
Quadratic Payments: A Primer - gabcoh
https://vitalik.ca/general/2019/12/07/quadratic.html
======
awelkie
Great article; very interesting and well written.

A bit of a tangent, but something that bothers me is the assumption in
economics that the amount of money one is willing to pay for a good is equal
to the utility provided by that good. And then it follows that if I am willing
to pay €2 for a coffee and another person is only willing to pay €1 for that
same coffee, then I value the coffee twice as much as the other person.

But to me that doesn't make much sense. What if I am a billionaire and the
other person is very poor? It could very well be that the other person values
the coffee a lot more than I do, but because I have so much more disposable
income than they do I am willing to pay more for it. To me, the assumption
should be something like the amount of money _as a percentage of my total
wealth_ that I'm willing to pay is equal to the utility of the good.

And because this assumption is so fundamental to economics, it determines the
conclusions that the field reaches. For example, the definition of an
"efficient market" or the optimal level of production of some good both embed
this assumption that willingness to pay equals utility. And then one can
imagine that policy decisions and such are influenced by this assumption. (And
in fact the article itself mentions this problem: "Another challenge is that
quadratic payments, being a payment-based mechanism, continues to favor people
with more money.").

So I'm wondering if anyone has looked into an alternative formulation of
economics with a different fundamental assumption (perhaps something closer to
the one I proposed above). If so, do certain things that are determined to be
"optimal" in classical economics turn out not to be optimal in this
alternative formulation (and vice-versa)? Apologies if this is a bit of a
naive question; Econ 101 is the most I've ever studied the subject.

~~~
QuesnayJr
Economics specifically _does not_ make that assumption. You will see it in
cost-benefit analysis, but it is not anything like a fundamental assumption in
economics. I don't know where you got the idea that it was -- if you learned
it from your econ 101 class you should demand your money back.

The fundamental idea in economics is "Pareto efficiency". Something is Pareto
efficient if there is a no way to make someone better off without making
anyone worse off. An idealized perfectly competitive market would be Pareto
efficient, but the bulk of microeconomics these days studies market
imperfections.

A level of production is "optimal" if it's Pareto efficient. Again firms in
idealized perfectly competitive markets will produce a Pareto efficient
output, but real markets can fall short of the ideal. For example, a polluting
industry will overproduce, unless pollution is taxed.

IIRC, there are conditions where your alternative criterion matches Pareto
efficiency, but they are somewhat special.

~~~
littlestymaar
> Economics specifically does not make that assumption.

As everything in economics, it depends on which branch you're talking about,
but this assumption is the core of the _marginalist revolution_ which is
fundamental to the whole _classical_ branch and it's derivatives, which makes
the vast majority of mainstream economics nowadays, because the _neoclassical
synthesis_ made the biggest part of the Keynesian school move toward this
assumption (say hello to micro-founded macro).

Anecdotally, claims that [insert a foundational hypothesis of classical
economics] isn't really that important in the whole model has been the
favorite defense of neoclassical economics against criticism since at least
Friedman in 53 ( it might have existed before, but none of them had the
popularity of his _Essays in positive economics_ )

~~~
selectionbias
I don't see how micro-founded macro models equate utility with willingness to
pay? Work-horse New Keynesian models begin with a representative agent so
willingness to pay of different consumers doesn't even make sense in this
context. Moreover, these models are (to my knowledge) seldom used for welfare
analysis but rather to examine things like the effects of montetary policy on
employment and growth. Models with heterogeneous agents certainly don't assume
willingness to pay is the same as utility. I'm an econometrician not a
macroeconomist though so perhaps I'm missing something.

~~~
QuesnayJr
They don't equate the two in macro.

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jawns
This post describes a system of voting/payments where you can make multiple
votes, depending on how strongly you value your preferred outcome, but each
vote costs more than the vote before.

Identity management and collusion are big issues with these systems, as the
essay points out.

For programmers, one way to think about this is that each voter has a state,
n, that tracks how many of times they've voted. And each vote is more
expensive than the last. Eventually you either run out of money or you lack
the desire to spend more money on another vote.

But if you can create a new voter account as easily as you can create a new
Gmail account, then once n gets sufficiently high, you just switch to a new
account to lower the price of your vote.

Or if a really rich voter with a high n-value pays someone with a low-n value
to make a vote on their behalf, the system collapses as well.

