[eru]

Arrow's Theorem only applies to some voting systems and only in some situations.

Yes, the theorem doesn' apply to approval voting nor does it apply to score voting.

Arrow's theorem only applies to deterministic voting systems. So sortition (or other method based on random sampling) are not affected.

The theorem also doesn't apply to proportional representation systems. (Though they have their own problems, of course.)

Most RCV systems are very gameable with tactical voting. Though they aren't that useful, I guess.

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Arrow's theorem also doesn't guarantee that you will have problems. It just says that for some votings systems you can construct voting populations with preference that can't be captured well. It doesn't say whether these situations are likely to occur in practice.

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Arrow's theorem also doesn't apply when you allow bargaining, or people compensating each other.

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Of course, the problem with democracy in practice isn't so much that existing voting systems don't capture what voters want. Even first-past-the-post seems to be doing a reasonable job of that.

The problem is that voters want bad things like protectionism or war or price controls etc. See https://en.wikipedia.org/wiki/The_Myth_of_the_Rational_Voter

[paganel]

And who’s going to decide that those things you mentioned at the end are good or bad? If not (elected) leaders, that is. Take the exemple of the most famous democracy, the US, its current dominance was built on a few wars (the Civil War, to settle things domestically, and the two World Wars that allowed it to extend its dominance worldwide) and big periods of protectionism (like at the end of the 19th century).

[eru]

Who's going to decide what voting system is good or bad? At some point, you have to inject some judgement calls, if you want to end up with a judgement call.

Btw, the protectionism was bad for the US economy, and did not help its dominance at all. (That's assuming you like US dominance?)

[ClayShentrup]

> Arrow's theorem also doesn't guarantee that you will have problems. It just says that for some votings systems you can construct voting populations with preference that can't be captured well.

no, it has nothing to do with capturing preferences. it simply says that no ordinal social welfare function can simultaneously satisfy these criteria:

    There is no dictator.
    If every voter prefers A to B then so does the group.
    The relative positions of A and B in the group ranking depend on their relative positions in the individual rankings, but do not depend on the individual rankings of any irrelevant alternative C.

[eru]

> If every voter prefers A to B then so does the group. [...]

That's (part of) what I mean by 'capturing preferences'.

[ClayShentrup]

well, yes. https://www.rangevoting.org/ArrowThm

but technically it only applies to social welfare functions, not voting methods.

i had a chance to visit kenneth arrow at his home in palo alto circa 2015 and we had a nice little chat about this.

[ClayShentrup]

> Even first-past-the-post seems to be doing a reasonable job of that.

utterly false. https://www.rangevoting.org/PConsumer.html

[eru]

To be clear: I am saying that in practice people get the _policies_ they mostly agree with, not that the candidates they prefer over other candidates get elected.

That's (partially) because the candidates in order to attract voters pick policies that voters prefer.

[dataflow]

> Arrow's Theorem only applies to some voting systems

Yes, but... https://politics.stackexchange.com/a/14245

[eru]

Yes, you can extend Arrow's theorem a bit. But again, it doesn't apply to people who can negotiate or compromise or who play repeatedly. And it also only applies to aggregating an ordering of preferences. It doesn't apply to eg filling up a parliament for proportional representation.

(Btw, the random dictatorship doesn't sound too bad. As a slightly modified form, I think it would be a good experiment to fill up parliament with a few hundred randomly selected people amongst all who are willing.)

[dataflow]

> Yes, you can extend Arrow's theorem a bit

I would call it "a lot"!

> But again, it doesn't apply to people who can negotiate or compromise

You want hundreds of millions of people to negotiate and compromise with each other in a way that would eventually produce representatives that reflect the population's resulting preferences somehow? How would that work?

> or who play repeatedly.

I don't see why I should expect that to make the problem easier.

> I think it would be a good experiment to fill up parliament with a few hundred randomly selected people amongst all who are willing

That sounds like it could go incredibly wrong. Everyone who is willing will sell themselves out to the highest "bidder" (maybe bidding via money, maybe promises of future laws...), and the population unwilling or unable to become a member of parliament will have no say in the matter.

[eru]

> You want hundreds of millions of people to negotiate and compromise with each other in a way that would eventually produce representatives that reflect the population's resulting preferences somehow? How would that work?

Tacit negotiations can work. And in practice, it's often your representatives that do the negotiations with other people's representatives.

See https://en.wikipedia.org/wiki/Logrolling

>> or who play repeatedly. > I don't see why I should expect that to make the problem easier.

Check out the repeated Prisoner's Dilemma for some inspiration for how repeated play can breed cooperation.

> That sounds like it could go incredibly wrong. Everyone who is willing will sell themselves out to the highest "bidder" (maybe bidding via money, maybe promises of future laws...), [...]

