IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?)
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@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
"Least polarizing candidate (in the Schwartz set)": I had hoped that my example on the page would clarify this (the example is supposed to signify R=Right, L=Left, CR=Center-right)
Right. I missed that. This is a huge advantage over IRV. If you are going to point out that STAR also gets the same winner as IRV you have to give an interpretation of the translation of ranks to scores. A reasonable interpretation is
47 = L:5, CR:4
39 = R:5, CR:4
5 = R:5
5 = CR:5, R:4in which case CR wins (or my math is bad). In any case I see the argument you are trying to make. Consider
49 = L:5, CR:4
51 = R:5, CR:4where R wins and the clear best winner is CR. This is why I invented STLR.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
"Dishonest strategy": I think the best definition here would be "voting counter to what I want (lying) to get something I want" - a great example would be to rank a non-favorite higher to eliminate a frontrunner so that your favorite can win - IRV prime is immune to it because the only way a candidate can win is by having a larger majority
I am no expert on these proofs but Gibbard-Satterthwaite theorem would forbid this. Making such a claim will require a proof.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
And in fact C wins in IRV Prime (so it does seem to satisfy monotonicity, so you may actually be interested)
Arrow's impossibility theorem would also forbid this. Passing it in a situation then IRV fails does not prove monotonicity. You are likely just shifting the failures to another spot. If this does pass either of these criteria that would make you very famous very quick. I am quite skeptical. My suggestion is for you to look into proofs.
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@Keith said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
Right. I missed that. This is a huge advantage over IRV. If you are going to point out that STAR also gets the same winner as IRV you have to give an interpretation of the translation of ranks to scores. A reasonable interpretation is
47 = L:5, CR:4
39 = R:5, CR:4
5 = R:5
5 = CR:5, R:4in which case CR wins (or my math is bad). In any case I see the argument you are trying to make. Consider
49 = L:5, CR:4
51 = R:5, CR:4where R wins and the clear best winner is CR.
Exactly; I'll expand on why STAR also fails because CR is eliminated before the runoff (similar issue as IRV)
This is why I invented STLR.
Very interesting, let me take a look & understand it first before replying.
I am no expert on these proofs but Gibbard-Satterthwaite theorem would forbid this. Making such a claim will require a proof.
Arrow's impossibility theorem would also forbid this. Passing it in a situation then IRV fails does not prove monotonicity. You are likely just shifting the failures to another spot. If this does pass either of these criteria that would make you very famous very quick. I am quite skeptical. My suggestion is for you to look into proofs.
Agreed; passing a situation that IRV fails means nothing (I mean, it could be an indication; but it's not enough) & a proof is necessary. I think I've found what's wrong with Gibbard-Satterthwaite theorem, but I'm not sure how to put it in a proof.
In essence, the crux of it is that it assumes the method picks the wrong winner; effectively, it says "given a system which eliminates Paper & then has Scissors run against Rock" - the problem is, why is this assumption being made? Why would we eliminate Paper first if we know Scissors voters prefer Paper over Rock?
If the system picks the candidate with the most support via elimination (which IRV-Prime does) while at the same time only transferring your votes to your next preferred candidate if your candidate can't win, then by definition tactical voting does no good.
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Why are you stuck on using a ranking system? A cardinal system will given you more information by definition so if you want to do something fancy it is typically simpler to calculate.
Non-monotonicity tends to come from sequential elimination. Cardinal methods that do this tend to be non-monotonic too (eg IRNR). The problem is that ranking forces you to do elimination.
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Later-no-harm is the main reason; my main worry is that if major parties feel that ranking a candidate after them will ruin their chances of winning, they'll encourage their supporters/voters to bullet-vote, which will degrade to ~plurality (a single max-point vote for the favorite & no one else ranked)
Let's look at the flip-side, though (just theoretically): suppose that IRV-Prime does satisfy the monotonicity criterion as well as later-no-harm (I realize that seems to break every rule but let's go with it)
What would be the reason not to go with it (besides possibly that the counting is too complex?)
Wouldn't its benefits (i.e. having major parties actually encourage voters to rank others, actually giving 3rd parties a chance, as well as monotonicity) outweigh that detriment?
I.e. isn't it worthwhile trying to see if if it at least does satisfy these criteria like it seems to?
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Trying to understand Arrow's impossibility theorem (the informal proof, part 2)
It says that with Profile K we have:
B > C > A: k -1 A > B > C: 1 A > B > C: N - k - 1(Here, A wins, as expected, in IRV as well as IRV-Prime)
And with Profile N:
C > B > A: k -1 B > A > C: 1 A > C > B: N - k - 1In IRV, A wins. In IRV-Prime, B wins.
So I think by this definition:
dictatorship is the only ranked voting electoral system that satisfies unrestricted domain, Pareto efficiency, and independence of irrelevant alternatives. Similarly, by Gibbard's theorem, when there are at least three alternatives, dictatorship is the only strategyproof rule.
