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> 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?

This is the punchline for me. At the end of the day, the whole point of democracy is that the majority is in charge. Majority control is the general rule; protection of minorities is the exception to the general rule.

Which is very problematic, the minority will forever be limited to the whim of the majority.

On the otherhand if you look at the super wealthy minority, allready have a disproportionate say in poltical matters, donations, lobbyists etc.

That's a great way to phrase it.

The wealthy are a minority class with extreme views.

Well, the concept of QV is that it only rewards fairly large minorities who have intense preferences (not "extreme" ones). So if the top 1% want to buy enough votes to overcome the other 99%, then they have to buy 98 votes each, which costs something in the general vicinity of 10,000 times the base price of a vote. And that's assuming that the subject is so not extreme that nobody in the other 99% is willing to pay 1/10,000th of that much to get an extra vote.

If you like the idea of rewarding fairly large minorities with intense preferences, but think that quadratic voting isn't sufficiently steep a curve, I don't see any really strong reason to think that the third or fourth power, or even an exponential curve, are that different in concept.

That's the concept. The implementation can't distinguish between 'fairly large minorities' and 'large amount of wealth', nor can it distinguish between 'intense' and 'extreme.'

Or non-primitive recursive! I just invented the AV (Ackermann-Function-Voting)!

Honestly I don't see how it's an improvement at all to turn votes into a commodity nor how one would balance the conceptual idea of 'giving rights to a minority with intense preferences' (picking a function that grows relatively slowly) against the threat of 'giving control to a wealthy minority with malicious aims' (picking a function that grows extremely quickly). And as far as I can tell it's pretty much impossible to do real world case studies with to get empirical data without putting some very fundamental things in jeopardy.

Okay, first, on the intense versus extreme thing: you're just wrong.

If a minority "intensely" prefers something, it means they value it a lot.

If a value is "extreme," it means that it has a lot of opponents.

Of course, a minority might "intensely" prefer an "extreme" position, but they aren't the same, and just like in regular voting, "extreme" causes a problem -- in fact, maybe more of a problem, because here's how it goes:

Say the 5% wealthy minority intensely prefers a non-extreme position -- that is, the other 95% are against it, but don't care. So the 5% have to buy 18 votes each -- let's say that the first bought vote costs $50, so they need to pay $16,200 each.

Now say that the 5% wealthy minority intensely prefers an extreme position -- so extreme that of the other 95%, 20% of them will buy one extra vote, and 10% will buy 5 extra votes. The 95% now equal the 165%, and the 5% have to buy 32 extra votes each, now costing them $51,200 each (their opponents, meanwhile, have spent $50 each for the 20% and $1,250 for the 10%).

How turning votes into a commodity is an improvement: well, I don't totally buy this argument, but the argument itself is pretty straightforward. You say, "If something would massively improve the lives of 40% of the population, but would be kind of vaguely disconcerting to 60% of the population, a better society would do that thing, but democracy as it stands tends to not do it."

It's not particularly difficult to design a function like this that is arbitrarily resistant to small minorities taking over the system. If you make it 2^n, then buying 20 votes costs you a million times buying one vote. There is no definition of "the wealthy" that creates a group that can buy a majority that way. But it's still pretty cheap for a population of 30 or 40% to buy 1 or 2 extra votes each and do what the system is designed to do: allow them to triumph over a majority population with only a MILD preference.

I never intended 'extreme' to mean 'has a lot of opponents.' I think this is my fault, and I should have used 'intense.' It's all semantics, but I'll take the blame for being unclear.

That said, I would argue that even in the case where there is an 'extreme' view by your definition the numbers you suggest both seem arbitrarily unmotivated by real example is not reassuring to me monetarily.

It also still does not address questions I raised about those with no expendable income whatsoever (either as the 'aggressor' minority or as the 'defensive' majority). It does not account for the question I raised about voter mobility (which looks nothing like you've pictured in the above imagined case study). Nor does it address the issue of finding a function that balancing the political mobility of the disenfranchised and capital poor with the power and financial elite. Nor does it address example groups (given both for historical and current political groups).

And there are more issues, such as enforcement (how do you prevent fronts from buying votes or families or employees from buying votes so that n becomes n/m and this f(n/m) << f(n))?

