
Voting is a Sham Mathematically Speaking - eibrahim
http://haacked.com/archive/2012/11/27/condorcet-paradox.aspx?utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+haacked+%28you%27ve+been+HAACKED%29
======
maratd
This is off. Voting is not a system for selecting the best candidate. Voting,
in whatever forms it exists, is a system to avoid violence and conflict.

Each side feels it had a fair shot, regardless of outcome. The purpose of
voting is to leave you with that feeling, to avoid unpleasant behavior from
the losing party. The best person for the job almost never gets it. That's why
we don't vote people in when hiring somebody at a company.

~~~
diego
Yes, and in addition it's also a system to ensure that elected officials and
their parties have accountability. If you win an election and then "betray"
your voters, you won't be reelected. If you can't be reelected, you could
damage the chances of your party. In essence, democracy in its current form is
not so much about choosing the right/best candidate. It's more about making
sure the winner cannot become a despot.

~~~
ontheotherhand
_"If you win an election and then "betray" your voters, you won't be
reelected."_

That ain't accountability, that's a joke. If you pay me 5000$ to do a job, and
I don't lift a finger, and your "punishment" is that we won't do that a second
time, then I have free money and you're a fool. It doesn't hurt the party one
bit either; that's the whole point of corporatism, you can swap out
individuals while the "brand" rolls on, saying "whoops, bad apple" every 5
seconds, with people forgetting after 2.

 _"It's more about making sure the winner cannot become a despot."_

Correction: it replaces a single despotic individual with a tag team of people
who basically can do whatever they want - within boundaries, sure, they at
least have to be somewhat slick about it, and know how to make a puppy face,
too; but certainly not within boundaries defined by the actual will of the
people who handed their power as souvereigns over to their representatives.
Having despotic entities control you is not one iota better than despotic
humans, not in the long run.

Despotism is marked by the control going only down, accountability going only
up -- period. Not by angry men on podiums necessarily, and not by bloodshed.
(Not that there isn't plenty bloodshed, but that's besides the point) If you
seriously see a huge difference or improvement there, you've fallen for it I'm
afraid.

~~~
maratd
You know, it's pretty easy to poke holes in something. It's another thing
entirely to come up with something better.

There hasn't been a single political system that hasn't been corrupted.

~~~
ontheotherhand
_"You know, it's pretty easy to poke holes in something. It's another thing
entirely to come up with something better."_

I have no problems with coming up with something better. More like 3 a day
before breakfast; I'd just have problems making people actually go along with
whatever I would come up with. But you know what? If people are so fucked that
even I can't magically solve it, that doesn't mean I can't say they're fucked.
It just means they're gonna pout and roll their eyes, none of which is news or
unexpected.

 _"There hasn't been a single political system that hasn't been corrupted."_

What's your point? That therefore criticism isn't allowed? That naive believe
in cynical manipulation is not an issue?

Also, was I talking about a "system"? No, I was talking about specific
circumstances, an actual situation, and individuals and their responsibilitie.

But of course, it's easier to just throw some mud into a completely different
direction, not hitting anything, and then deluding oneself into having dealt
with the issue just nicely, than to actually address any of it.

~~~
maratd
> I have no problems with coming up with something better. More like 3 a day
> before breakfast; I'd just have problems making people actually go along
> with whatever I would come up with.

Perhaps because you don't actually share your "something better"?

Two posts in, lots of words, still no alternatives.

------
mtgx
Approval Voting mostly solves the "strategic voting" part that almost forces
you to choose the "most likely to win" candidate, or if you hate that one, the
one closest to him, while eliminating the spoiler effect, and giving 3rd party
candidates a much higher chance of winning than with current traditional
voting systems.

<http://www.electology.org/approval-voting>

<http://en.wikipedia.org/wiki/Approval_voting>

~~~
DennisP
Plus it doesn't run into trouble with Arrow's theorem, since it's not a "rank-
order voting system," unlike plurality, instant runoff, and various others.

Range voting has the same advantage. In computer simulations measuring how
well the election result matches voter preferences, either range or approval
is as much an improvement over plurality as plurality is over picking someone
at random (or, if you like, monarchy).
<http://rangevoting.org/BayRegsFig.html>

~~~
gus_massa
I'm not sure about the definitions, but if the Arrow theorem doesn't apply to
the Approval Voting sistem them I think that it must not be applicable to the
"majority rules" criterion.

In this two system the idea is that you get very little information from the
voters (best candidate / a set of candidates) and don't know all the
information about the order of preference and the relative strength. So I
don't understand why having less information is better (theoreticaly).

