
Arrow's Theorem (2014) - cscurmudgeon
https://plato.stanford.edu/entries/arrows-theorem/
======
Iv
So, if some of you have felt despair at the idea that this may indicate that
true democracy is impossible, fear not: it hinges on the fact that some
preferences can be cyclic: A wins over B who wins over C, who wins over A.

These situations are possible but rare and in such a case, it is arguable that
all potential winners are legitimate.

~~~
fny
Arrows theorem is misleading because it only applies to rank order systems.

Range voting (i.e. 0-5 rating system) satisfies all the criteria. [0] So yes,
democracy is theoretically possible.

[0]: [https://youtu.be/e3GFG0sXIig](https://youtu.be/e3GFG0sXIig)

~~~
macawfish
Good video, thanks for sharing that!

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marcoperaza
I think plurality/first-past-the-post gets an unjustified bad rap. If you
focus only on the moment of election, it is not a very good system. But a
broader view reveals something else. The process of settling on two options,
that each represent a coalition of factions that have come together and
compromised on a common platform, is doing most of the work that other systems
try to do within the voting system itself.

Proportional voting also solves the problem in a similar way, except that the
politicians representing each faction, rather than the faction at-large, do
the work of forming coalitions with other factions.

Of course the distinction between the two is a little more blurry, since
broad-coalition parties also exist in proportional systems, and politicians do
play a large role in the at-large coalition-forming in plurality systems. But
nonetheless, they clearly lead to different outcomes.

As for ranked and approval-type voting systems, I’m not really a fan since I
think they don’t have any hope of representing coherent thought about
politics. People have a hard enough time making a principled choice of one
party to vote for; asking people to rank them seems likely to produce even
less principled choices.

~~~
roenxi
I have a favorite article on voting [1]. It has good visual descriptions of
how different systems favour different styles of candidates.

Plurality voting is a lot better than not having a democracy; imho at least
the worst candidate will be excluded. My understanding is also that
democracies of any form (including republics) tend to get much better military
results than dictatorships, but I don't have any actual evidence to cite :(.

[1] [http://zesty.ca/voting/sim/](http://zesty.ca/voting/sim/)

~~~
sampo
While good and illustrative, that page is based on the very restrictive view,
that of choosing only one candidate. This applies to presidential elections,
sure. There can be only one president.

But most countries don't have one-member sized voting districts in their
parliament elections, rather they choose 10 to 30 members per voting district.

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inputcoffee
One of the cognitive science labs was hiring experts in graph theory, and it
turns out they wanted to express Arrow's Theorem -- and the related theories
-- in the form of a graph so they could reason about decision making in the
brain.

If I recall correctly, the paradox of voting gets represented as a top cycle
which leads to irrational decisions. They wanted to come up with mechanisms
where they break top cycles. (In these graphs a higher ranked decision was
higher on the Y axis.)

~~~
baddox
The paradox of voting usually refers to a different claim: that the cost of an
individual voting tends to be greater than the expected benefit to the
individual.

Confusingly, the term (and the extremely similar “voting paradox”) sometimes
refers to the Condorcet paradox, which notes that collective preferences
between three or more options can be intransitive. I expect that is the
concept you are referring to.

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

~~~
inputcoffee
Yes, the latter.

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dnautics
I find this is one of the best videos on the subject:

[https://www.youtube.com/watch?v=tJag3vuG834](https://www.youtube.com/watch?v=tJag3vuG834)

~~~
throwaway613834
Great video except that it's misleading at the end. Arrow's theorem is only
about rank-order voting. But if e.g. you can express your preferences as
numbers (e.g. if you can state your preferences as 10% strawberry, 30%
vanilla, and 60% chocolate) then it no longer applies.

~~~
Bromskloss
Indeed. It seems that those voting systems too can be proven [0] to have these
problems, though.

[0] [https://politics.stackexchange.com/questions/14015/does-
gibb...](https://politics.stackexchange.com/questions/14015/does-gibbard-
satterthwaite-theorem-apply-to-all-voting-systems/14245)

~~~
throwaway613834
Holy hell, that is mindblowing. Thank you for sharing this.

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straightarrow
Like a car swerving side to side as 2 drivers wrestle for control of the
wheel, the 2 party system is an erratic vehicle.

But I have good news: we can steer a more stable course with score voting.

Score voting doesn't violate Arrow's Theorem (because it's not a ranked-choice
system).

Here's how it works:

* Each voter gives candidates a score from 0 to 1.

* The highest average score wins. (The average can be weighted to account for abstentions.)

The upshot:

* No political parties are needed.

* It resists gerrymandering because it's non-partisan.

* If there's a bias in the system, it's towards the center.

* Simulations indicate score voting is socially optimal.

* Arrow, himself, expressed preference for approval voting (a variant of score voting)

Further reading:

electology.org

en.wikipedia.org/wiki/Range_voting

~~~
domador
It sounds appealing, but I wonder if in practice range voting tends to
collapse into first-past-the-post, with people voting tactically to maximize
the chances of a popular candidate winning (instead of voting for the
candidate they most prefer). This is why systems such as optional preferential
voting appeal to me despite their (different) flaws. I wonder if monotonicity
and trying to avoid circular electoral preferences are slightly overrated
goals. I suspect that a good electoral system might involve a bit of
satisficing, of producing great outcomes even when the theoretically best
outcome isn't consistently achieved.

~~~
OscarCunningham
In fact it collapses into aproval voting, which is like range voting except
every score is 0 or 1, or equivalenty like FPTP except that you can vote for
more than one person.

But it turns out that approval voting is itself considered a very good voting
system (I remember reading an article about how a conference of experts voted
on their favourite voting systems and approval voting won, but I can't find it
because "voting system vote" isn't a very good Google search).

~~~
baddox
I think The main theoretical problem with most approval and range voting
methods is that they fail the Condorcet and majority criteria. A candidate who
is preferred over every other candidate by a majority of voters can lose,
which sucks, but in practice it is debatable how common such an occurrence
would be.

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Iv
Am I the only one who finds that the Stanford encyclopedia of philosophy is
generally less clear than the matching Wikipedia article?

~~~
baddox
I almost always scroll down for the Wikipedia article when Google puts sources
like the Stanford Encyclopedia of Philosophy or Investopedia or WebMD or IMDb
first.

For me, it’s less about which source I trust more, and more about my
familiarity with and enjoyment of the writing/organizational style of
Wikipedia articles.