Enforcing strict identity management (e.g. requiring valid state-issued ID
cards) and implementing secret voting can help address these problems, but my
guess is that if there is a strong enough incentive, people will try their
hardest and come up with novel ways to thwart these safeguards.

~~~
6gvONxR4sf7o
I don't think secret voting is as much of an issue as people make it out to
be. Vote buying would in theory be a problem with today's usual voting
systems, but in practice doesn't seem to be an issue. If we're voting on
Proposition 1234 and I really really care but you don't, I should be willing
to pay you to vote my way. But we don't see that happening.

~~~
bluGill
You don't see it happening (much) because we have a secret ballot. If I really
care about Proposition 1234 I can sell my vote to you, collect the fees, and
still vote however I want. There have been cases where someone felt compelled
to vote for something they didn't want because they didn't want to be seen
voting the other way [their boss would fire them, or such situations], thus we
no longer allow anyone to find out how an individual voted.

~~~
6gvONxR4sf7o
Ah, I thought this was about another kind of secrecy emphasized in the
article:

>We don't just need votes to be anonymous and private (while still making the
final result provable and public); _we need votes to be so private that even
the person who made the vote can 't prove to anyone else what they voted for._
[emphasis theirs]

This is the part I was saying doesn't seem so necessary.

~~~
superturkey650
I think that goes along with what the parent mentioned. If someone can prove
how they voted, then Person A can buy Person B's vote and request proof that
Person B voted that way. However, if Person B can't prove which way they voted
and it is just based off trust then Person B can lie and still vote however
they'd like.

~~~
6gvONxR4sf7o
You can do that today. You could have sold your vote in the 2016 election. It
just doesn't seem to be a thing people do.

~~~
superturkey650
How can you do that today? Can you get the equivalent of a receipt from
voting?

~~~
6gvONxR4sf7o
One possibility that comes to mind is filling out a vote-by-mail ballot and
letting them verify and send it in.

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6gvONxR4sf7o
This is a fascinating collective decision making scheme. One potentially
serious nitpick. In the "one dollar one vote" scheme, it makes a
simplification that seems really bad. It's the same flavor of mistake as when
you have the option of making a bet. If the expected return is positive, it
says you should bet all of your money. In reality, people don't do this.
Rational actors shouldn't even do this.

I'd love to see what an attempt at this same sort of number-of-votes-is-
proportional-to-value comes to with a less simplified model of behavior. If I
value outcome A at price $x and outcome B at price $y, I might not be able to
afford $x^2+y^2, and this model doesn't say what I would or should do. A
corresponding model that talked about how people _allocate_ their finite money
rather than a unit by unit _spending_ description seems like it would better
apply to reality.

~~~
joosters
It's simply not true that if EV is positive, you should bet all of your money.
There's a classic formula called the 'Kelly criterion' to calculate how much
of your money should be bet given your expected edge. The original paper
(which came out of Bell labs, based upon noise over a transmission channel!)
is a good read:

[https://en.wikipedia.org/wiki/Kelly_criterion](https://en.wikipedia.org/wiki/Kelly_criterion)

[http://www.herrold.com/brokerage/kelly.pdf](http://www.herrold.com/brokerage/kelly.pdf)

~~~
lifeisstillgood
Can I check something - reading the wikipedia article on Kelly Bets it seems
that one should take the expected chance of winning, double it and subtract
1.0 and use that as percentage of bet size

So when I win 3/4 times, that's .75 -> 1.5 -> .5 of my total wealth.

But this basically means never gamble till the odds are in your favour. (ie
above .5 chance of winning)

What does this say about founding a startup?

~~~
seangrogg
The most insightful thing the Kelly criterion says about founding a startup is
"don't bet unless you have an edge".

