
Voting Paradoxes [video] - butterfi
https://www.exploratorium.edu/blogs/tangents/voting-paradoxes
======
john111
I found this video really interesting. I knew that the current US system,
first past the post, has a lot of problems from watching CPG Grey's [1] videos
on it. I didn't know that the alternative systems, like ranked voting, had all
these other weird problems.

It's depressing, really.

[1]
[https://www.youtube.com/watch?v=s7tWHJfhiyo](https://www.youtube.com/watch?v=s7tWHJfhiyo)

~~~
quicklime
While it's true that every voting system has paradoxes, I don't feel that this
makes every system equally bad.

The US has what I would consider a big systemic problem, which is that the
first-past-the-post system leads to spoiler effects, and the result is a two
party system. When I've talked to some people about this, the response I got
was "well all voting systems have problems so we can't fix it without
introducing new problems".

But the monotonicity paradox for elimination voting doesn't seem quite as
serious. It seems to only be likely to come up when the two major choices are
close anyway. If all voting systems are evil, it's the lesser evil.

If the US could implement elimination voting, we could remove a big problem
(the two party system) and replace it with a smaller one: an occasional wrong
choice between the two major parties. But this can happen anyway, for other
reasons, eg one candidate wins the popular vote and the other wins the
electoral college.

I'm aware that the Democratic and Republican parties benefit from the two
party system, so they might not want this, but it seems to me that this is
what voters should want.

~~~
Terr_
I'd like to add that changing the "front-end" of voting (having people rank
choices rather than pick-one) enables a whole slew of potential better-
algorithms, because the input data is fundamentally better.

------
anderskaseorg
This is a great introduction to voting theory, but there are several notable
omissions.

The video doesn’t tell the whole story about what it presents as “ranked
voting”, usually known as Condorcet voting. There are systems that always
yield the Condorcet winner when one exists, and do a good job of resolving the
unavoidable but rare preference cycles as consistently as possible. The most
standard one is the Schulze method, which is used by the Debian, Ubuntu, and
Gentoo projects, among many other organizations.

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

The video asserts that what it presents as “elimination voting”, usually known
as instant-runoff voting, doesn’t suffer from the third-party spoiler effect.
But that’s only true as long as the third party never gains enough support to
have a real chance of winning.

[https://www.youtube.com/watch?v=JtKAScORevQ](https://www.youtube.com/watch?v=JtKAScORevQ)

(I wonder: can you think of a pair of powerful organizations who might want to
ensure that third parties never gain enough support to have a real chance of
winning? Hmmm.)

Finally, the video doesn’t talk about approval voting or score voting, which
use a different ballot type to which Arrow’s impossibility theorem does not
apply. Some game theorists argue that these systems actually do a better job
of finding the ideal Condorcet winner than Condorcet systems do, in the
presence of strategic voting.

[http://rangevoting.org/stratapproval4.pdf](http://rangevoting.org/stratapproval4.pdf)

------
achr2
That's not how ranked voting should work - why would you look at pairs
individually? You can simply take the average rank of all flavours and be done
(in which case Vanilla wins definitively).

Also, most party systems tend to clump together in ideology making the
'paradoxical' choices rare. For instance in Canada we have two leftist main
parties and one conservative. Ranking the conservatives in the middle would be
virtually unheard of.

~~~
unclenoriega
I really wish they would have gone into more voting methods (and counting
methods) than they did. The video as-is seems to be very incomplete.

I thought the same thing about party rankings in the US. If we had ranked
voting, and the Green and Libertarian Parties ran serious campaigns, it seems
that the vast majority would rank G/D and L/R together. I suppose if we had
many parties, though, we could see a 'paradoxical' choice.

