
Quadratic Voting - k2enemy
https://en.wikipedia.org/wiki/Quadratic_voting
======
lalaland1125
One key principle that a lot of people miss is that quadratic voting doesn't
work with real money because people don't value wealth in a linear fashion. $5
is worth much more for a homeless person than for a millionaire. Proof of this
can be seen in preference surveys or other studies of human behavior. This
fact breaks the key assumption of quadratic voting and causes skewed results
in that people with more money can buy more votes even with "weaker"
preferences.

~~~
elpin
This is addressed in the Wikipedia page under "Criticisms of quadratic voting
mechanisms".

Potential solutions include giving everyone the same amount of starting
artificial "money", using one-person-one-vote when issues are polarized along
wealth-lines, or making votes more expensive for the wealthy.

To me, the first option of delegating everyone the same starting votes seems
the most reasonable. However, I think allocating vote prices based on wealth
could create some interesting incentives and resulting politics.

~~~
sandworm101
What the wikipedia criticism doesn't mention issue flooding/packing. Quadratic
voting works, on paper, when applied to set piece issues. It doesn't address
the reality of legislatures, that "issues" are not fixed pieces on a
chessboard. Issues can be split across multiple referendums. Whoever is in
control can use splits to dilute votes, causing voters to spend their votes
repeatedly winning a minor issue until their are depleted. Then those who
'lost' the first rounds now have the votes to win the last round. Giving
everyone equal footing on every vote stops this.

~~~
bullfightonmars
I had the same thought. This system does not account for the introduction of
legislation that can be voted on. Who decides which legislation to consider.
Surely the party in power could sway the outcome by stacking the decions
against each other.

This is equivalent to gerrymandering political districts. Spread out the votes
on the issues based on the electors in favor of a predtermined outcome.

------
BorisTheBrave
If I care strongly about an issue, but I also know it's likely to win, isn't
the best tactic for me to not vote for it to save my credits for more marginal
issues?

If everyone votes tacitcally, it seems like a lot of votes would be won with
slim majorities. But that risks random upsets, even on issues which everyone
basically agrees on!

~~~
vivekv
Principles of game theory come into play at that time isnt it?

------
sohamsankaran
What frustrates me most about Quadratic Voting, and in general a lot of ideas
promoted by Glen Weyl and his coterie, is that arguments in its favour almost
completely ignore the significant additional cognitive burden it places on the
populace. American Voters barely understand the difference between the popular
vote and the electoral college -- to ask them to view the results of QV votes
as fair and legitimate would be a bridge too far. Hell, I know a fair bit of
math and CS, and I would feel uncomfortable quickly deciding how to divide my
votes across issues, let alone advising other people on what to do.

~~~
dunkelheit
> American Voters barely understand the difference between the popular vote
> and the electoral college -- to ask them to view the results of QV votes as
> fair and legitimate would be a bridge too far.

It is not like simpler voting methods are without subtleties (and I certainly
wouldn't call electoral college simple!), but these subtleties are well-known
and everybody is kind of accustomed to them. Again, immediately abandoning
ordinary voting and switching to QV on the level of countries would be stupid,
but I don't think they are advocating that.

> Hell, I know a fair bit of math and CS, and I would feel uncomfortable
> quickly deciding how to divide my votes across issues, let alone advising
> other people on what to do.

This can probably be less of a problem with sufficiently good UI. Imagine that
you can play with some sliders and immediately see the consequences of your
actions. After some fiddling you will probably get pretty close to what you
want. Some friction can even be beneficial, encouraging people to be more
thoughtful about issues. There was a study (link:
[https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2755844](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2755844))
where they used QV in opinion polls and were able to get more information
about relative preferences of participants because they were forced to think
about correctly allocating their credits instead of blindly answering
"strongly agree"/"strongly disagree" even if they didn't really care about a
particular issue.

------
xchaotic
Actually, I think what would be more useful is the ability to vote directly on
all things and delegate your vote on specific topics or in general when you
want not every 4 years. We can have the technology to enable this and it would
effectively kill a full time politician as a job. That think would instead be
done by retirees in their spare time. And if things were not going to work in
the right direction, you can vote immediately, any time. If, on the other hand
you don’t care or don’t know enough about the subject, you can delegate your
vote and that person can also delegate your and her vote too.

~~~
learnstats2
Who sets the questions?

In a parliamentary democracy, the full-time politicians decide what is
debated; what is up for debate; what is possible to change through a vote (and
what is not possible to change by not putting it up for a vote).

