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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

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.)

jfengel 2y ago
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 nothing else it's an opportunity to give the current deadlock a shove.
- wffurr 2y ago
  Approval voting with multi member districts.
  - AnthonyMouse 2y ago
    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.
    - jfengel 2y ago
      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 committee but that has other downsides.
      - eru 2y ago
        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.)
      - AnthonyMouse 2y ago
        > List voting might work as an alternative to single member districts. But now you don't have a cardinal voting system and that's even worse than single member districts. > It doesn't solve the problem that there is still exactly one chief executive. You can try making that a committee but that has other downsides. Committees are dealing with it the wrong way. The right way to deal with it is to take away all of the executive's power. Constrain the national government from doing hardly anything and instead pass local laws to do whatever you want to do. Then create elected positions responsible for different portions of the government. Directly elect the Attorney General and the heads of the major government departments. Let the President be like the Queen of England -- a figurehead with minimal responsibilities.
- eru 2y ago
  > 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.
  - edflsafoiewq 2y ago
    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.
    - AnthonyMouse 2y ago
      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.
      - jfengel 2y ago
        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 candidate and a mainstream candidate, on the off chance people will love the radical candidate if they just get on the general ballot. I'm not convinced that will ever happen, and such people will be not just disappointed, but continue to be convinced the system is rigged against them.
- AnthonyMouse 2y ago
  > 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.
  - jfengel 2y ago
    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.
    - eru 2y ago
      So they _should_ vote tactically, and only send the message when it doesn't hurt them.
    - ClayShentrup 2y ago
      tactical voting is normally what we call it when you DON'T vote for your favorite, e.g. a green party supporter votes democrat. with approval voting they'd obviously vote for green too. some of the people who normally vote green under the current system might _still_ only vote green with approval voting, but very few would do it unless green actually had a chance to win. https://www.rangevoting.org/BulletVoting https://www.rangevoting.org/BulletVoting
eru 2y ago
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. --- 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. --- Arrow's theorem also doesn't apply when you allow bargaining, or people compensating each other. --- 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 https://en.wikipedia.org/wiki/The_Myth_of_the_Rational_Voter
- paganel 2y ago
  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 2y ago
    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?)
- deleted 2y ago
  [deleted]
compumetrika 2y ago
Is there a proof or demostration somehwere about maximizing the consent of the governed? Arrows theorem always has implied to me that the next step should be quantifuing some welfare measure for voters and then exploring which system maximized that welfare measure. "Consent of the governed" sounds like a welfare measure so I an intrigued.
- Spivak 2y ago
  I don't really think you need too much to prove it yourself. You are being governed with consent when the person who's elected is someone you are okay being governed by. And the person who wins an approval election is the person with that has the most people fine with being governed by them. Because approval voting doesn't ask people to rank candidates voting for someone you disapprove of only hurts you and voting for any subset of people you do approve of is sincere. It's not some deep thing because it changes the target to something much easier. Finding the best candidate is hard, finding the candidate most people find acceptable is less so. Approval voting gets more mathematically interesting when you assume people have preferences among the candidates they approve of and whether the best candidate gets elected but IRL you don't actually care about that anymore. You're fine electing someone who isn't the best.

jfengel 2y ago

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 nothing else it's an opportunity to give the current deadlock a shove.

wffurr 2y ago
Approval voting with multi member districts.
- AnthonyMouse 2y ago
  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.
  - jfengel 2y ago
    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 committee but that has other downsides.
    - eru 2y ago
      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.)
    - AnthonyMouse 2y ago
      > List voting might work as an alternative to single member districts. But now you don't have a cardinal voting system and that's even worse than single member districts. > It doesn't solve the problem that there is still exactly one chief executive. You can try making that a committee but that has other downsides. Committees are dealing with it the wrong way. The right way to deal with it is to take away all of the executive's power. Constrain the national government from doing hardly anything and instead pass local laws to do whatever you want to do. Then create elected positions responsible for different portions of the government. Directly elect the Attorney General and the heads of the major government departments. Let the President be like the Queen of England -- a figurehead with minimal responsibilities.
eru 2y ago
> 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.
- edflsafoiewq 2y ago
  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.
  - AnthonyMouse 2y ago
    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.
    - jfengel 2y ago
      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 candidate and a mainstream candidate, on the off chance people will love the radical candidate if they just get on the general ballot. I'm not convinced that will ever happen, and such people will be not just disappointed, but continue to be convinced the system is rigged against them.
AnthonyMouse 2y ago
> 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.
- jfengel 2y ago
  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.
  - eru 2y ago
    So they _should_ vote tactically, and only send the message when it doesn't hurt them.
  - ClayShentrup 2y ago
    tactical voting is normally what we call it when you DON'T vote for your favorite, e.g. a green party supporter votes democrat. with approval voting they'd obviously vote for green too. some of the people who normally vote green under the current system might _still_ only vote green with approval voting, but very few would do it unless green actually had a chance to win. https://www.rangevoting.org/BulletVoting https://www.rangevoting.org/BulletVoting

eru 2y ago

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. --- 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. --- Arrow's theorem also doesn't apply when you allow bargaining, or people compensating each other. --- 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 https://en.wikipedia.org/wiki/The_Myth_of_the_Rational_Voter

paganel 2y ago
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 2y ago
  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?)
deleted 2y ago
[deleted]

compumetrika 2y ago

Is there a proof or demostration somehwere about maximizing the consent of the governed? Arrows theorem always has implied to me that the next step should be quantifuing some welfare measure for voters and then exploring which system maximized that welfare measure. "Consent of the governed" sounds like a welfare measure so I an intrigued.

Spivak 2y ago
I don't really think you need too much to prove it yourself. You are being governed with consent when the person who's elected is someone you are okay being governed by. And the person who wins an approval election is the person with that has the most people fine with being governed by them. Because approval voting doesn't ask people to rank candidates voting for someone you disapprove of only hurts you and voting for any subset of people you do approve of is sincere. It's not some deep thing because it changes the target to something much easier. Finding the best candidate is hard, finding the candidate most people find acceptable is less so. Approval voting gets more mathematically interesting when you assume people have preferences among the candidates they approve of and whether the best candidate gets elected but IRL you don't actually care about that anymore. You're fine electing someone who isn't the best.