The argument you give doesn't seem to defend turning votes into a commodity, but appears to be a general argument for 'this thing I'm proposing is good.' I could use the words in the exact quote as an 'advertisement' (it really isn't an argument...) for any system, take say for example a Parliamentary system. I also disagree with it on the grounds that it claims, without any substantive analysis, that democracy as it stands tends not to improve the lives of people who are 40% in numbers for something. But I won't mention voter mobilization again...

The whole point of democracy is to limit the minorities to the whim of the majority. This is unfortunate when we're talking about harmless racial or social minorities. However, the alternate state of humanity, where the majority is subservient to minorities, such as warlords or hereditary feudal lords, is worse.

As for the super wealthy, in a democracy the manner in which they exert influence is very different. In a non-democratic system, minorities have direct power (they own the guns). In a democratic system, wealthy minorities can't beat the majority with firepower. This is a fundamental distinction. They have to rely on indirect power--usually by leveraging their ownership of the means of production. This is inevitable so long as capital resides in private hands. "My factory creates 10,000 jobs in your district, so you had better vote against that environmental legislation" will always be a disproportionately powerful argument, even in the total absence of direct exchange of money for political influence.

Personally I view that as being a pretty big flaw in democracy, but it also works the other way when the extremist element has a hard time gaining influence. But that is not a guarantee either, the Tea Party being a good example.

It may be a distiction, and the second way is more subtle and covert, but the net result of a power imbalance is still the result.

Flaw in democracy relative to what?

Thought experiment. Zuck & Co., fed-up with U.S. immigration policy, skip the PAC and just import foreign labor in heavily-armed gunships past Navy defenses. Sounds preposterous, but that just goes to show how desensitized people living in democratic countries are to the plight of humanity. A system that forces elite minorities to get buy-in from the majority instead of unilaterally imposing their will is a historical aberration and still not enjoyed by most of the world.

The Tea Party is a great example of the resiliency of democracy. Money buys influence, but billionaires must at least make the case that their interests are aligned with those of the majority. Again, it's not clear what you can do about this within a capitalistic system. The factory owner can always tell his workers: "universal healthcare will be bad for you because I won't be able to keep all of you employed if my taxes go up." And that message will always be tremendously compelling.

Does a flaw in a system have to be relative to another system, or can it be a flaw in isolation?

How does that show resilience, numerous Tea Party members have been elected, it may have been under a Republican banner, but that is more a symptom of a 2 party electorial process.

> Does a flaw in a system have to be relative to another system, or can it be a flaw in isolation?

I think talking about flaws in political systems without any point of reference is navel-gazing and not very interesting. Kind of like talking about whether the Flash or Superman would win in a fight.

> How does that show resilience, numerous Tea Party members have been elected

Even $80 billion between the Koch Brothers can't buy the election of proper statist libertarians, much less railroad through actual policies consistent with the ideology. The Tea Party is libertarian ideas watered down to the point of almost being unrecognizable. In the end, it's just a bunch of Republicans running on a platform of lower taxes, less regulation, and, inexplicably, conservative social issues--ideas that have always had tremendous traction among the majority.

While this mechanism may seem as though it may work for minority groups with strong preferences, it's important to point out the implicit assumption of class equality between majority and minority voters. That is, the example of gay rights works because homosexuals are spread evenly across the wealth distribution (and in fact are more financially and socially successful in the aggregate than non-homosexuals).

But compare this to transgender peoples, who are marginalized, disproportionately homeless, almost universally imprisoned, and make up a very disproportionate percentage of the lower class (usually they 'fall' to this class rather than being 'borne of it'). It is unlikely that transgender people could buy the votes to achieve policy measures they felt necessary just as it would have been impossible for slaves and poor indentured whites and immigrants in the 1700s and 1800s, Native Americans pushed from their land and made to walk trails of tears, children working in factories, or women for these same centuries (who in addition to having effectively no political voice also had few reasonable financial options) to 'buy' freedom.

Additionally, entrenched interests within classes - and in disputes between them - make it easy for the upper division of the wealth distribution to buy political power to block the opposing classes vote, this exacerbated by high wealth inequality. That is to say so-called Quadratic Voting also depends on the wealthier class having no strong opinion - yet its very easy to find examples both today and historically where this is easily shown not to be the case.

So its suspect whether today's working poor, child laborers, blacks and latinos, immigrants, or members of small (or no) unions would benefit from a system like this.

Finally, these market based solutions to voting would be yet another way to trade financial power for political power. The history of all governments show how strongly political power already responds to wealth. Is it smart (and ethical) to make votes market commodities?