They also decide what civil servants act upon - and what they don't. What is
researched and evidenced - and what is not.

Deciding what direction you want to vote on a particular single issue is
relatively late in the process of democracy (and conveys relatively little
power).

The power to elect a representative is thus much greater, fairer, and more
desirable, than the power to flex your vote on single issues.

~~~
rrrrrrrrrrrryan
A liquid democracy would have to be much closer to direct democracy than
representative democracy in this regard.

In California you need to collect a certain percentage of the population's
signatures to get something on the ballot, and I imagine it'd have to work the
same way. You could increase the frequency to yearly, or even quarterly, and
build a system where you can endorse anything you want to be added to a
ballot, then once a quarter you can vote on the issues you care about, and
give the rest of your voting power to any other citizen, who can do the same
for any other issues.

~~~
learnstats2
Parliaments set the agenda on a _daily_ basis.

How do you cope with coronavirus by making decisions on a quarterly basis?

------
tromp
> For example, a voter with a budget of 16 vote credits can apply 1 vote
> credit to each of the 16 issues. However, if the individual has a stronger
> passion or sentiment on an issue, they could allocate 4 votes, at the cost
> of 16 credits, to the singular issue, effectively using up their entire
> budget.

It would be better for this individual "A" to find another one "B" who feels
strongly about another issue, and agree to both use 2 votes each on A's cause
in exchange for both using 2 votes each on B's cause. That way they each pay
only 2^2+2^2 = 8 instead of 16, for the same outcome. This assumes some amount
of trust between A and B in case they cannot provide each other with evidence
of how they voted.

------
cryptonector
> Under various sets of conditions, quadratic voting has been shown to be much
> more efficient than one-person-one-vote in aligning collective decisions
> with doing the most good for the most people.

That's a severe misunderstanding. We don't have elections to make collective
decisions that yield "the most good for the most people". We have elections
because the alternatives to not having elections are worse.

Moreover, "the most good for the most people" is subjective -- any objective
measures of that that you come up with will be subjectively chosen. Some will
say that maximizing the health of the environment does the most good for the
most people, while others will say that maximizing GDP per-capita does -- if
those two are in conflict, who's right? Elections sidestep the matter: it's
not about being right, but about what people want.

Sometimes people want things they really really shouldn't, and they may try to
get their way via elections. For that we have institutions (e.g.,
constitutions, courts, separation of powers, etc.) that keep them from getting
those things for some time. The alternative to all that is absolute monarchy,
caudillos, dictatorship, war, anarchy (for a while until you get a strongman)
-- all bad things.

If you manage to impose a technocracy not headed by a strongman, soon it will
be, and either way may well lead to revolt, possibly civil war.

I too would like a better system, because "democracy is the worst system of
governance, except for all the others", but like Churchill, I'm skeptical that
there is something better than a constitutional, democratic republican form of
government.

Utopia peddling seems very commonplace nowadays. That's a bit worrisome.

~~~
zodiac
I think research into voting systems like this shouldn't be read as coming
from a point of view of "we have the correct objective function we prove that
our system is unequivocably optimal under this objective function". Rather the
objective function is a "toy model" which we understand does not capture all
of reality, but hopefully captures enough of it to provide some interesting
insight.

I mean, obviously policies and outcomes at stake in any voting system are
subjective, so that's an objection that can be levelled against any objective
function, but that includes anything you choose as well. E.g. if you say that
your objective function will be to minimize the risk of participants getting
dissatisfied enough to violently go out of the system (i.e. revolt / civil
war), well, one-person-one-vote can fail like that too; who's to say that that
system is really optimal with respect to this objective function?

------
mirekrusin
Why not simply allocate weights of preference between choices so they sum up
to 1 (100%)?

If you require that some peoples votes are of higher weight, run the same
thing but on population that votes - assigning weight to every individual - so
it sums up to 1 (100%) as well.

With problem defined in this way you have this intuitive tool to easily
compose/merge or compare outcomes, ie. voting run for shareholders (weighted
on shares) can be merged with votes of ie. employees (could be weighted on
salary and/or time spent in the company) - all those can be merged givig
weight to each vote run.

This can be extended with more exotic things like votes (at any level)
attached to probablity of some yet unknown "fact" or time or any arbirary
input which is an output of any DAG created by this voting rule. This makes
the whole setup dynamic. Complexity always collapses into simple, intuitive
values that can be interpreted (and used as input for other voting-like
decisions).

Weighted voting all the way down.

------
orbifold
Prussia had a three tiered voting system, which allotted electors by dividing
the tax income per district in three parts and awarding equal numbers of
electors to each of the subpopulations (4.7%, 12.7%, 82.6% of the population
in 1849). That it was applied per district had the interesting consequence
that even wealthy people could easily be in the lowest of these three brackets
([https://en.wikipedia.org/wiki/Prussian_three-
class_franchise](https://en.wikipedia.org/wiki/Prussian_three-
class_franchise))

------
tgv
So, for this to work \- you need a reasonably large set of decisions to be
decided in one big election, \- rational agents, even though the topics is
emotional.

And how do they reach the conclusion that "the system will be predisposed to
dominance by special interest groups with strong, concentrated interests"?
That might be in some limit towards infinity case, but in practice? And why
that would be a good thing, is beyond me.

