
Quadratic voting (2014) - alansammarone
http://ericposner.com/quadratic-voting/
======
Nuzzerino
This is fascinating, as I've done some work with weighted voting systems in
the past.

If I understand correctly, some emergent effects would occur.

1\. The poor would collectively have less voting power.

2\. The poor would likely become less poor due to distribution of voting
funds. This would be roughly proportional to the amount of voting power lost.

3\. The middle class, assuming it still exists the way we know it, may or may
not have increased collective voting power.

4\. Upper-middle class will gain proportionally more collective voting power
than what middle class gained, but they are fewer in population. The 1% will
gain even more, but they are only 1% of the population. Each social class
(aside from the poor) will have more representation, while the poor will
receive money (and a tiny amount of representation).

5\. More passionate voters will pay more, and polarizing or strongly
motivating issues will create a less-predictable situation at the polls. This
could be a very good thing or a very bad thing, I don't know. Perhaps this is
where the magic happens.

6\. Political groups will form voting coalitons to vote certain ways, and may
be paid to do so, beyond the voting fees, unless legally prohibited. However,
this may prove to be not the most viable use of resources.

I think that this could work in positive ways. However, I wouldn't bet on it,
as there are as many things that could go wrong. When dealing with complex
strategy or architecture choices with unknown consequences, it is a hard sell
to willingly go with one that brings significant risk. However, one can argue,
especially with the current political climate and lack of faith in the system,
that not switching to this would be the bigger risk.

I'm interested in finding smaller scale applications of such a system, as a
crude proof of concept.

------
igitur
I accept that this is a superior voting system to one-person-one-vote.
However, for it to succeed, it should not merely be superior, it should also
appear superior. The trust the voters put into the system is paramount. And
for that to be true, the vast majority of the voters have to understand
exactly how it works. Unfortunately, and, yes, I'm a cynic, I don't believe we
are close to having a voter base that is capable of understanding, and hence
accepting an outcome of such a voting system.

Disclaimer: I'm not a US citizen.

~~~
ZenoArrow
How is this a superior voting system? It just seems to be a way for those with
more money to have more influence in the voting process. We've got enough
problems with money in politics as it is, we don't need any more of them.

~~~
ACow_Adonis
Your post is actually extremely important and spells out one of the primary
weaknesses of such a system. As long as the budget obtained for the vote does
not have an opportunity cost with the rest of a person's wealth/budget (and I
can't think of any practical way to make that happen in reality), what the
voting system will in effect create is increased voting power by the wealthy,
as they suffer comparatively less marginal loss from expending their entire
voting budget goals towards their agenda, irrespective of their strength of
belief: the downside comes from their lack of any real real-world budgetary
pain.

Unless one can come up with a way to inflict the same budgetary pain on each
individual for each vote-expenditure, I don't really see how you would argue
for its implementation/superiority in practice (against the other forms of
voting out there I mean, not necessarily contrasted just against first past
the post...).

Though this all depends on what one means by "optimal voting" or "efficient",
since I don't believe there can be an objective definition of such.

~~~
papaf
As I understood it, "buy" does not have to be money. It could be hashing
ability as in Bitcoin or maybe everyone gets X voting credits every few years
which they "buy" votes in local and national elections.

I could be wrong, but I prefer the possibilities of such a system not directly
involving money. The distribution of wealth is so imbalanced that I cannot see
buying votes to have any kind of positive impact.

~~~
ultrafilter
Yes. Perhaps the voting currency should be hours, not dollars. Make the first
vote free. But N-1 more votes costs you N^2-1 hours from your "registered
community service" account maintained by the government. No overdrafts
allowed: the hours must be credited before they can be debited.

------
dcuthbertson
Is this a fair system? It looks to me like the very wealthy get there own way.

Let's say I'm a very wealthy person, and I have $4M to spend. It looks like I
can buy 2000 votes. However, money is very fluid. So I decide I'm going to
find 10,000 "budget-constrained" voters and give them each $400. I'll say,
"Here's $100 for buying 10 votes, and keep the remaining $300 for yourself."
Now I've just purchased 100,000 votes.