~~~
Empact
> I don't understand why having less information is better (theoreticaly).

A ranked-choice ballot only encodes the orders the candidates against one
another, whereas approval and score votes also encode the candidates'
positions within the voter's range of subjective preferences. That is, if we
have 3 candidates (A, B, C) and a few voters which each voters has a range
from love to hate for each candidate, like so:

    
    
      Love                       Hate
       |-A--B-------------------C-|
       |-A-------------B-----C----|
       |-------------------A-B-C--|
       |-A-B---C------------------|
    

Under ranked choice voting, every one of these voters' ballots would look the
same:

    
    
       1)A, 2)B, 3)C
    

Ranked choice voting encodes the ordering of the preferences, but the
intensity of those preferences is lost when the ballot is cast. Whereas under
approval and score voting, every one of these voters represents their
preferences differently, because they're reflecting their personal response to
each candidate:

    
    
         Approval | Disapproval
       |-A--B-----|-------------C-|
       |-A--------|----B-----C----|
       |----------|--------A-B-C--|
       |-A-B---C--|---------------|
    

Of course, some information is lost in the fact that we only have 2 values
approval/disapproval to encode positional preferences. But I would argue this
information is already more meaningful than a fully-expressed ranked ballot.
And if necessary, score voting can capture more of that information by
offering > 2 levels to divide the candidates into.

~~~
gus_massa
OK, this method recollect some information that the ranked choice voting
ignores. But I still don't understand why the Arrow's theorem doesn't apply.

If in a hypothetic population everyone loves/hates each candidate equally
spaced, then in that population it is possible to apply the Arrow's theorem
and prove that for that population this method doesn't work. But the method
should be useful for every population, even the pathological ones.

------
gabemart
I found this article quite frustrating.

>Condorcet formalized the idea that group preferences are also non-transitive.
If people prefer Hanselman to me. And they prefer me to Guthrie. It does not
necessarily mean they will prefer Hanselman to Guthrie. It could be that
Guthrie would pull a surprise upset when faced head to head with Hanselman.

I found this by far the most interesting assertion, but the examples under
"Historical Examples" don't demonstrate this phenomenon at all.

For instance, the author asserts that the Nader spoiler effect demonstrates
nontransitive preference relationships. But from my reading, it wasn't the
case that that group as a whole preferred (Gore over Nader) and (Nader over
Bush) but (Bush over Gore). It was simply that due to the structure of the
election, they happened to elect Bush. While this ties into the author's point
about the "unfairness" of elections, it doesn't demonstrate nontransitive
relationships in group preferences.

Could someone post an example of a group preference configuration in which the
group prefers (A over B) and (B over C) but (C over A)?

I understand the concept of nontransitive relationships in general, but in the
specific domain of fitness for office, I can't work out how this would come to
be.

~~~
Dove
_Could someone post an example of a group preference configuration in which
the group prefers (A over B) and (B over C) but (C over A)?_

Sure, that's easy to construct.

    
    
        Peter's preferences: A, B, C
        Paul's: B, C, A
        Mary's: C, A, B
    

The group prefers A over B, by a 2-1 vote. Likewise B over C, and C over A.

------
saraid216
> Voting is a method that a group of people use to pick the “best choice” out
> of a set of candidates. It’s pretty obvious, right?

And like many other pieces of "common sense", this isn't correct.

Wikipedia says, "Voting is a method for a group such as a meeting or an
electorate to make a decision or express an opinion—often following
discussions, debates, or election campaigns. Democracies elect holders of high
office by voting." This is _very_ different from "picking the best choice".

I realize that the American public has been indoctrinated for the past few
decades that voting is the only way you make yourself heard, but this isn't
true and never has been. I recently learned about Wellstone Action (
<http://en.wikipedia.org/wiki/Wellstone_Action> ); I encourage everyone to
look into enrolling. (I haven't done so myself yet. I probably will at some
point, though.)

> On one hand, this seems to be an endorsement of the two-party political
> system we have in the United States.

Actually, what it's an endorsement of is all of our other voting systems where
the choice is between APPROVE and REJECT. You have to endorse the existence of
political parties in the first place before you can endorse a two-party
system, and Arrow's theorem goes nowhere near that.

~~~
bo1024
> _Wikipedia says, "Voting is a method for a group such as a meeting or an
> electorate to make a decision or express an opinion—often following
> discussions, debates, or election campaigns. Democracies elect holders of
> high office by voting." This is very different from "picking the best
> choice"._

I don't see how they are different. The author never said that candidates have
to be people. Substitute the word "alternatives" if you prefer.

