Ranked Choice Approval Voting

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Ranked Choice Approval Voting

Postby Brilliand » Sun May 09, 2021 11:28 pm

I noticed that Ranked Choice Voting and Approval Voting attempt to fix the voting system in very different ways:
  • In Ranked Choice voting you cast a single vote, but you can automatically change your vote based on how other people voted
  • In Approval Voting you can vote for multiple candidates at once, but your vote doesn't change from the moment you cast it
So... what happens if we set up a system in which you can vote for multiple candidates at once, AND you can automatically change your vote based on how other people voted?

I present to you: Ranked Choice Approval Voting!

The rules:
  • Cast a ranked ballot, in exactly the style of Ranked Choice Voting
  • Initially you vote for only your first choice
  • In each round of voting, if 1) you aren't currently voting for the winner, and 2) the best candidate you haven't voted for isn't winning, then you cast an additional vote for the best candidate you haven't voted for yet.
  • Continue until no one wants to change their vote according to the previous rule
  • Whoever has the most total votes wins
To show off this voting system in action, I'll use this classic example of IRV going horrible wrong:
  • 18 votes for A>B>C
  • 24 votes for B>C>A
  • 15 votes for C>A>B

Round 1:
  • 18 votes for A>B>C
  • 24 votes for B>C>A
  • 15 votes for C>A>B
B is in the lead with 24 votes.

The 15-vote group casts additional votes for A in an attempt to make B stop winning.

Round 2:
  • 18 votes for A>B>C
  • 24 votes for B>C>A
  • 15 votes for C>A>B
A is in the lead with 33 votes.

The 24-vote group casts additional votes for C in an attempt to make A stop winning.

Round 3:
  • 18 votes for A>B>C
  • 24 votes for B>C>A
  • 15 votes for C>A>B
C is in the lead with 39 votes.

The 18-vote group casts additional votes for B in an attempt to make C stop winning.

Round 4:
  • 18 votes for A>B>C
  • 24 votes for B>C>A
  • 15 votes for C>A>B
B is in the lead with 42 votes.

No one can do anything about that. Nash equilibrium and all that crap. B wins!

So, what are the advantages over...
Ranked Choice voting: IRV (the most popular implementation of RCV) elects A in this case, which is dumb. RCAV actually elects the best candidate - the most-loved and the least-hated.
Approval voting: How do you know where to draw the line between "good enough" and "not good enough"? RCAV automatically draws the line for you in the most advantageous place.
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Re: Ranked Choice Approval Voting

Postby alex1234321 » Mon May 10, 2021 7:29 am

Wow that's interesting, I've never heard of it. The main downside that I see with this is that it's difficult to tally all the votes, and calculating the Nath equilibrium would make it even harder. Are there any other downsides or situations where this voting system gives the wrong result? Are there any situations where someone is better off ranking choices differently?
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Re: Ranked Choice Approval Voting

Postby Brilliand » Mon May 10, 2021 7:45 am

alex1234321 wrote:Wow that's interesting, I've never heard of it.


I made it up.

alex1234321 wrote:The main downside that I see with this is that it's difficult to tally all the votes, and calculating the Nath equilibrium would make it even harder.


Oh, I don't mean it should always calculate the Nash equilibrium; such a thing doesn't always exist. The rules I wrote for it are guaranteed to finish, but only fairly likely to find the Nash equilibrium.

alex1234321 wrote:Are there any other downsides or situations where this voting system gives the wrong result? Are there any situations where someone is better off ranking choices differently?


Dunno. I only thought of this a few days ago, so there hasn't been much time to find flaws. I'll keep looking.

There's a theorem stating that every voting system using a ranked ballot has to have at least one of several flaws, so there's got to be something.
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Re: Ranked Choice Approval Voting

Postby alex1234321 » Mon May 10, 2021 8:31 am

The people who have the preference order C>A>B would benefit from choosing A>C>B to make A win instead of B. I believe this would be a Nash equilibrium since the B>C>A people wouldn't be able to do anything to stop A from winning unless they made a deal with another group.