Ah! ZenoArrow
([https://news.ycombinator.com/item?id=15206589](https://news.ycombinator.com/item?id=15206589))
beat me to it. Well done.

~~~
troupe
If we have a system that allows you to buy votes from other people, how is
that any more of a flaw than simply using our current method of voting and
allowing the same type of vote buying?

It sounds like you are saying that a system that allows you to buy other
people's votes skews toward rich people. We don't outright allow that today
unless you count advertising. With the quadratic system proposed, rich would
have to choose between advertising or putting more money into the voter pool
(is distributed to everyone and thus increases the voting power of the poorer
majority).

~~~
notahacker
In this system rich people have the opportunity to buy a couple of extra votes
for (e.g.) everyone who has been a member of Party X for four or more years.
Unlike the present one-man, one-vote system, they can swing the election in
favour of their cause without changing a single person's mind.

------
lindig
> 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.

Calling the majority tyrannous and assuming fringe interests to be naturally
benevolent reeks of an agenda.

~~~
ComputerGuru
That’s a phrase, well-accepted and very famous in this domain.
[https://en.m.wikipedia.org/wiki/Tyranny_of_the_majority](https://en.m.wikipedia.org/wiki/Tyranny_of_the_majority)

Please don’t insinuate bad intent where there needn’t be any.

~~~
ZenoArrow
The suggestion being made is that the unwashed masses don't know what's best
for them, and need to be guided by the enlightened minority. The problem with
this is that there isn't a minority that's fit to lead. No one group fully
understands the needs and wants of a society. That's why, as imperfect as it
is, it makes sense for every citizen (of voting age) to have an equal say in
how a society is run.

~~~
mac01021
The phrase "tyranny of the majority" does not usually refer to an
unenlightened majority making suboptimal decisions for itself (and therefore
requiring the rule of a more enlightened minority).

It more often refers to settings where a majority and a minority have
conflicting interests, and in which the majority is inclined exploit the
minority in ways where the damage endured by the exploited far outweighs the
benefit to the beneficiaries. The phrase has been uttered: "Democracy can be
like two wolves and a sheep deciding what to have for dinner."

    
    
      EG:
    
     - A majority of city-dwellers will vote to destroy the homes of the forest people to improve the development of their cities, however slightly.
    
     - A majority of old people will vote to tax the young more heavily to achieve a transfer of wealth, even though the gains of each beneficiary is smaller than the loss of each loser
    
     - That same majority of old people, finding that their preferences in nearly every domain are different from those of the young, might vote to raise the voting age.
    
     - ...

~~~
ZenoArrow
> "It more often refers to settings where a majority and a minority have
> conflicting interests"

Look beyond the surface level. If you can't trust the majority to make the
right decisions, who do you trust to do so? The only reason to bring up the
tyranny of the majority is to imply that another (smaller) group could do it
better.

~~~
tentaTherapist
Good question, but although I'm too stupid to come up with an answer, I hope
there is one, because the whole majority-exploiting-the-minority scenario
sounds awful.

------
FeepingCreature
Why would you ever pay for an additional vote yourself, instead of giving the
money to someone likely to vote in your favor? If you want 50 votes, just give
3$ to 1/p * 50 people with a p probability of voting for the thing you want.
1/p * 150$ is almost certainly massively cheaper than 2500$.

~~~
dagss
Because the people you pay could just take the money and then cast the
(secret) vote the other way. Secret voting is what prevents buying votes
today.

~~~
Toboe
Could. With a better choice you can get a better chance: 1\. Take an
organization working for your cause, 2\. identify a subset of org members you
assume to be zealous enough for your taste 3\. give all of them some money

Now: Your vote can be bought once Then: Your vote can be bought arbitrarily
often with diminishing returns.

------
ivanhoe
Hmm, but what if "a minority that cares passionately" are nazis or religious
fanatics or some other extremist group? They fit the description pretty well,
and just being a minority doesn't validate your ideas or views automatically.
This system would, as a side-effect, effectively give more political leverage
to all extremist groups out there, too.

In many European countries ethnical minorities are given a few guaranteed
seats in the parliament to ensure that their voices are heard. The same could
be done for a wider spectrum of minority groups that are of interest to
society, selectively boosting their political influence, but still filtering
out the crazy ones. Problem with this is that it's not as stable as giving
everyone the same rights unconditionally, as it's much more prone to
manipulations, like cutting deals with minority representatives who got
elected without voting and making wide coalitions with them in order to take
over the power, against the will of the majority.

