it would be advantageous to Poland and Germany killed it for the same reason. However, the math was right and it was one of the rare times, where highly political math papers were widely discussed in German newspapers.

Google "EU Poland square root" for more discussion. Direct link to a survey:

In fact [Lalley and Weyl, Quadratic Voting, 2004] seems painfully unaware of the previous literature on the topic. If I were a referee, I would ask them to at least discuss how their approach relates to Penrose. Disclaimer: not an economist. Not a game-theorist (at least not by vocation).

There's a reason the Senate has two representatives per state that relates to checks and balances within government and serves to introduce a different integration of preferences via representatives sent to government. Part of the bi-cameral thing we do here in the states.

Sounds like a plan for rule by geriatric plutocrats.

A fun mathematical analysis of various voting methods (plurality, etc.):

Why don't more people advocate a jury duty-like model for elections? For each individual race, a small but statistically sufficient sample population could be randomly chosen from the office's jurisdiction. Selected individuals would have the opportunity to accept the voting privileges, but voting would come with some commitment -- at a minimum, a few closed-door education sessions where candidates and their supporters could present their platforms and issues to a captive (to the extent that human attention span allows) audience whom they know with certainty will control their fate. Voters would be compensated for this time so that potential voters, particularly low-wage or non-salaried workers whose turnout is perpetually a concern and whose interests are therefore arguably under-represented, would not be dissuaded from participating by possible loss of income.

I see this concept as having several potential benefits:

1. Less waste, both of public and private resources during elections, including the scarcest and most important resource, human attention.

2. It should result in truer representation of the population as a whole, thereby being more democratic, despite the much smaller number of voters.

3. It would put more proportionately appropriate levels of attention on local races, which are frequently overshadowed by races for larger offices.

4. It would give the average voter the opportunity to make a more informed decision and potentially deemphasize brand affiliation, particularly in local offices.

5. Reducing the total number of participants should curtail public hoopla surrounding elections, thereby mitigating some of the tribalism that dominates politics.

Obviously, most of the failings of our political system would persist, and I am likely overlooking some very major downsides (besides the sheer improbability / impossibility of this ever coming to be). That said, I think it would be better than what we have and would not involve vote selling.

There's understandable opposition to any system that so directly implements "buying and selling" of votes, something that we've generally disallowed.

However, this system would work (and I think it would be an interesting experiment to test) if individuals could only "buy" votes in this system with time (which is a finite resource and available in equal amounts to every individual in a given year). This would have to be handled on a per-issue basis; from an efficiency point of view, you could simply have people 'buy votes' by sitting in a waiting room, but from a societal point of view you could have them engage in any number of civic activities that are generally unobjectionable (like street cleaning or city beautification projects, etc.)

The leisurely rich and retired would obviously have more "free" time (as in, incur less of an economic hit for investing time in an issue), but then again, if you're in that position you're likely to generally be ok with the system as-is anyways. (Plus, if retirees really wanted to invest time in an issue important to them, like improvements to Medicare, they'd also be putting votes in a pool that others could use). Single parents, those with multiple jobs, etc. may have less "free" time, but if a single issue was of great importance to those groups, they may care more by 'investing' in that specific vote than others.

Using personal time thereby gives everyone the same 'capital stock' at the beginning, though mobilization around a given vote is still a concern (which gives issues that have organizations behind them - like churches and abortion - an upper hand over more diffuse interests, like a more efficient tax system).

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