So I think the key here is that IRV-Prime simply satisfies the dictatorship mechanism, which is why it's strategyproof, i.e. voter k chooses the winning candidate by whatever they rank as #1
But later-no-harm is also satisfied.
So the question is: why do people believe that Arrow's impossibility theorem & Gibbard–Satterthwaite theorem imply a voting method cannot satisfy later-no-harm + Monotonicity criterion + Condorcet criterion?
That's not at all correct in the case of a method which has a dictatorship mechanism
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@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
Later-no-harm is the main reason;
I have never viewed this as a good thing. It is equivalent to never making a compromise or consensus. I had always equated it with the majoritarianism we discussed in the last post. Your system shows that they are not the same (or that it fails later-no-harm).
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
my main worry is that if major parties feel that ranking a candidate after them will ruin their chances of winning, they'll encourage their supporters/voters to bullet-vote, which will degrade to ~plurality
This is why Cardinal systems are good. There have been studies showing people do not bullet vote.
If your system passes monotonicity, is not fully majoritarian and is at least as strategy resistant as STAR then I would begrudgingly support it. The reason why it would be begrudging is that it is easy to dismiss all ranking systems as low quality at the moment. Most people have a low resolution view of this topic so the narrative that rank implies poor quality is useful. If that was no longer true then I suspect that organizations like FairVote would use IRV-Prime to gain support for regular IRV.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
IRV-Prime simply satisfies the dictatorship mechanism
Dictatorship implies it is non-democratic. This is bad
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I have never viewed this as a good thing. It is equivalent to never making a compromise or consensus
I don't disagree with you that people being unwilling to compromise is a bad thing (my goal, as you've seen, is to give people no choice but to compromise)
It ends up being counter-intuitive; effectively what IRV-Prime is getting people to do is: "look, be uncompromising, stick to your guns; but there's nothing to lose by setting up your priorities as #1 uncompromising 100% of what I want & #2 if #1 is impossible, compromise & get 50%"
It's giving in to people's needs while at the same time using the sum of the parts to an advantage (that as a population, we fall somewhere in the middle)
There have been studies showing people do not bullet vote
I don't think those studies take into account the macro, i.e. what happens at large scale when large-scale targeted campaign ads kick in; a system must be immune to that
Dictatorship implies it is non-democratic. This is bad
The name is horrible, perhaps why people have strayed away from it
. It is not at all implying undemocratic; rather, it's saying that in a perfect all-way tie, a single voter chooses any winner they want; in plurality, this is straightforward: if there's 5000 voting for L & 5000 voting for R, then I alone get to choose who winsWith ranked, it's a little more complicated; but you can still imagine a scenario where it does (reworking the example I posted on electowiki):
Right voters (R > CR > L) N
Pivotal Voter (?) 1
Left voters (L > R > CR) N(It's a little strange here that L voters prefer R over CR; perhaps in practice we don't ever get such a perfect cycle, but just to communicate the idea)
So the pivotal voter here is considered the dictator; whatever they choose as #1 (CR, R, L; doesn't matter), wins - that's true in IRV Prime
You can see that they're a "dictator" because they are a single voter whose choice is all that matters; but they're only in that position because their choice becomes the majority (so it's democratic)
In the plurality vote, the 5001th voter to vote for L & beat out R's 5000 would also be considered the dictator; had he chosen R, R would win; but it's a poor choice of terms, they're really the decider; their choice only matter because they're in the majority
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@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
my goal, as you've seen, is to give people no choice but to compromise
later-no-harm is the opposite of that. It is that no matter what you never need to compromise. Does the compromise candidate win in this situation when you use IRV-prime?
49 = L:5, CR:4
51 = R:5, CR:4Or in ranking
49 = L> CR > R
51 = R > CR > LCR should win under this situation given an ethos of Utilitarianism. I think IRV-Prime does find a good balance for a ranking system. However, ranks cannot tell between the first scoring and this
49 = L:5, CR:1
51 = R:5, CR:1where R is the Utilitarian winner.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
I don't think those studies take into account the macro, i.e. what happens at large scale when large-scale targeted campaign ads kick in; a system must be immune to that
Yes, but you are assuming that such effects will have a net push toward bullet voting. I think it will be the opposite. Real world approval voting examples give evidence to that.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
It is not at all implying undemocratic; rather, it's saying that in a perfect all-way tie, a single voter chooses any winner they want
I am not sure that is correct. I need to double check
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@Keith-Edmonds said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
later-no-harm is the opposite of that. It is that no matter what you never need to compromise.
