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Topological Problems in Voting

ryantolsma.com

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Re: Topological Problems in Voting

#21

Post by edflsafoiewq »

eru wrote: post #17
jfengel wrote: post #11

Earlier quoted context omitted.

I'm not convinced it can actually achieve that. There is still just one winner, just as now, and I'm not sure the people who picked them under duress will really feel they were listened to. (Or they can approve of only one, and almost certainly lose if it's not one of the two most popular parties.) Still, I'm not averse to trying. Either it will help, or tactical voting will leave us more or less where we are now. If…

> There is still just one winner, just as now, and I'm not sure the people who picked them under duress will really feel they were listened to. Huh, where is that duress coming from? > (Or they can approve of only one, and almost certainly lose if it's not one of the two most popular parties.) Huh, why can they approve of only one? The whole point is that you can approve more than one.

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 if there is a "hidden" commonground between the two parties which can be revealed by the extra approval votes.

Re: Topological Problems in Voting

#22

Post by j16sdiz »

BriggyDwiggs42 wrote: post #12
johnkpaul wrote: post #3

Hmm, is this author related to the Physics for the Birds YouTube channel? That channel just released a video on the same topic. https://youtu.be/v5ev-RAg7Xs?si=X1LY6Qc_s-HDqI3S

I was thinking that too. Could be -plagiarized- inspired by the birds, since the flow of the article starts out the exact same way

The first paragraph linked to the YouTube video and mentioned

> (we’ll take a slightly different approach).

Re: Topological Problems in Voting

#23

Post by j16sdiz »

unfamiliar wrote: post #4

Am I missing something or does the article fail to explain the point of Arrow’s Theorem? Is it satisfied for the discrete case, provably impossible, or what? > While this applies to discrete rankings and voter preferences, one might wonder if it’s a unique property of its discrete nature in how candidates are only ranked by ordering. Unfortunately, a similarly flavored result holds even in the continuous setting! It…

Arrows theorem says it is impossible to have a system that always resolves (it is possible to have something work "sometimes" however.

The paragraph you quoted introduce a generalized version, where voters can give continuous scores and have full spectrum of choice.

Re: Topological Problems in Voting

#24

Post by paganel »

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.…

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).

Re: Topological Problems in Voting

#25

Post by TaylorAlexander »

rtolsma wrote: post #13
johnkpaul wrote: post #3

Hmm, is this author related to the Physics for the Birds YouTube channel? That channel just released a video on the same topic. https://youtu.be/v5ev-RAg7Xs?si=X1LY6Qc_s-HDqI3S

Yes, I saw that! Inspired me to look at the original paper. The video takes a slightly different approach from the paper and uses a retraction on the möbius strip to its boundary as a contradiction. That particular argument doesn’t generalize as well in higher dimensions (in particular, the symmetric product won't always have a boundary to retract to), so I followed the original paper’s one instead. I'll add a link t…

Yeah you don’t want to get hbomberguy’d.

Re: Topological Problems in Voting

#26

Post by [deleted] »

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.…

[deleted]

Re: Topological Problems in Voting

#27

Post by AnthonyMouse »

jfengel wrote: post #11
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.)

I'm not convinced it can actually achieve that. There is still just one winner, just as now, and I'm not sure the people who picked them under duress will really feel they were listened to. (Or they can approve of only one, and almost certainly lose if it's not one of the two most popular parties.) Still, I'm not averse to trying. Either it will help, or tactical voting will leave us more or less where we are now. If…

> 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 only change something in determining whether the winner is A or B, so you avoid voting for your preferred candidate.

With approval voting you vote for them and one of the major parties. Then people notice that third party candidates are immediately getting 30-40% of the vote because the people afraid of wasting their vote no longer have to refrain from voting for their preferred candidate. In some districts they even win. Which dissolves the two party system because people have to take third party candidate seriously and starting a new party has a real chance at succeeding rather than being an exercise in futility.

Re: Topological Problems in Voting

#28

Post by AnthonyMouse »

edflsafoiewq wrote: post #21
eru wrote: post #17

Earlier quoted context omitted.

> There is still just one winner, just as now, and I'm not sure the people who picked them under duress will really feel they were listened to. Huh, where is that duress coming from? > (Or they can approve of only one, and almost certainly lose if it's not one of the two most popular parties.) Huh, why can they approve of only one? The whole point is that you can approve more than one.

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, someone can run on a ticket which is similar to one of the major parties and should get approximately the same level of approval as that party's candidate. Which is to say, they can potentially win. Then more third party and independent candidates run, giving people more options.

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

Re: Topological Problems in Voting

#29

Post by AnthonyMouse »

wffurr wrote: post #15
jfengel wrote: post #11

Earlier quoted context omitted.

I'm not convinced it can actually achieve that. There is still just one winner, just as now, and I'm not sure the people who picked them under duress will really feel they were listened to. (Or they can approve of only one, and almost certainly lose if it's not one of the two most popular parties.) Still, I'm not averse to trying. Either it will help, or tactical voting will leave us more or less where we are now. If…

Approval voting with multi member districts.

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.

Re: Topological Problems in Voting

#30

Post by jfengel »

AnthonyMouse wrote: post #27
jfengel wrote: post #11

Earlier quoted context omitted.

I'm not convinced it can actually achieve that. There is still just one winner, just as now, and I'm not sure the people who picked them under duress will really feel they were listened to. (Or they can approve of only one, and almost certainly lose if it's not one of the two most popular parties.) Still, I'm not averse to trying. Either it will help, or tactical voting will leave us more or less where we are now. If…

> 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.

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