Time for some logic that is almost certainly faulty in some way:

Then the people choosing B>C>A could make a deal with the C>A>B group where the C>A>B group doesn't change their order while the B>C>A group goes C>B>A. That would make candidate C win. But the A>B>C group could vote B>A>C and tell the B>C>A group not to make a deal with the C>A>B group, which would make candidate B win again regardless of how C>A>B votes. But that brings us back to square one, where C>A>B could vote A>C>B to make candidate A win. So it doesn't seem like there's a pure strategy Nash equilibrium here. I believe straight IRV would play out the same way.
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Re: Ranked Choice Approval Voting

Postby Brilliand » Mon May 10, 2021 2:01 pm

alex1234321 wrote:The people who have the preference order C>A>B would benefit from choosing A>C>B to make A win instead of B. I believe this would be a Nash equilibrium since the B>C>A people wouldn't be able to do anything to stop A from winning unless they made a deal with another group.


Yep, that's the sort of flaw I suspected this would have: switching your votes to control whether some other group automatically sets their voting bar lower. Good catch.

alex1234321 wrote:Then the people choosing B>C>A could make a deal with the C>A>B group where the C>A>B group doesn't change their order while the B>C>A group goes C>B>A. That would make candidate C win. But the A>B>C group could vote B>A>C and tell the B>C>A group not to make a deal with the C>A>B group, which would make candidate B win again regardless of how C>A>B votes. But that brings us back to square one, where C>A>B could vote A>C>B to make candidate A win. So it doesn't seem like there's a pure strategy Nash equilibrium here. I believe straight IRV would play out the same way.


We usually ignore the possibility of large groups of voters forming political agreements with each other, because at that point the precise voting system used ceases to matter - the coalition of the majority will have their way, unless something especially perverse (such as Borda Count) is involved.

The main concern when deciding between alternate voting systems is how to make the situation as favorable as possible for large groups of people that can't coordinate with each other.
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Re: Ranked Choice Approval Voting

Postby alex1234321 » Mon May 10, 2021 6:24 pm

Brilliand wrote:
alex1234321 wrote:Then the people choosing B>C>A could make a deal with the C>A>B group where the C>A>B group doesn't change their order while the B>C>A group goes C>B>A. That would make candidate C win. But the A>B>C group could vote B>A>C and tell the B>C>A group not to make a deal with the C>A>B group, which would make candidate B win again regardless of how C>A>B votes. But that brings us back to square one, where C>A>B could vote A>C>B to make candidate A win. So it doesn't seem like there's a pure strategy Nash equilibrium here. I believe straight IRV would play out the same way.


We usually ignore the possibility of large groups of voters forming political agreements with each other, because at that point the precise voting system used ceases to matter - the coalition of the majority will have their way, unless something especially perverse (such as Borda Count) is involved.

The main concern when deciding between alternate voting systems is how to make the situation as favorable as possible for large groups of people that can't coordinate with each other.


Yeah that makes sense.

I like approval voting because there's very little you can do to strategically vote. All you can do is change the cutoff between "good" and "bad." The problem with any sort of ranking system is that placing one choice above another necessarily involves voting against that other choice to some extent, so it's almost always beneficial to rank a popular but unfavorable choice artificially low. Of course the point of your idea was to fix that, and I'm not aware of any ranked choice systems that are more resistant to strategic voting than approval voting.

Btw who's the "we" that you were referring to in that post?
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Re: Ranked Choice Approval Voting

Postby Brilliand » Mon May 10, 2021 6:37 pm

alex1234321 wrote:Btw who's the "we" that you were referring to in that post?


Me and... well actually I just noticed that none of the articles I read were bringing up the possibility, and I realized that there was a good reason for it. I don't represent a tight-knit group that discusses this regularly or anything like that.
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Re: Ranked Choice Approval Voting

Postby cob709 » Mon May 10, 2021 8:42 pm

alex1234321 wrote:
Brilliand wrote:
alex1234321 wrote:Then the people choosing B>C>A could make a deal with the C>A>B group where the C>A>B group doesn't change their order while the B>C>A group goes C>B>A. That would make candidate C win. But the A>B>C group could vote B>A>C and tell the B>C>A group not to make a deal with the C>A>B group, which would make candidate B win again regardless of how C>A>B votes. But that brings us back to square one, where C>A>B could vote A>C>B to make candidate A win. So it doesn't seem like there's a pure strategy Nash equilibrium here. I believe straight IRV would play out the same way.