~~~
drostie
I haven't fully investigated it yet but at one point I played with the idea of
a "Markov election" based on the fact that Arrow's impossibility theorem
assumes determinism. Nondeterminism is not necessarily a bad thing, if people
agree that it was fair! [1]

In this case your rankings for the candidates constitute a Markov matrix where
you specify that your vote should "flow" from these candidates over to those
candidates. For example someone voting for Alice over Bob over Carol might
have a Markov matrix which states their vote is:

    
    
        1.0  1.0  0.5
        0.0  0.0  0.5
        0.0  0.0  0.0
    

saying "All of the A votes I make should ideally stay for A, all of my B votes
I would like to flow to A, all of my C votes I would like to flow to B or A."
Part of the reason that I haven't figured this out yet is that I don't know
how one should pick these numbers, exactly, to be robust against Arrow's
problems (like adding another candidate not affecting the relative preferences
of two existing ones).

Anyway, based on the election, we average everyone's Markov matrices together!
Then we start from a state where each candidate has an even share of the vote
and everyone collectively determines the flow of the votes in successive
cycles. This basically selects out the eigenvector of the Markov matrix with
the highest eigenvalue, which represents some probability distribution among
the candidates. Now to resolve the pesky problem of cyclic preferences, we use
a fair random number generator to choose from the resulting probability
distribution. Thus everyone has an even say in who they want to win, someone
gets chosen at the end, and if someone really is strongly dominated by someone
else then they will generally get eliminated by the flow of votes from the
other to them.

[1] While I have you excited about randomness I am also a fan of choosing a
leader at random out of the entire population, educating them during a
transition period, then handing them the reins. If you happen to disbelieve in
the Buddhist metaphysics then an example is the _tulku_ system for obtaining
leaders, where they follow somewhat-ambiguous instructions from the previous
holder of the seat to seek out a child born at a specific place at a specific
time who is believed to be the specific reincarnation of the previous holder
of the seat. If you don't believe that metaphysics is right then the search
essentially chooses a child at random to be the leader. Seems to usually work
pretty well for them either way. There's another example from Muslim history
where the leader of the dynasty did not go to one's child because one did not
have children; instead it was transferred from eunuch slave-soldier to eunuch
slave-solder.

~~~
Asooka
I'm also a fan of Monte-Carlo sampling and would like to see it implemented
more in choosing a government, but fully random people wouldn't have
legitimacy to their rule. Social order only works if people believe in it and
I don't see how we can make people believe in fully random choice. That person
could only have power if they fully control the army and why would the army
let themselves be controlled rather than kill the random person and put
someone else in charge, who will promise them the cushy life.

You did mention giving the person training. The problem with that is this will
result in a fully self-perpetuating system that finds ways to not give power
to people who disagree with it.

It still sounds better than the current system, so I'm all for it.

------
akshayB
The presentation is extremely nice and detailed oriented. This also co-relates
to how messed up 2016 US election cycle is and in general how complicated
elections are in USA.

1) You have few candidates on each side Democratic & Republics and eventually
folks get eliminated

2) Then you can have independent candidates that can jump in

3) People finally vote for the president

\- But we have winner takes it all by state

\- The number of electoral votes is decided by the population distribution on
the state

\- Another complication each state can have a different way of solving ties

~~~
dclowd9901
I still maintain one of the best voting systems has you vote successively for
a majority winner.

\- Many candidates run \- If someone has a majority (more than 50% of vote),
that person wins \- Otherwise, top x number of candidates move on to next
round \- repeat

This way, changes in availability are addressed, so people can make fair
choices between one item and the next.

~~~
antognini
That would basically be instant runoff voting. The main issue with that is
that in a polarized election you can have a moderate compromise option
eliminated early. For example, suppose the election is between a far-left,
moderate, and far-right candidate. 40% prefer the far-left candidate, 20%
prefer the moderate candidate, and 40% prefer the far-right candidate. In this
case 60% of the population prefers the moderate candidate to the far-right
candidate, and 60% prefer the moderate candidate to the far-left candidate and
so the moderate candidate should win the election. But in an IRV-type system,
the moderate candidate gets eliminated immediately and the election is then
between the extreme candidates.

------
clarkmoody
Could we conclude that it's better to choose individually in as many
circumstances as possible, since choosing in groups has so many flaws? It
seems the more choices are made by some for all the more people are
dissatisfied.