~~~
saraid216
> I don't see how they are different.

"I think this is the way we should proceed" is qualitatively different from "I
think this is the best choice".

> The author never said that candidates have to be people. Substitute the word
> "alternatives" if you prefer.

Substitute it in place of what? Where did I require that the candidates must
be people?

------
wam
Learning about Arrow's theorem definitely changed the way I think about
elections in the US. It also changed the way I think about election news
coverage. I used to be an ardent "horse race news" hater. I still am, in terms
of how utterly it dominates election news, but now I see some utility in it as
well.

Arrow and these others have focused how I look at the game-theoretic
underpinnings of elections and the importance of being up to speed on exactly
how candidates and interested parties are crafting strategies around the
complexities built into the game. When people conflate the "message" of the
candidate with the strategy (which is always) I still get irritated. I have a
tendency toward partisanship and that kind of thing clouds my judgment. But
the day-in day-out workings of the campaigns and PACs are more interesting to
me now, because they shed light on what's fundamentally "broken" (from my
point of view) in the underlying system, as opposed to what I simply find
distasteful or disappointing.

Math!

~~~
saraid216
Social choice theory is One Of Those Things which everyone (myself included)
needs to spend more time learning about.

------
basseq
> A voting system can only, at times, choose the most preferred of the options
> given. But it doesn't necessarily present us with the best candidates to
> choose from in the first place.

Reminds me of HHGTTG: "Anyone who is capable of getting themselves made
President should on no account be allowed to do the job."

------
Tloewald
The article confuses two issues, one illustrated by Arrow's Theorem which is
more relevant to parliamentary procedures (where any set of more than two
choices has to be resolved as a series of binary choices, and the voting
population is small and its preferences well understood) and first past the
post electoral systems which are completely hopeless, especially when tiered,
as in the US.

Most of the article is essentially discussing an example of Arrow's Theorem
where if you know people's preferences and can present them with binary
options in an order of your choosing you can obtain any outcome except the
least popular option. This is very artificial and not a real flaw of
preferential and proportional electoral systems where (a) individual
preferences are not known and (b) the entire vote is done in one step, not in
a carefully chosen series of binary options. Great for gaming a committee,
lousy for elections.

As others have observed, the chief purpose of voting is allowing government
transitions without violence and with the appearance of procedural fairness,
but the fact remains voting works just fine when the population has a clear
cut preference ("throw the bastards out").

Well, modulo corrupt redistricting.

Americans who want to talk about voting really need to understand that there
are other voting systems than the horse and buggy system used in the US and
UK.

------
aprescott
_In this case, Hanselman is the clear winner with three votes, whereas the
other two candidates each have two votes. This is how our elections are held
today._

This is dependent on the exact election taking place. With the US presidential
elections, my understanding is that a plurality of electoral college votes is
not enough to win, you need an actual majority. In the event of a simple
plurality win with no majority, the result is decided by the House of
Representatives (which may itself be tied).

~~~
rjzzleep
is it? the actual candidates already get preselected.

even if youre right, which is likely, it doesn't matter, because any majority
was previously generated by pluarility.

------
mmphosis
Mixed Member Proportional (MMP) Representation solves some of the problems.
[http://www.youtube.com/watch?v=QT0I-sdoSXU&feature=relmf...](http://www.youtube.com/watch?v=QT0I-sdoSXU&feature=relmfu)

The problem with MMP is when the parties choose the ranking of their list of
representatives. I think it would be even better if rather than use a party
generated list, instead the representatives are determined by people's votes.

------
streptomycin
Also, there's this: <http://papers.nber.org/papers/w15220>

------
Noughmad
I find it interesting that in all those discussions about voting systems,
which are mostly focused on USA president elections, nobody mentions two-round
voting, also known as run-off voting.

This is what we have in Slovenia for electing our president. In the first
round, there are many candidates, and each voter can vote for one. If any
candidate gets at least 50% of votes, he automatically wins.

If, on the other hand, there is no majority winner, the two best candidates
compete head-to-head in the second round.

Such a system allows you to always vote for your favourite candidate in the
first round, and if your candidate doesn't make it into the second round, you
can vote for the fallback one.

Details: <https://en.wikipedia.org/wiki/Two-round_system>

~~~
kscaldef
I don't believe this satisfies the Condercet criterion either. Consider these
rankings of preferences:

    
    
        20% A ...
        20% B ...
        15% C ...
        15% D C ...
        15% E C ...
        15% F C ...
    

In a two-round run-off, one of A or B will be elected, despite the fact that
60% of voters prefer C over either A or B.