We usually ignore the possibility of large groups of voters forming political agreements with each other, because at that point the precise voting system used ceases to matter - the coalition of the majority will have their way, unless something especially perverse (such as Borda Count) is involved.

The main concern when deciding between alternate voting systems is how to make the situation as favorable as possible for large groups of people that can't coordinate with each other.


Yeah that makes sense.

I like approval voting because there's very little you can do to strategically vote.


Chicken dilemma

https://electowiki.org/wiki/Chicken_dilemma


edit: actually the article explains it poorly. but the point is unvote 1st place so that favorite becomes 1st place

edit 2:
Candidates: A, B, C
Group 1(5 people): Approve A over B, Disapprove C
Group 2(5 people): Approve B over A, Disapprove C
Group 3(7 people): Approve C, Disapprove A and B
Group 4(1 person): Approve A, Disapprove B and C
Results: {A(11), B(10), C(7)} - A wins, 11 people happy, 7 people sad

In group 2, 2 people strategically unvote A
Results: {A(9), B(10), C(7)} - B wins, 10 people happy, 8 people sad

In group 1, 2 people strategically unvote B
Results: {A(9), B(8), C(7)} - A wins, 11 people happy, 7 people sad

In group 2, 3 people strategically unvote A again
Results: {A(6), B(8), C(7)} - B wins, 10 people happy, 8 people sad

In group 1, 3 people strategically unvote B again
Results: {A(6), B(5), C(7)} - C wins??, 7 people happy, 11 people sad

(assuming everyone votes at once)
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Re: Ranked Choice Approval Voting

Postby alex1234321 » Mon May 10, 2021 9:05 pm

cob709 wrote:
alex1234321 wrote:
Brilliand wrote:
alex1234321 wrote:Then the people choosing B>C>A could make a deal with the C>A>B group where the C>A>B group doesn't change their order while the B>C>A group goes C>B>A. That would make candidate C win. But the A>B>C group could vote B>A>C and tell the B>C>A group not to make a deal with the C>A>B group, which would make candidate B win again regardless of how C>A>B votes. But that brings us back to square one, where C>A>B could vote A>C>B to make candidate A win. So it doesn't seem like there's a pure strategy Nash equilibrium here. I believe straight IRV would play out the same way.


We usually ignore the possibility of large groups of voters forming political agreements with each other, because at that point the precise voting system used ceases to matter - the coalition of the majority will have their way, unless something especially perverse (such as Borda Count) is involved.

The main concern when deciding between alternate voting systems is how to make the situation as favorable as possible for large groups of people that can't coordinate with each other.


Yeah that makes sense.

I like approval voting because there's very little you can do to strategically vote.


Chicken dilemma

https://electowiki.org/wiki/Chicken_dilemma


edit: actually the article explains it poorly. but the point is unvote 1st place so that favorite becomes 1st place


Nobody is going to unvote their favorite option though, would they? The only strategic voting that happens is whether or not to choose the second choice. Approval definitely isn't perfect here but I think unvoting your second choice is acceptable since it's not nearly as significant as placing a less favorable candidate above someone you prefer, which is very common in most other voting systems. The only reason why the chicken game happens is because there is a tie, which is highly unlikely in real life. Usually there would be 1 or 2 unusual ballots that cause the supporters of one choice to unvote their second choice. The other group would then unvote their second choice, and the spoiler candidate would win. Personally I think the more popular of the two other choices should win instead, but you can argue both ways. As long as the less popular non-spoiler candidate wins it's alright.

Approval certainly isn't perfect here, but this is much less severe than the instant runoff situation described in the OP.
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Re: Ranked Choice Approval Voting

Postby Brilliand » Mon May 10, 2021 9:53 pm

Had to look around a bit for that one - it seems rangevoting.org calls the "Chicken dilemma" the "Burr dilemma".

