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There is a chapter in the excellent book "Why Flip a Coin" dedicated to exploring voting alternatives. The main point of the chapter is that given three intuiti

There is a chapter in the excellent book "Why Flip a Coin" dedicated to exploring voting alternatives. The main point of the chapter is that given three intuitively obvious requirements (like adding a 3rd candidate should not change the relative order of the first two) - it can be mathematically proven that NO voting scheme will satisfy them. See https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...

NathanielLovin 5y ago
Arrow's impossibility theorem only applies to ordinal voting systems. Quadratic voting is a cardinal system. Cardinal voting still isn't perfect, but it does get around some of the problems with ordinal systems.
- notahacker 5y ago
  This form of cardinal voting has a particularly egregious equivalent of the "additional candidate affects preference ordering" issue in ordinal voting systems though. Unlike the weird edge cases with preference ordering in ordinal votes, the effects of adding additional votes on reducing certain voting blocs' influence on other issues where ppeoplemust divide a budget across multiple issues often lead to intuitive (trivially simple, even) strategies to manipulate a particular outcome. If you can add a proposition to the ballot paper which sufficiently threatens a particular group, they're forced to waste votes defending themselves against it, which means they have less influence on other issues they might also care about. As far as I can see the quadratic nature makes it worse, by making it more plausible a minority could actually lose a vote that threatens them if they only spent most of their credits defending themselves against it. That's a bigger UX issue than non-sophisticated voters not really grasping the budgeting detail.
- contravariant 5y ago
  I'm not sure quadratic voting is the best cardinal voting system though. In particular it still fails to satisfy independence of irrelevant alternatives. So sure Arrow's impossibility may not apply, but the conclusion isn't actually different.
dane-pgp 5y ago
> adding a 3rd candidate should not change the relative order of the first two This is, I think, the least justified requirement, since humans do naturally reframe situations when extra information is given, which can cause them to change their mind about previous decisions. To give a trivial example, suppose you were in a district which historically had a Democrat and a Republican candidate, and you always voted Democrat, but one year a far left independent candidate became popular and you feared they would attract most Democrat voters over to their camp. Given that scenario, it might make sense for you to vote for a moderate Republican instead. In any case, I think that the significance of Arrow's impossibility theorem is generally over-estimated (and it spreads as a meme because people like to think that all voting systems are bad so there's no reason to change the terrible one they have). For example, the theorem only applies to ordinal (ranked) voting systems, not cardinal (rated) ones, and only proves that the system cannot output "a community-wide (complete and transitive) ranking", so it is still possible to elect a small set of politicians who collectively embody the same preferences as the voters, and in direct proportion to them.
- wtallis 5y ago
  You've described an example where the addition of a third candidate causes a voter to strategically change who they're going to vote for, based on the expected outcomes under a particular voting system. That's not the same thing as the voter's actual preferences changing, it's just a manifestation of a limitation of a particular voting system.
  - couchand 5y ago
    What exactly do you mean by "the voter's actual preferences"?
- twic 5y ago
  But all along, this person's preference is Democrat > Republican > Independent. That doesn't change. The fact that their best interests are served by casting a ballot which doesn't reflect that is exactly the problem!

NathanielLovin 5y ago

Arrow's impossibility theorem only applies to ordinal voting systems. Quadratic voting is a cardinal system. Cardinal voting still isn't perfect, but it does get around some of the problems with ordinal systems.

notahacker 5y ago
This form of cardinal voting has a particularly egregious equivalent of the "additional candidate affects preference ordering" issue in ordinal voting systems though. Unlike the weird edge cases with preference ordering in ordinal votes, the effects of adding additional votes on reducing certain voting blocs' influence on other issues where ppeoplemust divide a budget across multiple issues often lead to intuitive (trivially simple, even) strategies to manipulate a particular outcome. If you can add a proposition to the ballot paper which sufficiently threatens a particular group, they're forced to waste votes defending themselves against it, which means they have less influence on other issues they might also care about. As far as I can see the quadratic nature makes it worse, by making it more plausible a minority could actually lose a vote that threatens them if they only spent most of their credits defending themselves against it. That's a bigger UX issue than non-sophisticated voters not really grasping the budgeting detail.
contravariant 5y ago
I'm not sure quadratic voting is the best cardinal voting system though. In particular it still fails to satisfy independence of irrelevant alternatives. So sure Arrow's impossibility may not apply, but the conclusion isn't actually different.

dane-pgp 5y ago

> adding a 3rd candidate should not change the relative order of the first two This is, I think, the least justified requirement, since humans do naturally reframe situations when extra information is given, which can cause them to change their mind about previous decisions. To give a trivial example, suppose you were in a district which historically had a Democrat and a Republican candidate, and you always voted Democrat, but one year a far left independent candidate became popular and you feared they would attract most Democrat voters over to their camp. Given that scenario, it might make sense for you to vote for a moderate Republican instead. In any case, I think that the significance of Arrow's impossibility theorem is generally over-estimated (and it spreads as a meme because people like to think that all voting systems are bad so there's no reason to change the terrible one they have). For example, the theorem only applies to ordinal (ranked) voting systems, not cardinal (rated) ones, and only proves that the system cannot output "a community-wide (complete and transitive) ranking", so it is still possible to elect a small set of politicians who collectively embody the same preferences as the voters, and in direct proportion to them.

wtallis 5y ago
You've described an example where the addition of a third candidate causes a voter to strategically change who they're going to vote for, based on the expected outcomes under a particular voting system. That's not the same thing as the voter's actual preferences changing, it's just a manifestation of a limitation of a particular voting system.
- couchand 5y ago
  What exactly do you mean by "the voter's actual preferences"?
twic 5y ago
But all along, this person's preference is Democrat > Republican > Independent. That doesn't change. The fact that their best interests are served by casting a ballot which doesn't reflect that is exactly the problem!