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Topological Problems in Voting

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Re: Topological Problems in Voting

#41

Post by ClayShentrup »

eru wrote: post #16
lukifer wrote: post #7

Arrow’s Theorem is often invoked as a criticism of alternative voting systems (RCV, etc). And not while not wrong exactly, it seems textbook “perfect being the enemy of the good”. (It’s also one reason I prefer Approval Voting, which in addition to its benefit of simplicity, sidesteps Arrow by redefining the goal: not perfectly capturing preferences, but maximizing Consent of the Governed.)

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.…

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

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

Re: Topological Problems in Voting

#42

Post by eru »

AnthonyMouse wrote: post #28
edflsafoiewq wrote: post #21

Earlier quoted context omitted.

I think the idea is that if there are two popular candidates A and B, one of whom is almost certain to win, a voter feels forced to approve of whichever of A or B they prefer even if they don't really want either one, just to hedge against the other winning, exactly as in FPTP. Or they can approve of only the candidates they really want, but they will likely lose. Approval only seems to be able to break this gridlock…

The problem with FPTP is that as soon as you have more than two parties, the two most similar parties split the vote among their common constituency and give the win to the least similar party. As a result any candidate who wants a chance at winning has to run on the ticket of the major party they most agree with, or else they split the vote with them and lose. Hence two party system. With a cardinal voting system, s…

> It's not just about what voters do, it changes what candidates do.

Yes, exactly, the indirect impact on candidate and voter tactics are what's important!

Re: Topological Problems in Voting

#43

Post by eru »

jfengel wrote: post #31
AnthonyMouse wrote: post #28

Earlier quoted context omitted.

The problem with FPTP is that as soon as you have more than two parties, the two most similar parties split the vote among their common constituency and give the win to the least similar party. As a result any candidate who wants a chance at winning has to run on the ticket of the major party they most agree with, or else they split the vote with them and lose. Hence two party system. With a cardinal voting system, s…

That's not necessarily all that different from now. We have a two stage system. In the primary people with broadly similar platforms run against each other. The "third parties" are factions within the two major ones. Those options exist, and it's a multi way election. Primaries receive far less attention but they are where the real work of democracy is done. I believe people are hoping they can vote for a radical can…

> In the primary people with broadly similar platforms run against each other. The "third parties" are factions within the two major ones.

No, you still have that problem of splitting the vote in the primaries.

Remember how Donald Trump used to be the most hated Republican candidates within the Republicans in around 2015 / 2016? As in the one that the most people actively disliked in polls; but he was different enough from the other candidates that he didn't suffer from the internal vote splitting that they did.

The primaries still use first-past-the-post in the US, don't they?

Re: Topological Problems in Voting

#44

Post by eru »

ClayShentrup wrote: post #40
eru wrote: post #16

Earlier quoted context omitted.

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.…

> 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…

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

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

Re: Topological Problems in Voting

#45

Post by eru »

ClayShentrup wrote: post #41
eru wrote: post #16

Earlier quoted context omitted.

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.…

> Even first-past-the-post seems to be doing a reasonable job of that. utterly false. https://www.rangevoting.org/PConsumer.html

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.

Re: Topological Problems in Voting

#46

Post by eru »

ClayShentrup wrote: post #39
eru wrote: post #16

Earlier quoted context omitted.

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.…

> 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.

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.

Re: Topological Problems in Voting

#47

Post by eru »

dataflow wrote: post #34
eru wrote: post #16

Earlier quoted context omitted.

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.…

> Arrow's Theorem only applies to some voting systems Yes, but... https://politics.stackexchange.com/a/14245

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.)

Re: Topological Problems in Voting

#48

Post by eru »

paganel wrote: post #24
eru wrote: post #16

Earlier quoted context omitted.

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.…

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).

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?)

Re: Topological Problems in Voting

#49

Post by eru »

jfengel wrote: post #30
AnthonyMouse wrote: post #27

Earlier quoted context omitted.

> Or they can approve of only one, and almost certainly lose if it's not one of the two most popular parties. "They can only approve of one" is FPTP, the existing system. Everybody knows that sucks. The whole point of approval or score voting is to avoid that. Right now if you favor candidate C but they have 5% of the vote and candidate A and B each have 45%, your preferred candidate has no chance and your vote can o…

I phrased that badly. I meant that they may choose to vote for only their favorite, as tactical voting. It says they don't approve of any other, to send a message. But it's not clear they will feel the message is sent if their candidate loses, and they are stuck with least favorite choice because they didn't select an alternative.

So they _should_ vote tactically, and only send the message when it doesn't hurt them.

Re: Topological Problems in Voting

#50

Post by eru »

jfengel wrote: post #33
AnthonyMouse wrote: post #29

Earlier quoted context omitted.

That's likely to reduce diverse representation vs. single-member districts. If there are e.g. 8 seats a party could run 8 identical candidates and they'd all get the highest approval ratings for the combined district if one of them would, and other parties wouldn't get any.

List voting might work as an alternative to single member districts. You vote for your favorite party, and they are allocated a proportion of the total seats. You lose the ability to know your local candidate, but how many people really do these days? It's what we set up in Iraq, but we don't do it ourselves. It doesn't solve the problem that there is still exactly one chief executive. You can try making that a commi…

Germany has an interesting hybrid voting system that combines proportional representation via parties with local representatives.

In Germany, you cast two different votes. The first vote elects your local representatives via a first-past-the-post system; they all go to parliament. Then you fill up parliament with more people to make the proportions match those of the second votes cast all over the country. (There's lots of special cases and rules involved. Eg to handle the case when a party gets lots of first votes, but no second votes.)

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