I see that site includes an example of the Burr dilemma occurring within IRV, so electowiki is wrong in saying that IRV is exempt. I'd be curious to see a voting system that is exempt - it seems hard to come up with one, since "bullet voting" (acting like you're in a FPTP election even when you're not) is the simplest form of tactical voting. Voters try to use it in every system, even ones that go completely haywire when abused in that fashion.
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Re: Ranked Choice Approval Voting

Postby cob709 » Mon May 10, 2021 10:44 pm

alex1234321 wrote:
cob709 wrote:
alex1234321 wrote:
Brilliand wrote:
alex1234321 wrote:Then the people choosing B>C>A could make a deal with the C>A>B group where the C>A>B group doesn't change their order while the B>C>A group goes C>B>A. That would make candidate C win. But the A>B>C group could vote B>A>C and tell the B>C>A group not to make a deal with the C>A>B group, which would make candidate B win again regardless of how C>A>B votes. But that brings us back to square one, where C>A>B could vote A>C>B to make candidate A win. So it doesn't seem like there's a pure strategy Nash equilibrium here. I believe straight IRV would play out the same way.


We usually ignore the possibility of large groups of voters forming political agreements with each other, because at that point the precise voting system used ceases to matter - the coalition of the majority will have their way, unless something especially perverse (such as Borda Count) is involved.

The main concern when deciding between alternate voting systems is how to make the situation as favorable as possible for large groups of people that can't coordinate with each other.


Yeah that makes sense.

I like approval voting because there's very little you can do to strategically vote.


Chicken dilemma

https://electowiki.org/wiki/Chicken_dilemma


edit: actually the article explains it poorly. but the point is unvote 1st place so that favorite becomes 1st place


Nobody is going to unvote their favorite option though, would they? The only strategic voting that happens is whether or not to choose the second choice. Approval definitely isn't perfect here but I think unvoting your second choice is acceptable since it's not nearly as significant as placing a less favorable candidate above someone you prefer, which is very common in most other voting systems. The only reason why the chicken game happens is because there is a tie, which is highly unlikely in real life. Usually there would be 1 or 2 unusual ballots that cause the supporters of one choice to unvote their second choice. The other group would then unvote their second choice, and the spoiler candidate would win. Personally I think the more popular of the two other choices should win instead, but you can argue both ways. As long as the less popular non-spoiler candidate wins it's alright.

Approval certainly isn't perfect here, but this is much less severe than the instant runoff situation described in the OP.

they would unvote their 2nd favorite in order to make their 1st favorite on top
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Re: Ranked Choice Approval Voting

Postby Brilliand » Tue May 11, 2021 1:10 am

Hang on, wait. What's going on with that "definition" on the Chicken Dilemma page? It goes:
  • 5 votes for A>B>C
  • 4 votes for B (bullet vote)
  • 6 votes for C (bullet vote)
  • Requirement to pass: B doesn't win
But that requirement is stupid. B should win. The A voters have made it clear that they are willing to vote for B if it's necessary for C to not win. And it is necessary for C to not win - so the first group's vote for B should be counted, causing B to win. This is actually an example of IRV breaking, because IRV makes the mistake of eliminating B in the first round!

The only way this bizarre behavior of IRV is a good thing is if you presume that group B is "cheating" and should be "punished". But that isn't a fair assumption.
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Re: Ranked Choice Approval Voting

Postby alex1234321 » Tue May 11, 2021 6:57 am

Brilliand wrote:Hang on, wait. What's going on with that "definition" on the Chicken Dilemma page? It goes:
  • 5 votes for A>B>C
  • 4 votes for B (bullet vote)
  • 6 votes for C (bullet vote)
  • Requirement to pass: B doesn't win
But that requirement is stupid. B should win. The A voters have made it clear that they are willing to vote for B if it's necessary for C to not win. And it is necessary for C to not win - so the first group's vote for B should be counted, causing B to win. This is actually an example of IRV breaking, because IRV makes the mistake of eliminating B in the first round!

The only way this bizarre behavior of IRV is a good thing is if you presume that group B is "cheating" and should be "punished". But that isn't a fair assumption.