~~~
erispoe
How do you get rid of collective decision?

~~~
marcosdumay
By liberalism.

You literally allow both choices, and each person gets to make their.

That obviously does not work for everything. But it's always important to keep
in mind, and if you look at any modern government by those lenses you'll see
plenty of superfluous regulation that does nothing but put people down.

------
erikb
Easy enough: (1) You choose any method, (2) if you hit the paradox you declare
the result as invalid, (3) there is only ice cream after a valid vote, and (4)
if there's no ice cream yet goto step 2.

Now the worst case is not that you make a few people unhappy (the majority),
but the worst case is that people start killing each other in the hopes to
change the result. But if you think about it that is also not a bad result,
since then there is more ice cream for you.

~~~
nothrabannosir
I like your optimism! Unfortunately, when Arrow got the nobel prize for
proving that there is no way to avoid this, it's possible that your solution
was considered...

For example: there is no upper bound on the loop. Why would anyone change
their vote when you retry? I.o.w. you might be voting and getting the same
result forever.

:/

~~~
erikb
There is an upper bound to the loop. People die. People lose interest (thereby
changing the population). People get annoyed and thereby more willing to do
stuff to change. Not mathematically provable, but works in most situations
because humans are adaptable.

*edit: I feel a little disappointed that people don't seem get the humor in my post. Maybe dying because people voted chocolate ice cream but you wanted vanilla is a reasonable scenario for some.

------
Joof
We don't always have to vote on one outcome. Multiparty systems often split
representatives by party percentage. This has its own problems, but seems to
allow more party mobility.

------
sdegutis
There's no decent voting system for a body of government this large. Every
kind has critical flaws. The best solution is not to have a nation as gigantic
as the U.S., but obviously that's not gonna happen any time soon. It used to
be a flawed option too, before WMDs, but now all nations are on roughly the
same playing field. Plus there's still something to be said for owning as much
land as you can, for things like oil more so than farms.

~~~
patcon
I feel like the world would be better if some nation(s) were legislatively
stream-lined for experiments in secession (perhaps with trial periods and
other conditions). Would allow for governance innovation without the calamity
of conflict that's required for carving out space today.

EDIT: Perhaps it could involve a hypothesis of sorts before secession, with
baked-in options to re-join the parent state if the parent considers adopting
some learnings after a successful experiment. Lots of possibilities. Would
likely involve re-gearing the concepts of how quasi-independent states (child
+ parent) would keep relations open, so as not to polarize populations
unnecessarily. I don't normally think of diplomacy as exciting, but learning
how to make such a system work effectively would be pretty interesting

------
IIAOPSW
How can anyone vote for Chocolate. Chocolate is clearly CORRUPT. He's openly
buying votes! This election is rigged! I just watched a video on youtube
explaining how the ELITES plan to trigger an election paradox! Investigate the
WILLY WONKA FOUNDATION. Vote Vanilla or we won't have a COUNTRY in 5 years!!!

------
tunesmith
I have seen a few too many voting-system presentations that all seem to have a
few of the same common arguments, arguments that I believe are flawed.

Here I can isolate it to these statements. First, "The whole point of the
election was to force the group to make a choice about an ice cream flavor."
This is false. The election's point was to interpret the preference of the
electorate. We then use that preference to come to a choice. In the cyclic
cases, this is no failure of the voting system. This is an accurate portrayal
that the group is not able or ready to come to a decision.

"In its inability to identify a clear winner, ranked voter has failed in its
primary task." This is also not true. It was not its primary task, and didn't
fail at all. It succeeded wildly in identifying a confusion in the electorate
itself.