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miki123211
I don't think this idea is actually implementable in a large-scale, real-world
setting. One person, one vote democracy is pretty understandable to an average
Joe who doesn't even remember what "squared" means. I think that a normal
person would have no idea how much to spend on a particular decision, as the
formulas would seem like black magic to them. Normal voting is pretty
intuitive, quadratic is not. This problem is not that noticable for HN people,
as our average intelligence is probably way above the societys', but before
deploying this on a large scale, it has to be considered. I don't think that
internal workings of democracy should be something that an average school
child can't easily grasp.

~~~
naringas
part of the reason the so-caleld "average Joe" doesn't remember what squared
means is becuase they don't really have to.

If this scheme were part of the world form the minute "Joe" is born, Joe would
_have to_ understand this.

education must improve. the current paradigm of education is reminiscent of an
assembly line. if kids aren't manufactured goods, why is their education
treated as such?

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moultano
We tried quadratic voting for our team choosing a new name, and we did not
find it to work well. I think the analysis that the scheme even converges
makes simplifying assumptions that aren't well justified, particularly that
everyone knows the marginal probability of each candidate winning (when that
itself is behind a fairly inscrutable voting method.) Without that assumption
I think it falls apart.

The optimal strategy is to vote maximally for your preferred most likely
contender, and maximally against the nearest competitor, but if you don't know
who those are, the system provides no means of discovery. So strategic voting
is not just possible, it is critical to have any influence, but the evidence
needed for optimal strategic voting is neither obvious, nor revealed by the
system, (and from our experience I don't think it has any stable Nash
equilibria.)

After a few days with the system, we finally abandoned it and switched to a
condorcet election.

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steenreem
While reading I wasn't convinced this was going to work due to the collusion
problem, until I read the comments on collusion which add an extra condition:
"we need votes to be so private that even the person who made the vote can't
prove to anyone else what they voted for."

However, this condition is not enough, it doesn't cover the case where someone
is being watched while they are voting. The condition should be something
like:

"we need votes to be so private that only the voter can know what he voted on"

I don't see many solutions to this, except the '19th century' way of voting at
a voting station, or a voting machine that can read minds. Obviously it would
be pretty strange inputting your vote through thoughts, especially since this
system might never allow you to confirm what you voted on.

However, I guess even ballot voting could suffer from collusion since it's not
fundamentally private. You could take a hidden camera into the voting box and
record your vote, and afterwards get a payout.

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seangrogg
I've always enjoyed the concept of exponential costs for incremental gains.
I've had the benefit of only really utilizing them in strong-identity systems
(games) but I've considered some of the drawbacks of using them in weak-
identity systems and come to a few ideas:

1) A participation barrier can be used to prevent identities from
participating until they've overcome something. A simple example would be an
age barrier (identity must exist for some period of time before participating)
which prevents spinning up multiple identities on-demand to try to increase
voting power. Ideally, in practice there would be multiple barriers that would
be naturally-occurring for a real participating identity but too expensive to
create/maintain several identities.

2) Similar to (1), have an ongoing cost to maintaining identities. Something
such as a "subscription fee" may serve as a deterrent as the value of one
identity needs to be weighed against the cost of maintaining it. This can be
made additionally effective if the issue being voted on recurs every period
rather than one-time (i.e. revisiting regulation votes every cycle instead of
just voting once and having the regulation remain until stricken). For the
normal participant, the value of this subscription could be offset by access
to a non-scaling benefit - i.e. access to private content/events.

3) While the article focuses on the economics in terms of dollars there's the
very real question of allowing votes to be purchased with other forms of
currency that either complement or replace traditional currency. This is
common in MMOs where you can have multiple characters (weak identities) each
with their own in-game currency that can be acquired from in-game activities
and may or may not be exchanged with real-world currency depending on the
stance the owners of the game take.

Suffice it to say there aren't really silver bullets to "general purpose
quadratic payments with weak identities" but you could create some limited-
purpose constraints that are particular to the problem/community and make some
strides from there.

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creeble
It seems like solving the Sybil problem (a prerequisite to this scheme having
any use whatsoever) might be something better on which to focus attention
first, as it has other useful applications, even in one-person, one-vote
democracies.

~~~
rytill
Pushing this idea doesn't mean other problems in the space aren't being
thought about.

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say_it_as_it_is
Really great to see Vitalik working with Glen Weyl's ideas. Weyl's collection
of "radical ideas" may actually become more than just thought experiments.

~~~
DennisP
They actually authored a paper together:
[https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3243656](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3243656)

On arxiv: [https://arxiv.org/abs/1809.06421](https://arxiv.org/abs/1809.06421)

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rajacombinator
The main topics of interest here are how non “quadratic” voting converges to
quadratic via influence peddling or subquadratic in the form of rigged/kabuki
elections.

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slowhand09
Interesting article.