~~~
erentz
And who decides what the issues are that get voted on? This is an important
flaw IMO against multi issue voting with this system.

If the people making the list of issues are biased they can make one big issue
for all the stuff they care about, and a thousand little issues for the stuff
other people care about.

Every issue needs equal footing to overcome this, meaning each issue needs to
be its own independent election, effectively making QV useless.

~~~
tgv
I too think it's totally possible to rig such elections. E.g., if there's
something group A wants, but you don't, you add something group A is totally
against, so all their votes will go to the latter issue, and the status quo is
kept as far as group A is concerned. Meanwhile, their votes are lost for other
issues.

------
noodlesUK
I really like the idea of this assuming it’s some kind of vote credit rather
than money, and the vote credits are distributed equally per person. However,
it doesn’t take into account that the number of things to vote on might not be
fixed (or even finite). As more things to vote on are added, do people get
more votes? How are they distributed? This would create a whole new variable
to gerrymander.

------
bsurmanski
This is the voting mechanism used in the game "Civilization VI" (Gathering
Storm expansion), if you are interested in checking it out

------
antiquark
Odd that they didn't mention Arrow's impossibility theorem:

[https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem](https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem)

[https://plato.stanford.edu/entries/arrows-
theorem](https://plato.stanford.edu/entries/arrows-theorem)

~~~
naniwaduni
Arrow's theorem is an interesting result on its own, but its practical
applicability is kind of undermined by the fact that the dictatorship
criterion is actually pretty rarely interesting (and is almost totally
irrelevant to a ballot).

~~~
contravariant
You do realise that the dictatorship criterion simply replicates the vote of
one particular voter _no matter what_? [1]

In most realistic implementations this is likely either the first or the last
voter. Surely we can agree that those wouldn't really be desirable?

[1]: See here for a somewhat easy to follow proof:
[https://www.math.ucla.edu/~tao/arrow.pdf](https://www.math.ucla.edu/~tao/arrow.pdf)

~~~
naniwaduni
The dictatorship criterion is slightly more wide-reaching than that specific
construction which makes it sound silly (though, honestly, not really
tremendously unfair). Your link gives a decent enough definition:

> (No dictators) If a single voter prefers X to Y, but all other voters
> disagree, then the voting system should override the wishes of that single
> voter and rank Y higher than X.

~~~
contravariant
The problem is that that criterion combined with the other conditions becomes
equivalent to there being no 1-man quorums. As the rest of the proof shows the
negation of this implies that there is a dictator, who completely determines
the result for all votes.

I guess in a ballot system it might be pretty tricky to figure out who this
person is, but in the end it just boils down to the order in which the votes
are put into the sorting system.

No while sortition has it's advantages it goes against most people's intuition
of what a fair voting system is. And technically arrow's definition of voting
systems is deterministic, although you could always shuffle the votes
beforehand.

------
nabla9
Quadratic Election Law (great article)
[https://www.law.uchicago.edu/news/quadratic-election-
law](https://www.law.uchicago.edu/news/quadratic-election-law)

------
arnejenssen
I wonder how it would work on popular TV shows like American Idol. Maybe it is
not in the interest of the broadcaster that the voters get less
frustrated/angry with the outcome?

------
munfred
Nice to see this here, I spent the last weekend reading about quadratic
voting/funding. The core idea is that in order to decide how much
"endorsement" each project amongst many receives, you take the square root of
how much each person gave to that project, sum that, then square it to decide
how much of a matching contribution to be given.

It has a couple interesting properties that make it appealing for the funding
of "public goods" (such as software) via grant matching mechanisms. The main
ones:

\- Projects with distinct supporter bases will receive more funding if they
join forces as a single project with more supporters

\- Projects with few supporters that give a lot of money/endorsement will
receive very little boost from this

\- You can also implement the possibility of "negative votes/funding" that
allow people to "short" the projects that they consider a net negative

Over the past year a grant matching mechanism using quadratic funding has been
trialed in a platform called Gitcoin, which supports crowdfunding Ethereum
development projects: [https://gitcoin.co/blog/everything-you-need-to-know-
about-gi...](https://gitcoin.co/blog/everything-you-need-to-know-about-
gitcoin/)

A post by Vitalik Buterin describing quadratic funding is here:
[https://vitalik.ca/general/2019/12/07/quadratic.html](https://vitalik.ca/general/2019/12/07/quadratic.html)

Vitalik also wrote about the last 3 rounds of this funding on Gitcoin, they’ve
been making tweaks and the results are extremely promising:

[https://vitalik.ca/general/2020/04/30/round5.html](https://vitalik.ca/general/2020/04/30/round5.html)
[https://vitalik.ca/general/2020/01/28/round4.html](https://vitalik.ca/general/2020/01/28/round4.html)
[https://vitalik.ca/general/2019/10/24/gitcoin.html](https://vitalik.ca/general/2019/10/24/gitcoin.html)

The idea of quadratic funding came from quadratic voting, which was discussed
in the 2018 book Radical Markets:
[https://vitalik.ca/general/2018/04/20/radical_markets.html](https://vitalik.ca/general/2018/04/20/radical_markets.html)

In september 2018 Vitalik together with one of the book authors and another
person put out a preprint describing their ideas for quadratic funding, which
is very interestingly written:
[https://arxiv.org/pdf/1809.06421.pdf](https://arxiv.org/pdf/1809.06421.pdf)

The broader field under which this fits is called "mechanism design", which
means inverse game theory: instead of specifying the rules and seeing what the
outcome is, you decide which outcome you want and try to design a game that
leads to it...a very enticing idea.

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

------
godelski
If you like this, you'll probably be interested in STAR[0]. It has a really
high voter satisfaction efficiency[1]. Pretty much it is the best if you want
to account for strategic voting[2] (Condorcet methods don't handle these as
well, but do have a higher VSE when it isn't accounted for, but we're talking
pretty close anyways).

So why Cardinal systems? They are a lot easier than ranked systems. You like
two people equally? You hate two people equally? No worries, just give them
the same number. You basically have all the advantages in this case (I'll
mention that Gibbard's[3] is an extension of Arrow's and it applies here). But
why we would want this system is because it makes for the best of both worlds
between the "we need parties" and "fuck parties" groups.

Let's take an example: Pick your favorite outside candidate: Bernie, Tulsi,
Warren, Yang. If the general election was using STAR it wouldn't matter who
the Dems pushed. You could still vote for these candidates and it wouldn't
help you're candidate win. So I'd imagine a HN ballot could look something
like this

Biden: 5

Gabbard: 7

Sanders: 10

Trump: 3

Warren: 9

Yang: 8

If Bernie, Tulsi, Warren, and Yang did not get enough votes to win, it would
still be like the same election where we are choosing Biden v Trump, even
though Biden wasn't your first choice. This means you can vote honestly (i.e.
which candidate is closest to your opinion and not which candidate you think
can win). It entirely removes the "electibility" question.

Why cardinal over ranked? One simple answer is that when cardinal breaks down
it turns into approval voting. Approval voting is "I like this candidate" vs
"I dislike this candidate". It is essentially the way we pick where to eat
with friends. Everyone says "I don't know". So you start listing off places
and once enough people say "sure", you pick that. It doesn't get you the best
place to eat, but no one is really unhappy either. What STAR does is basically
give you the options: "Hate it", "no", "ehhh", "I guess", "fine", "yes", "hell
fucking yeah" (that'd be STAR06).

STAR is simple to understand, leads to high voter satisfaction, removes the
electibility issue, let's parties exist without parties dominating (i.e. other
parties can actually compete), easy to pick a winner, and more qualities we
like in voting systems (if you're trying to make a fair system where people
get representatives that represent their ideals). Of course, this does not fix
the issues of money in politics, people lying, and all that.

This is just one component, but I think an essential component that will have
huge effects on any democratically elected system and I think it is something
that we really should fight for. It is also easy to sell the idea because
everyone wants a more fair voting system.

[0]
[https://en.wikipedia.org/wiki/STAR_voting](https://en.wikipedia.org/wiki/STAR_voting)

[1][https://electionscience.github.io/vse-
sim/VSE/](https://electionscience.github.io/vse-sim/VSE/)

[2]
[https://en.wikipedia.org/wiki/Tactical_voting](https://en.wikipedia.org/wiki/Tactical_voting)

[3]
[https://en.wikipedia.org/wiki/Gibbard%27s_theorem](https://en.wikipedia.org/wiki/Gibbard%27s_theorem)

