glenweyl

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.

That is the point of the software!

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_...

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.

Look above; I address this extensively in the paper.

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

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.

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...

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?

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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

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.

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 deal with this in another paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2571012

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.

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

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...