~~~
versteegen
I think you actually have it back to front at least in the most extreme
example. Suppose group A strongly wish to do horrible things to group B,
expel/exterminate/incarcerate, whatever. A might care passionately, but B's
lives are at stake, they care even more about the issue. A wouldn't actually
get their way unless they are the majority.

As long as one group's actions are considerably detrimental to another, that
other group will care.

~~~
emerongi
A could be a big enough threat that B will buy a lot of votes.

In a way, A can blackmail B, because the money gets distributed later (A will
get a lot more back than they put in, because B bought an unnecessarily high
amount of votes).

Is this scenario acceptable?

------
jacquesm
The real problem is that there is a tyranny of sorts involved, whether by the
majority or the minority is not really all that important. Consensus building
should be the norm, not to ram your view down other people's throats because
you can.

~~~
zo1
We can't have genuine consensus until people reason with arguments and facts,
instead of emotions. And emotions are currently extremely manipulatable. The
entire media ecosystem is built around doing just that.

~~~
ZenoArrow
That's why school subjects like media studies and civics aren't bullshit
wishy-washy ones, they're essential for getting us out of this rut. We should
teach the young how to be better citizens than we are by equipping them with
the tools to see through propaganda and to help them set the direction they
see as best for their country.

Also, there should be room for both rationality and emotion in public debate.
Emotion is a key part of the human experience, making decisions based on
rationality alone will stop us seeing why certain rational decisions should
not be followed.

~~~
zo1
I'm fine with that as long as they're not used for indoctrination. I.e. Every
single issue and previous decision by society needs to be "re-decided" by the
children in the civics class, without influence by the teachers. If you're not
doing that, you're reinforcing previous generations' biases in the form of
indoctrination. It's a very precarious line to walk, and a very important one
because you're dealing with innocent and impressionable minds.

~~~
ZenoArrow
Yes, it would be best to let the students explore the subjects with only a
minimum of guidance. I'd suggest that for this reason it'd make sense if these
subjects were not graded.

------
ykler
I didn't read the whole article, so maybe they address this, but instead of
letting people buy votes with money, which favors the rich, why not allocate
an equal number of special credits to everyone that they can apportion among
different issues (still using the quadratic system, if that there are reasons
to think that is optimal)?

~~~
troupe
Interesting idea. The difference I see is that with the payments, the money
goes back to the voting pool. So a rich person buying lots of votes for
something they care about, gives money to everyone else which increases
everyone's ability to vote with more weight on things they care about.

~~~
ykler
I suppose, although with the money system it seem like there is this crazy
hyperparameter of how much a single vote costs. Plus, if you want to make
things more economically equal (which is something we should want), you can do
that with redistributive taxation. There are pragmatic considerations of what
can get passed, but the same is true of voting reform. (Many people will make
their decisions based on whether it will benefit their causes. This is why,
for example, we have gerrymandering and left-right polarization on issues like
making voter registration easy or allowing felons to vote or electoral college
reform. General principles take a backseat, perhaps even rightly to some
extent, to what one believes will lead to good outcomes.)

~~~
HelloNurse
Vote cost is not a crazy hyperparameter: it's only an arbitrary unit of
measure. If votes "cost twice as much" everyone buys sqrt(Xi/2) votes rather
than sqrt(Xi), by spending a fixed sum Xi that depends on the utility of
winning the vote. Results are unchanged.

------
simonsarris
Take note if you're thinking:

> Hmm, but what if "a minority that cares passionately" are nazis or religious
> fanatics or some other extremist group?

Then they cause an outcome by _paying all the people that are not in the
minority lots of money_ , and then next election the majority uses that money,
more effectively per voter, to reverse the outcome.

If you think the median individual is rational enough to be allowed to vote at
all (I don't), then the passionate minority still has to keep the majority
happy or else they transfer large sums of money and therefore a larger sum of
distributed-voting-power onto that group for future elections.