That's weird that it says that. In this case A is the only one that would be unacceptable imo. But you could argue that it's okay for C to win since C is the most popular choice. But A is dominated by C in terms of both first choice preference and general approval. So either B or C winning would be reasonable. Unless I'm missing something, approval would give B the victory since the A voters would vote for B as well to prevent C from winning. IRV would make C win, which is also acceptable.

I was looking at the scenario in the analysis section of that page where it shows that the B voters approve of A and hate C. In that case B would be objectively worse than A since the same number of voters approve of both but fewer voters have B as their first choice. You could argue that C is the superior candidate to A since more people want C as their first choice. More people are okay with it being A, which means that A is an acceptable choice but doesn't necessarily imply that A>C since C is more popular as a first choice.
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Re: Ranked Choice Approval Voting

Postby Brilliand » Tue May 11, 2021 5:14 pm

alex1234321 wrote:That's weird that it says that. In this case A is the only one that would be unacceptable imo. But you could argue that it's okay for C to win since C is the most popular choice. But A is dominated by C in terms of both first choice preference and general approval. So either B or C winning would be reasonable. Unless I'm missing something, approval would give B the victory since the A voters would vote for B as well to prevent C from winning. IRV would make C win, which is also acceptable.


C is the plurality voting choice. If you're going to let top-votes alone decide the election (ignoring the second vote that the A group cast), it kinda defeats the purpose of wanting an alternative voting system.
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Re: Ranked Choice Approval Voting

Postby alex1234321 » Tue May 11, 2021 6:24 pm

Brilliand wrote:
alex1234321 wrote:That's weird that it says that. In this case A is the only one that would be unacceptable imo. But you could argue that it's okay for C to win since C is the most popular choice. But A is dominated by C in terms of both first choice preference and general approval. So either B or C winning would be reasonable. Unless I'm missing something, approval would give B the victory since the A voters would vote for B as well to prevent C from winning. IRV would make C win, which is also acceptable.


C is the plurality voting choice. If you're going to let top-votes alone decide the election (ignoring the second vote that the A group cast), it kinda defeats the purpose of wanting an alternative voting system.


Plurality voting is bad because it leads to lots of strategic voting.

I'm saying that any choice that isn't dominated by another choice is arguably acceptable. You want the choice that maximizes the total payoff for all the voters for some abstract definition of payoff. Of course here it's assumed that the A and B voters hate C, but neither IRV nor approval voting takes into account the relative favorability of each choice beyond rankings. The only voting system that I know of that does is range voting, which just devolves into approval voting with strategic voters. For some combination of payoffs for each voter, any outcome that isn't dominated by another one can arguably be the "right" one. So here C is an acceptable outcome.

You can argue that C winning is still bad for an approval voting system since the A and B voters "approve" of the other candidate, which causes strategic voting to change the outcome. But approval is an abstract concept and it's very difficult to create a definition for it beyond "if a voter prefers A over B, they should never approve of B but not A."
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Re: Ranked Choice Approval Voting

Postby Brilliand » Tue May 11, 2021 8:09 pm

alex1234321 wrote:Plurality voting is bad because it leads to lots of strategic voting.


Specifically, because that strategic voting tends to create an oligarchy, by preventing people from voting for anyone who they don't predict will do well based on past history. Strategic voting isn't always a problem.

alex1234321 wrote:The only voting system that I know of that does is range voting, which just devolves into approval voting with strategic voters.


Approval voting is a special case of Range voting anyway - and if your election system is range voting with a small range, you can simulate range voting with a large range by rolling some dice while casting your ballot. For this reason, I view Approval voting and Range voting as the same thing.

There is a valid argument that using range voting with a wider range tends to promote honest voting, though. It's purely a psychological effect, not an incentive, but strategic voting does go down when voters have more freedom to express a very precise opinion.
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Re: Ranked Choice Approval Voting

Postby alex1234321 » Wed May 12, 2021 7:05 am

Brilliand wrote:
alex1234321 wrote:The only voting system that I know of that does is range voting, which just devolves into approval voting with strategic voters.