Of _course_ any attempt to "break that tie" will be flawed and invalid.

For those who don't know, the video up to that point explored Condorcet
Voting, and the Condorcet Winner criteria. The existence of a cycle is known
as a Smith Set or Schwartz Set (subtly different, but very similar).
Tiebreaking methods to elect single winners from Schwartz Sets are all flawed,
but that does not mean the Condorcet Winner method is flawed.

Elimination Voting is more commonly known as Instant Runoff voting. In his
example at 7:04, this is again a Schwartz Set. So it's improper to declare
that one of the three flavors is a winner, because the electorate is
inherently undecided. The gold coins scenario changes nothing; it is still a
cycle, and the electorate is still undecided. So the tiebreaker chooses a
different winner - it doesn't really matter, because it is already invalid to
pick a winner in that scenario.

But the bigger problem with IRV (elimination voting) is that it will sometimes
pick the wrong winner even when there ISN'T a cycle. This is awful.

Finally, the presenter glosses over his description of Arrow's Theorem. You
can practically hear the parentheses when he says, "given certain
assumptions". In truth, not all voting criteria are the same. All Arrow's
Theorem does is say you can't simultaneously meet four criteria, that he
chose, in all cases. It does not prove that those four criteria are required.
One of those criteria, the "Independence of Irrelevant Alternatives" criteria,
is particularly problematic - and if I recall correctly, it can only move an
election from a Condorcet Winner to a Schwartz Set. It cannot itself select a
new winner entirely. And in my view, that is not a problem, because if adding
a new candidate creates a Schwartz Set, then it only means that the electorate
was probably not given enough choice from the outset. Although, there is a
counterpoint that says that if you give voters more and more choice, cycles
will inevitably occur.

So really when we're talking about voting theory, the entire problem with the
subject is that we are conflating two needs. The first need is to measure the
public's preference for a choice. But the other need is for the public to
_come_ to a choice. Often times, the process of the voting system is what
motivates the public to do so. But it is not always sufficient. And at the
same time, the fact that the voting system is not sufficient for this, is not
a failing of the voting system itself.

I find it instructive to mull two questions, because I find that these two
questions drive a lot of opinions on who feels what voting systems are
superior.

1) If a candidate would beat all other candidates in a multi-candidate single-
winner election head-to-head, should that candidate be the winner?

2) If, in a two-candidate election, one candidate narrowly defeats the other,
but the other candidate's supporters are clearly more passionate, should the
first candidate still win?

(EDIT: Calmed some language)

~~~
euyyn
My main grip with these discussions is that nobody seems to have addressed how
they affect realistic scenarios. Finding an intricate scenario in which a
system fails is entertaining, but doesn't help in the real world.

------
macawfish
I'm curious about what paradoxes emerge with score voting.

~~~
drostie
If you mean that the top candidate earns N points and the Nth candidate earns
1 point, I answered that in this comment:

[https://news.ycombinator.com/item?id=12875982](https://news.ycombinator.com/item?id=12875982)

~~~
anderskaseorg
No, that’s the Borda count. In score voting, each voter assigns a score from
some range to each candidate independently
([https://en.wikipedia.org/wiki/Score_voting](https://en.wikipedia.org/wiki/Score_voting)).

~~~
drostie
Ah, what I know as "figure-skating voting". I don't know very much about these
except that Arrow's theorem can't apply directly to them because they have a
different ballot structure; however given that Borda is something of a special
case of score voting (in the same way as in crypto; random permutations are
special cases of random functions meeting different needs), presumably there
are some regimes where you can push it so that it has similar behavior.

~~~
anderskaseorg
Borda could be thought of as a ballot-restricted version of score voting, but
so could plurality; you can’t expect ballot-restricted versions of reasonable
systems to remain reasonable. Generally, there’s no reason for voters to cast
Borda-type ballots unless you force them to.

------
z3t4
They could start with voting for witch flavor to remove.