Understanding the quadratic effects and that _the money is returned per
capita_ is absolutely key to the beauty of it. Imagine 10 rich voters buying
an election out of 1000 voters. They spend $10 million to do so. The next
election, those 990 (now unhappy) voters, with the proceeds of the $10m money
they received, can all buy _many more_ distributed votes than the 10 voters
were able to buy, and reverse the decision overwhelmingly.

So if you're really worried about this (and think voters are rational), just
allow snap elections or votes of no confidence if there's enough protest, and
the majority with their new dollars can right the ship very quickly.

------
snarfy
I'm not sure the tyranny of the minority that we have now is any better.

~~~
zo1
Yeah, the minority of elected officials and bureaucrats. It's kind of sad
seeing how little say the voting-populace actually has. Not only are they
fragmented per-issue, but the entire establishment is built around not
actually getting things done. E.g. Look at how Trump is not actually able to
do any of the things he was voted in by the voting populace to do. What is the
point of voting him in then? Either you want all of what he platformed on, or
you want some of it and you're hoping that that "some" thing that he manages
to do is the thing you actually want?

It's all bread and circuses, with the media running the circus. Just spend 10
minutes watching one of the big networks and you quickly realize it's all just
rhetoric and bias, sprinkled with facts. No one reasons or argues, it's all
just emotions and word-juggling. E.g. the recent "undocumented citizens" and
"dreamers" double-speak when referring to illegal alien children under DACA.
They're children, they're illegal aliens, it's not that hard.

Edit. Grammar.

------
CuriousSkeptic
If you think of the market as another democratic institution (albeit with
another set of principles for what's considered fair), could this be a step
towards addressing both? (A market is afer all just another way to try and
select preferences fairly and effective)

I've long found it an interesting idea to allocate limited capital assets (aka
land) in a similar manner, select best use (aka owner) through highest bid
(aka vote), but offset the opportunity cost, and rent extraction, by
expressing said bid in a rent paid as a public dividend.

Perhaps when discussin public policy decision by means of voting with your
wallet it opens the door to also discuss market decisions as a democracy
implementation.

(Oh well, I have a 58-page paper to read to see if this comment was entirely
of topic)

------
XorNot
The real problem is the winners take small American electoral system and the
lack of mandatory voting.

Fix either one, preferably fix both, and I suspect people will stop proposing
brain dead ideas like this.

------
chestervonwinch
_> Weyl and Lalley prove that the collective decision rapidly approximates
efficiency as the number of voters increases. By contrast, no extant voting
procedure is efficient._

I'm assuming they're working within some mathematical formalism where
efficiency is defined in some manner, but I can't access the linked paper. Can
anyone explain what efficiency means in this context or provide some links to
the mathematical framework for this stuff?

~~~
VHRanger
Efficient usually refers to Pareto efficiency. Sometimes (rarely) Kaldor-Hicks
efficiency or "no deadweight loss" efficiency

------
rwmj
At a cursory read, this is similar to Demand-Revealing Referenda / Revealed
Preferences, I think?
[http://stumblingandmumbling.typepad.com/stumbling_and_mumbli...](http://stumblingandmumbling.typepad.com/stumbling_and_mumbling/2007/03/trident_how_to_.html)
[https://rwmj.wordpress.com/2014/03/27/half-baked-ideas-
deman...](https://rwmj.wordpress.com/2014/03/27/half-baked-ideas-demand-
revealing-referenda-applied-to-fedora-features/)

I love that there are so many better ways to vote, and I hate that we still
use FPTP.

------
lordnacho
Does anyone know whether this has any effect on Arrow's Impossibility Theorem?
Or does it violate some assumption, making it a separate (but related) issue?
(Of course a theorem is a theorem, so it's not going to invalidate it...)