Approval voting is a special case of Range voting anyway - and if your election system is range voting with a small range, you can simulate range voting with a large range by rolling some dice while casting your ballot. For this reason, I view Approval voting and Range voting as the same thing.

There is a valid argument that using range voting with a wider range tends to promote honest voting, though. It's purely a psychological effect, not an incentive, but strategic voting does go down when voters have more freedom to express a very precise opinion.


I would argue that approval voting is better than a larger range because you can't express more opinions. Range voting causes honest votes to count far less than strategic ones while the difference isn't as big for approval voting.
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Re: Ranked Choice Approval Voting

Postby Brilliand » Wed May 12, 2021 6:03 pm

alex1234321 wrote:I would argue that approval voting is better than a larger range because you can't express more opinions. Range voting causes honest votes to count far less than strategic ones while the difference isn't as big for approval voting.


How do honest voters have any less power under range voting than under approval voting?

Let's consider an honest voter who would vote (Bernie Sanders 100%/Hillary Clinton 10%/Donald Trump 0%) under range voting on a percentage scale. Such a person would bullet vote Bernie Sanders under Approval voting. Which version of the vote would count more? Well, that vote has slightly less power to cause Bernie to defeat Hillary, but in exchange it contributes somewhat to helping Hillary defeat Donald. Seems like a wash to me. (The voter would be happier, though, because presumably supporting Hillary "just a tiny bit" was exactly what he wanted.)
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Re: Ranked Choice Approval Voting

Postby alex1234321 » Wed May 12, 2021 7:42 pm

Brilliand wrote:
alex1234321 wrote:I would argue that approval voting is better than a larger range because you can't express more opinions. Range voting causes honest votes to count far less than strategic ones while the difference isn't as big for approval voting.


How do honest voters have any less power under range voting than under approval voting?

Let's consider an honest voter who would vote (Bernie Sanders 100%/Hillary Clinton 10%/Donald Trump 0%) under range voting on a percentage scale. Such a person would bullet vote Bernie Sanders under Approval voting. Which version of the vote would count more? Well, that vote has slightly less power to cause Bernie to defeat Hillary, but in exchange it contributes somewhat to helping Hillary defeat Donald. Seems like a wash to me. (The voter would be happier, though, because presumably supporting Hillary "just a tiny bit" was exactly what he wanted.)


In this case it would be a wash, but the problem arises when the voter doesn't completely love or completely hate any of the candidates. If the voter is (Bernie Sanders 60%/Hillary Clinton 10%/Donald Trump 0%) for example, they would never benefit from giving Bernie less than 100% of the range vote. But they would do that if they're honest, which would lower Bernie's chances of winning compared to approval, where the voter would approve of Bernie and give him 100% of the vote.

The flip side is a situation where the person dislikes all the candidates to varying degrees such as (Bernie Sanders 40%/Hillary Clinton 10%/Donald Trump 0%). There, the honest voter would not choose any candidate under the approval system and irl would probably choose not to vote. But with range they might come out and would somewhat help Bernie win.

So it's still a wash, but with some bigger consequences. Range is better for encouraging turnout than approval, but it can punish somewhat honest voters who would vote for their favorite candidate under the approval system. Since turnout is such a big issue in the US, I would actually argue that range is better. But in countries with compulsory voting approval would probably be better since fewer voters would turn in an empty ballot.
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Re: Ranked Choice Approval Voting

Postby Brilliand » Wed May 12, 2021 8:20 pm

alex1234321 wrote:In this case it would be a wash, but the problem arises when the voter doesn't completely love or completely hate any of the candidates. If the voter is (Bernie Sanders 60%/Hillary Clinton 10%/Donald Trump 0%) for example, they would never benefit from giving Bernie less than 100% of the range vote. But they would do that if they're honest, which would lower Bernie's chances of winning compared to approval, where the voter would approve of Bernie and give him 100% of the vote.


Oh, that... that's a very obvious sort of strategic voting, though. Obviously you rate your top choice 100% and your bottom choice 0% regardless of how much you may like those choices individually. I wouldn't even call the voter "dishonest" if all they're doing is rescaling their vote to match the voting range indicated on the ballot - the relative preferences between candidates are what actually matter.
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