A niggle on the term "transgendered" (via http://www.glaad.org/reference/transgender), specifically the final point:

Problematic: "transgendered"

Preferred: transgender

The adjective transgender should never have an extraneous "-ed" tacked onto the end. An "-ed" suffix adds unnecessary length to the word and can cause tense confusion and grammatical errors. It also brings transgender into alignment with lesbian, gay, and bisexual. You would not say that Elton John is "gayed" or Ellen DeGeneres is "lesbianed," therefore you would not say Chaz Bono is "transgendered."

Thank you for the education. Fixed in comment.
Can I ask a question? It seems surprising to me that we should compare transgender to lesbian, gay, and bisexual. Shouldn't we compare transgender to male, female, and other genders? It seems to me that being transgender is about an inward-facing personal identity, whereas lesbian, gay, and bisexual are about an outward-facing sexual preference. But these issues can be sensitive and sometimes not intuitive, so I'm never sure what to do except to try and learn the right thing.
The difference is a person is born gay, they don't need an operation to become gay. The Ed reflects this process. Hence you cannot be gayed, but you can become educated, indoctrinated, experienced, and transgendered.
I don't think that this is a meaningful complaint.

Let's say that a minority population has a strong preference and a majority population has a much weaker opposite preference.

So first of all, regardless of the socio-economic status of the two, note that in pure representative systems, the majority wins. If, in the quadratic voting system, the majority still wins, it's not like that's any worse than the status quo. There's no rule of super-losing a vote.

And the entire point of the quadratic voting system is that it allows fairly large minorities with strong preferences to triumph over fairly small majorities with weak preferences, without allowing a few billionaires to buy up all the votes.

If the situation is that there are two minorities with strong preferences, and then a majority with weak preferences, then the QV system will quadratically favor the larger minority over the richer one, but if your point is just that there are minorities with strong preferences that you don't think are just, well, that's more or less Cowen's point. As he points out, a minority with a strong preference includes the pro-life lobby.

Right now minorities win against majorities without strong opinions by vote mobility within a base. There seems to be some weird underlying assumption in this QV stuff that everyone is forced to vote on every issue? That is to say I take issue with sentence three. I don't see how sentence four or five really add much - but I guess I get the argument you are attempting to make ("It's not worse").

I do think it is worse. Wealth distributions essentially everywhere in the world from the third to the first and from all data we have of all nations from all times historically have an exponential distribution, i.e. the wealthy have exponentially more wealth than those beneath them, and in fact fractions of countries today own the vast majority of wealth (in America, I've seen estimates of 1% or less owning 70% or more when shares, stocks, bonds [financial holdings], land ownership, and foreign investments are taken into account along with income).

Not everyone comes out to vote (in America, for example, it is pitiful, sometimes barely two digits), voters are obscured from real issues and the 'wealthy' class is not necessarily the 'aggressor' or scenario we're talking about. Consider the examples I gave before: the working poor (who are often deeply in the red, meaning that they own 0% or less of national wealth - in America this makes up about a quarter of the country), transgender folk, child laborers, small unions, immigrants, or to the historical point similarly disenfranchised groups such as slaves, indentured servants, women, Native Americans, and poor Europeans.

Clearly there is a function in which an impassioned minority can overcome an apathetic majority in America right now (indeed, gay marriage, kind of the poster child for QV right now, was pretty much exactly that scenario). Presumably if you're the kind of person who wants QV, you regard the current method as insufficient or inefficient or both. (Personally, I think that QV is interesting, but I don't ultimately favor it).

Again, though, you're kind of weirdly trying to talk about situations with impassioned majorities. They already win. If they really want to pay extra to win by tons more, well, they're wasting their money.

If your ultimate point is that quadratic functions don't increase fast enough ("the wealthy have exponentially more wealth"), then just choose a faster-increasing function. As I pointed out in another sub-thread, 2^n means that the 20th extra vote you buy would cost 1,000,000 times as much as the first extra vote you buy, and the 100th vote you buy would cost more money than anyone has ever or will ever have. That should pretty solidly allay concerns that the top 5% or top 1% will ever buy a majority that way, while still leaving open some interesting things that happen with a minority of 20% or higher. (Personally, I doubt that an exponential function would be necessary, though a polynomial function of higher order than quadratic might).