I'd assume that this paper is written by someone who has intimate knowledge of
AIT, just looking for some perspective.

~~~
Ari_Rahikkala
AIT applies to:

\- Votes with at least three options. A simple majority vote between two
options does in fact satisfy all of Arrow's fairness criteria (if only
vacuously).

\- Ranked voting systems, i.e. ones where voters only give a rank ordering of
their options, not any more information.

Quadratic voting is neither of those: It applies only to binary decisions, but
for those decisions, it tries to be more fair than Arrow's criteria call for,
by getting out not only information about which option voters prefer, but how
strongly they prefer it. Whether it could be extended to more complex votes
than binary ones, I don't know.

------
Vinnl
One question that remains for me other than whether this is fair to groups
with income <x>, is: how do you decide which proposals to vote on? Otherwise,
there'd be incentive to submit ridiculous proposals that greatly disadvantage
the wealthy, who would then have to pony up to keep those proposals from being
implemented.

------
quickben
Allow me to shine some light on the title:

What does the general population think if aristocracy is about to buy back
it's way to power?

------
notahacker
HN thread from two years ago, featuring participation from the paper's
authors:

[https://news.ycombinator.com/item?id=9477747](https://news.ycombinator.com/item?id=9477747)

------
rurban
It only favors extremists and extremely rich over the normal democratic
process. But since the US is already an oligarchy, it makes sense for them.

And it's of course a cheap take on the tragedy of the commons.

------
Ygg2
How does it work?

If there is say - Aerith and Bob running for president, say there are Charlie
and Drako that want to buy two votes each for Aerith.

Do they each pay 4 or do they pay 16?

~~~
totalZero
They each pay 4.

Otherwise, a marginal vote purchased by a different voter would change the
total price of prior purchased votes. If votes were tallied per candidate,
voters would bid without knowing how much they owe until after the election.

------
scotty79
So basically a basic income scheme financed by people with financial interest
for the law to be one way or another.

------
igitur
I would like to see how this compares to exponential voting.

------
crazygringo
This is certainly an intriguing and creative proposal.

But as the paper notes, it is mainly around referendum voting. And referendum
voting can be viewed as opposed to representative democracy. Voters will
happily vote yes on one referendum for higher benefits, and yes on another
referendum on lower taxes, and the end result is laws that don't make sense.
This can be seen as an example of the Condorcet Paradox [1]. But the point is,
referendums are generally a terrible way to make decisions.

So on page 45 of the paper [2], the authors discuss that democracies are
generally run according to representation, not referendums. So first they
suggest using QV to elect candidates. Yet when given a choice between 2 (or
even a handful) of candidates, do we really expect QV to make a difference?
Republicans and Democrats are both extremely passionate, so I'd call it a
wash. There's such a mix of social and economic issues large and small, QV
doesn't seem to help untangle that.

The second thing the authors suggest is for representatives to "put their
constituents' money at stake" when voting on laws. The authors wisely don't go
too deeply into this, because it's clearly nonsensical when representatives
are from a district which contains significant members of both sides. They
actually admit as much ("QV in representative assemblies would probably make
more sense in a parliamentary system than in a presidential system") but
actually get their terminology wrong -- it would make more sense in a
_proportional representation_ system than in a _first-past-the-post_ system.
(Presidential/parliamentary refers to the relationship between the legislature
and the executive, which this proposal has nothing to do with -- which reveals
their amatueur-ish level of analysis in this case.) At least they're honest in
saying "many details clearly need to be worked out".

But I have an even more basic question, even for deciding referendums: who
determines the base price of a vote? If a single vote cost $0.10 or $100, I
imagine that could drastically affect outcomes, and I don't see them address
this question anywhere.

[1]
[https://en.wikipedia.org/wiki/Condorcet_paradox](https://en.wikipedia.org/wiki/Condorcet_paradox)

[2]
[https://poseidon01.ssrn.com/delivery.php?ID=2871141120741160...](https://poseidon01.ssrn.com/delivery.php?ID=287114112074116088083081078093027028127035061037007087028124077125100068075086098105101029122061103047118074117001004065016074013074027021053114119097009025082072058089039087066113081004111112107026019118092094008080003119026104024028079005074103100&EXT=pdf)

------
Banthum
What's the reasoning behind choosing the power of 2 for this?

It could be tuned to a power of 1.9 or 2.1 or 3 or 1.5.

Aside from being a round number, how do we know 2 is best? What would be the
pro/con of a higher exponent? What about the pro/con of a lower exponent?

~~~
Rangi42
As the paper's abstract states, "Quadratic cost uniquely makes the marginal
cost proportional to votes purchased". The full paper shows their proof and
the assumptions behind it, such as "an individuals’ value for votes is likely
to be approximately linear in the number of votes she casts so long as her
utility is driven by the impact she has on the vote total, as argued by
Mueller (1973, 1977) and Laine (1977)".