~~~
im3w1l
And in the real world, people would second guess this, and enough people would
tactic vote for C that it would't be a problem.

"But then they can't vote for their prefered candidate which was the whole
point"

Well, _some_ people can. D, E, F could still get a few percentage points. More
importantly, I don't think we would see convergence to a 2-party system.

Unless I am missing something, it looks like at least 3 parties could be
sustained.

------
gradstudent
Preferential voting solves all these problems. You vote by ranking the
candidates on order of preference. If your top candidate does not win the vote
goes to next guy down the line until eventually it ends up for one of two
candidates.

~~~
Pinckney
Preferential voting does not satisfy the Condorcet criterion.

[http://en.wikipedia.org/wiki/Instant-
runoff_voting#Voting_sy...](http://en.wikipedia.org/wiki/Instant-
runoff_voting#Voting_system_criteria)

~~~
bradbeattie
To demonstrate this, consider the following.

80 people: A, C, B

50 people: B, C, A

35 people: C, B, A

IRV eliminates C (as it has the fewest first-place votes) and elects B. But
voters on the whole prefer C over B (115 to 50). This is the failure that
Pinckney refers to.

------
hcarvalhoalves
If you look at Brazil, which has multiple parties and plurality voting, the
problems are pretty clear.

In this year's elections, the candidate with 28% of the votes was elected
mayor in my city.

------
nikatwork
I've always thought New Zealand's mixed-member proportional (MMP) voting
system [1] is the least bad solution currently in use.

I'm not from NZ so I'd be interested to hear what the locals think.

[1]
[http://en.wikipedia.org/wiki/New_Zealand_voting_system_refer...](http://en.wikipedia.org/wiki/New_Zealand_voting_system_referendum,_2011)

~~~
lmkg
Not a local, but... Proportional voting systems suffer from the problem that
voting "power" is not proportional to representation.

Consider a parliament with 100 members and 3 parties. Suppose the breakdown
is: A has 49 members, B has 48 members, and C has 3 members. Guess what... A,
B, and C all have equal voting power! Any two parties are enough to reach a
majority of 51 votes, and any one party is not. Despite A having, in theory,
over 16 times the representation of C, it does not have any voting advantage.

Keep in mind that any voting system based on parties will tend to have very
partisan voting blocs. Representatives in the US are more independent and
likely to break with the party because they are elected in geographically
isolated elections. Representatives elected directly by a party generally have
about as much independence as the Electors in the Electoral College.

~~~
NickNameNick
I'm from NZ...

To form a government, the party with the most votes, or a coalition of parties
which collectively holds a majority petition the governor general.

For a single party this is quite straightforward.

To form a coalition the member parties agree on a 'Confidence and supply
agreement" This is basically a statement that in the event of a vote of no-
confidence, all of the coalitions members will support the coalition, and also
a broad agreement on the budget. Getting an agreement on confidence usually
involves a certain amount of horse trading about ministerial and vice
ministerial positions. Likewise, the agreement on supply will probably involve
some intense budget and joint-policy negotiations.

If you had a parliament of 101 seats, split into an opposition of 50 seats,
and a government of 51, itself made up of a large party (48 seats) and a small
party (3 seats) what you will probably see is the small party only has the
tiniest influence on the coalition agreement. They probably traded everything
else to get their senior member a ministerial position.

------
fluxon
Wasn't this issue addressed rather well in a recent hackernews-linked item
which mathematically showed both that voting is not a sham, but that the
Electoral College system is more fair than it has been represented? (sorry
can't find the link!)

------
stretchwithme
Winner-take-all elections, no matter how they operate, leave many people
without the representation they prefer. Proportional representation is much
less likely to do this.

Proportional representation can used in the executive branch too. Switzerland
does it.

------
bo1024
This is a very nice summary of/intro to the classic/standard mathematical
approach to voting and Arrow's Theorem.

------
frozenport
This is why we have a 2 party system :-)

------
jQueryIsAwesome
Some of you are forgetting something; that even if you had some form of
"stadistical fairness" (whatever that may be); you still have the biggest
problem of most democracies: Uneducated people; people who think an atheist
shouldn't be president, people who like to reinforce their biases more than
they like to have deep discussions about the nation's issues, people who were
never taught to do critical thinking... and without doing exceptions for their
government, their parents, their religion and the law.

~~~
bluedanieru
That's not really in scope for choosing a voting system that best represents
the people. But yes, point taken.