I'm not exactly sure what to say. From my point of view I've made a large number of arguments and points that haven't been addressed - and many that haven't been acknowledged at all...
One thing that was helpful to me in making sense of this post was to understand that Quadratic Voting is trying to solve the problem of the "tyranny of the majority." It's a voting scheme that gives greater weight to minority preferences than the one-person-one-vote schemes we are mostly familiar with.

(Please note that this is "minority" in the "!majority" sense of the word, and not merely "!caucasians.")

Tyler's contribution here is to push back a little against the idea that we should be favoring minority preferences more than we do currently. He thinks this is too indiscriminate. Some minority preferences are quite good and others are pernicious. Favoring all minority preferences empowers the good and the bad.

I was also struck by the last paragraph: > "In any case the relevant question is what kinds of preference formation, and which kinds of groups, we should allow voting mechanisms to encourage."

In other words, all voting schemes favor certain preferences and groups over others. There is no perfectly objective voting scheme that would let us avoid this. We as a polity have no choice but to grapple with what and who to favor.

The implicit criticism in that final paragraph is that Quadratic Voting is leaping over the "what/who should we favor" question and optimizing for a particular answer. Tyler is saying "wait a minute, we haven't even agreed on the fundamental questions. So why are we already optimizing for a particular solution?"

While I broadly agree with your criticism and Tyler's, what I have to particularly ask about is the following:

>One thing that was helpful to me in making sense of this post was to understand that Quadratic Voting is trying to solve the problem of the "tyranny of the majority." It's a voting scheme that gives greater weight to minority preferences than the one-person-one-vote schemes we are mostly familiar with.

There have always been minorities insisting that we are under a moral imperative to avoid a dreaded monster known only as "tyranny of the majority". Strangely enough, they have never been required to prove the existence of any such creature by actually measuring the degree to which the status-quo system functions in a majoritarian way and represents majority preferences.

Since the status-quo system largely seems to represent the top 10% of the population by income, who are already a minority, I would say that contrary to talk of "tyranny of the majority", we actually need the system to represent the broad masses more.

(comment deleted)
Why purchase votes retail when you can just buy a Congressperson wholesale?
This system seems to encourage extremism - extremist groups are more able to affect political decisions than indifferent people.
The person who gets to decide how to break down policy into binary decisions and when to ask questions is the one with all the power here.

Suppose they want to suppress a 49% minority who care far more than the 51% majority and will pay far more. Assume that if the question (e.g. do you support gay marriage) was asked once, the minority could afford the votes for it to pass. If the person deciding what questions are asked wants to suppress this, they simply formulate the policy so that for the minority to get what they want, they have to answer 'No' to n binary questions (e.g. each of the n questions is a measure that bans gay marriage in a slightly different way). The minority can afford to overcome the majority on one question, but for some n, they can't afford to defeat the majority repeatedly. Therefore, asking the same question more than once would change the outcome.

Bundling decisions would also allow manipulation of binary preferences - for example, by mixing popular and unpopular measures (e.g. cutting taxes and re-establishing slavery) in a single decision so that just enough people considered it worth supporting, even though they don't support all line items.

The mechanism is therefore useless as a voting mechanism without some way of controlling how things get on the ballot.

Of course, the bigger issue (assuming, as the paper does, that a real currency is used and not an artificial one) is that the laws in place are never perfect, and measuring how much influence a group should have to make new laws based on how wealthy became under current laws will likely lead to dynamic evolution towards a solution that benefits a tiny minority.

For example, suppose we live in a fictional world where the currency is apples with 100 people. A person needs 1 apple a day to live (which is consumed, destroying it). The world has enough trees to produce 125 apples a day (and no more land to plant more trees). Due to an archaic and unfair law, people numbered 0-49 get 1.5 apples a day, while everyone else gets 1 apple a day. People 50-99 perform services to people 0-49 and get a little bit of extra apple in exchange. People 50-99 never vote, because they can't afford it (or if they do, it is the minimum - they always vote for everyone to get 1.25 apples per day), while people 0-49 put forward a bit over the minimum and easily win to retain the archaic law.

One day, people 0-48 decide they want more apples, so they propose to change the law so that person 49 gets only 1 apple per day. Person 49 puts in all their savings, but it is not enough, and the law is changed. Person 49 is now impoverished and in the same state as people 49-99. Gradually, this continues until one or two people have virtually all the superfluous apples - and everyone else even has to work hard for that small group of people to get even the one apple they need to survive.