~~~
naniwaduni
What's the appeal over straight approval voting, which can be explained and
justified in about three sentences, and almost self-evidently produces good-
enough results?

~~~
godelski
There's more finesse in STAR. Because you are better able to specify __how
much you approve__ this leads to higher voter satisfaction.

~~~
rrrrrrrrrrrryan
Is there any hard evidence for this? I'm sure there would be higher voter
satisfaction among the types of folks that study alternative election systems
and don't mind reading about every candidate on their ballot, but more
convoluted systems generally lead to lower voter satisfaction because they're
required to do more work/studying up front to maximize their voting power, and
the results are more difficult to interpret.

Most voters walk into a polling place with 1 or 2 people they like, 1 or 2
people they don't like, and a bunch of people they don't care about, which is
perfectly fine, and it should be taken into account with any proposed voting
system.

~~~
godelski
What do you mean hard evidence? In all the sims (which you can find many more
and much more detailed ones than what I listed, STAR's website has many
itself[0]) it yields better satisfaction than approval. This should be obvious
that it is.

> the results are more difficult to interpret.

Are you concerned about it being complicated? I'm sorry, but I just don't buy
this argument. These types of scales are in questionnaires everywhere. I don't
buy that people are so stupid that they can't just score a candidate. Even if
they just ranked them it wouldn't have a large effect on the outcome. In fact,
this can fix accidents with ranked choice where people accidentally rank
candidates the same rank.

And if a significant amount of people are that dumb, well it still works out.
Leaving an entry blank counts as a score of 0. You can score only a single
candidate if you want, that's fine.

> but more convoluted systems generally lead to lower voter satisfaction
> because they're required to do more work/studying up front to maximize their
> voting power

You aren't required to do anything. And honestly, a lot of people do look into
multiple candidates. Hell, the entire primaries are essentially people doing
background research on candidates. But if they don't, sure, that's just called
dishonest voting, which STAR handles better than ranked.

I honestly don't understand this type of criticism. It hinges on the idea that
the average voter is dumber than a rock.

> Most voters walk into a polling place with 1 or 2 people they like, 1 or 2
> people they don't like, and a bunch of people they don't care about, which
> is perfectly fine, and it should be taken into account with any proposed
> voting system.

You do realize that STAR accounts for this, right? You don't have to vote for
everyone. If you just liked Biden you could just give him any number greater
than 0 and your vote would be for him. At WORST STAR is identical approval.

[0] [https://www.starvoting.us/](https://www.starvoting.us/)

------
sandworm101
>> Using this anonymous ballot system provides identity protection from vote
buying or trading since these exchanges cannot be verified by the buyer or
trader.

I'm really split on that one. I'm not sure that anonymity does much to curb
vote buying. I think it allows vote buying to fly under the radar. If we know
how a politician votes we can then compare that to fundraising and lobbying
records. With anonymous voting we are blind.

A modern lobbyist doesn't care about verifying individual votes. They lobby
multiple people, entire parties, to shift trends. If they fail on an issue
that only means the people they were lobbying don't have control of their
party. The lobbyists move to other people for the next round. Eventually they
work out where to send their money and start winning regardless. At least with
non-anonymous voting outsiders have some hope of tracking what is going on.

~~~
mkolodny
Lobbying is very different from vote buying. Vote buying is saying to someone,
"I'll buy your vote for $X". If votes are anonymous, then there's no way to
verify that you actually got what you paid for.

~~~
cheerlessbog
Presumably there are reliable votes on either side that are well known :
subtract those from the result and you may have a fair idea whther your puppet
obeyed his master. It might not be easy to confidently disobey.

~~~
sokoloff
Votes by people in elections are what’s being contemplated as being bought,
not votes by a much smaller group of representatives on specific legislation.