How is that different from people selling their vote today?

Just make sure that the legal system does not enforce these contracts, and you are good. (You can also make such contracts illegal completely, just like selling your vote today is illegal in many countries.)

> [...] and the population unwilling or unable to become a member of parliament will have no say in the matter.

You can cook up slightly more complicated versions: every voter nominates a (willing) candidate on their ballot. Nationwide, you collect 600 ballots and fill up parliament with the people named on them. Pick your favourite resolution method, in case the same person gets picked multiple times in your sample.

(Eg you could give that person more weight in parliament, or you could pick the voter's second choice, or you could pick the ballot of the guy who got picked twice to pick a replacement, etc.)

[dataflow]

> Tacit negotiations can work. And in practice, it's often your representatives that do the negotiations with other people's representatives.

And now you're back to square one? How do you choose those representatives in a way that represents their constituents' views? That was literally the original problem.

> Check out the repeated Prisoner's Dilemma for some inspiration for how repeated play can breed cooperation.

Have you seen literature on this somewhere? On its face iterated prisoner's dilemma being more cooperative does not in any way suggest that iterates voting somehow admits an easier solution for finding collective preferences than non-repeated voting. The problems are drastically different so far as I can tell. If you've seen literature suggesting otherwise I would love a link or two.

> How is that different from people selling their vote today? Just make sure that the legal system does not enforce these contracts

You seem confused? The reason you can't sell your vote today isn't that it's illegal to sell your vote, but rather the fact that there's no way to prove how you voted, so you could just lie with no incriminating evidence.

Whereas it's pretty darn easy to see how the candidate who promised you tax breaks suddenly voted to raise them when he came into office.

> slightly more complicated version

I see nothing obvious suggesting that your (homemade?) scheme is better, so I'm gonna put the onus on you to explain it wouldn't suffer from similar problems...

Note that "theorem assumptions don't apply" doesn't imply "conclusion doesn't hold".

[eru]

> And now you're back to square one? How do you choose those representatives in a way that represents their constituents' views? That was literally the original problem.

No, why? Arrow's Theorem eg has nothing to say about proportional representation. And Arrow's Theorem only applies to aggregating orderings of a finite list of preferences. But the methods under investigation need to be 'generic', ie can't make use of any special properties of those preferences, either. (See eg https://people.mpi-sws.org/~dreyer/tor/papers/wadler.pdf for how being 'generic' limits what your methods can do.)

And to come back to iterated games: almost no matter how the representative was chosen in the first period, if she's standing for re-election, she has an incentive for keeping her represented happy.

Arrow's theorem just applies to a list of static choices; not to how the chosen might behave when trying to get re-elected.

> Have you seen literature on this somewhere?

I don't remember right now. But I think 'The Myth of the Rational Voter' might mention some research somewhere. (See https://en.wikipedia.org/wiki/The_Myth_of_the_Rational_Voter) That book mostly mentions this when it argues that the problem with democracy ain't that voters don't get their wishes, but the problem is that voters do get their wishes.

> Whereas it's pretty darn easy to see how the candidate who promised you tax breaks suddenly voted to raise them when he came into office.

Sure. But if millions of people are eligible to be drafted at random, you are going to have a hard time pre-emptively bribing them. That's equivalent to doing something nice for the entire country.

> I see nothing obvious suggesting that your (homemade?) scheme is better, so I'm gonna put the onus on you to explain it wouldn't suffer from similar problems...

Because eg people who don't want to stand for parliament still have a say? That was exactly one of the problem you brought up with naive sortition. Remember?

> Note that "theorem assumptions don't apply" doesn't imply "conclusion doesn't hold".

Well, if your theorem says A implies B; if A doesn't hold, your theorem doesn't apply, but B could still be true for other reasons. But you need a different argument or empirical data to convince people of B.

[ClayShentrup]

> Arrow's theorem also doesn't apply when you allow bargaining, or people compensating each other.

that doesn't make sense. the result you get after bargaining would just _be_ one of the options.

[eru]

Sorry, I don't understand that. Could you explain?

Arrow's Theorem applies when you have a discrete number of choices and you try to aggregate people preferences over them (in specific ways etc).

If instead of discrete elections, Alice and Bob can negotiate that _today_ they go to the football match and _tomorrow_ they go to the opera, that opens up new spaces for coordination that Arrow's theorem doesn't touch.

Similar, if Alice is allowed to pay Bob, or if they can do political horse-trading like 'I support your foreign policy, if you support my lowering the speed limit', that's also not covered by Arrow's theorem.

The theorem really only applies to deterministically aggregating people's individual orderings of a discrete set of options into some aggregated order for the group. That's it.

So it doesn't concern side-payments, or other continuous compromises. Or repeated play.