It does not necessarily mean that; it simply means that your ranking order is never disregarded. The problem is that if ranking order is disregarded, then it could motivate people to not rank & then you're back to square 1
The key here is: in a democracy, if you are part of the majority, then maybe you don't need to compromise; it's shitty but it's just a side-effect of democracy
But the key is: how often does that happen in practice, that you are part of the majority? You can see that in practice it flip-flops, like a pendulum from left-to-right, precisely because there is rarely a majority candidate
So we should try to address the practical case (i.e. taking advantage of that middle) & giving the best results by taking advantage of what people think they want
The fact that there is such a thing as a "spoiler candidate" I think is clear proof that a majority is easy to destroy.
Does the compromise candidate win in this situation when you use IRV-prime?
49 = L:5, CR:4
51 = R:5, CR:4Because IRV-Prime fulfills condorcet & thus majority winner, a majority winner will always win; but then, as I mentioned, how often does this happen in practice? Look at the 1856 & 1860 elections: when there are > 3 viable candidates, no candidate gets a majority.
Or in ranking
49 = L> CR > R
51 = R > CR > LCR should win under this situation given an ethos of Utilitarianism. I think IRV-Prime does find a good balance for a ranking system. However, ranks cannot tell between the first scoring and this
49 = L:5, CR:1
51 = R:5, CR:1where R is the Utilitarian winner.
They "can't tell the difference" because the majority candidate wins (what I mean is, if a ranking system "not telling the difference" was electing CR in both cases, that'd be really terrible; but it ends up electing R in both cases)
Though I agree that in the first scenario CR is more representative, I have to come back around to real-world practical: how likely would this be? That R would have a majority? I think it's almost certain that in practice there are centered people & they'd take a big enough chunk such that R does not have the majority, and then IRV-Prime would select the compromise candidate.
More importantly, the will of the voters (even if shitty) does have to be respected; it's like the king in the little prince; if people saw a result like this, they'd immediately want to eliminate the voting system because they'd feel short-changed when a majority winner loses.
Now, we can agree that's shitty - but it is also reality.
Yes, but you are assuming that such effects will have a net push toward bullet voting. I think it will be the opposite. Real world approval voting examples give evidence to that.
We just don't know - approval voting has never been used in a major election where campaigns would put significant funds into saying "bullet vote or I might lose."
What we do know is that campaigns are self-serving; if they think anything will give them an edge (which bullet voting would), if that incentive is there, they'll take it.
I am not sure that is correct. I need to double check
The best demonstration of this I could find (which made it really clear but took some thinking) is the informal proof of Arrow's impossibility theorem
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So your example actually perfectly demonstrates why it gets the bad name of "dictatorship mechanism"; you had this example:
49 = L> CR > R 51 = R > CR > LSo your thought is that CR, with wider support, should get elected; but in STAR/IRV/IRV-Prime, R (majority) gets elected
However, if we had this:
49 = L> CR > R 49 = R > CR > L 2 = CR > L > RThen in fact CR does win (with IRV-Prime), even though only 2 voters ranked them as #1; these 2 voters seem like dictators, as far more voters ranked L as #1 & R as #1
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@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
It does not necessarily mean that; it simply means that your ranking order is never disregarded. The problem is that if ranking order is disregarded, then it could motivate people to not rank & then you're back to square 1
I think this is only an issue in a ranking system.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
in a democracy, if you are part of the majority, then maybe you don't need to compromise; it's shitty but it's just a side-effect of democracy
Yes this is called the tyranny of the masses and is one of the major issues with majoritarian democracy. This is why I prefer Utilitarian democracy.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
how often does that happen in practice, that you are part of the majority? You can see that in practice it flip-flops, like a pendulum from left-to-right, precisely because there is rarely a majority candidate
And those like me get no say at all. I am a social liberal in a Country that flips between Neo-conservatism and progressivism. (If you do not know the terms look here ) I get no say even though I am a huge demographic. I suspect your system is less vulnerable to center squeeze than the regular IRV but I do not think that it has completely eliminated it.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
Because IRV-Prime fulfills condorcet & thus majority winner, a majority winner will always win; but then, as I mentioned, how often does this happen in practice?
It only does not happen in practice because the system makes it hard for such candidates to be viable. There are game theoretic effects. I posted about this recently in another thread.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
They "can't tell the difference" because the majority candidate wins (what I mean is, if a ranking system "not telling the difference" was electing CR in both cases, that'd be really terrible; but it ends up electing R in both cases)
Exactly. No ranking system can get around this issue.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
Though I agree that in the first scenario CR is more representative, I have to come back around to real-world practical: how likely would this be? That R would have a majority? I think it's almost certain that in practice there are centered people & they'd take a big enough chunk such that R does not have the majority, and then IRV-Prime would select the compromise candidate.
Maybe
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
More importantly, the will of the voters (even if shitty) does have to be respected; it's like the king in the little prince; if people saw a result like this, they'd immediately want to eliminate the voting system because they'd feel short-changed when a majority winner loses.
It depends on who you ask. In this situation
49 = L:5, CR:4
51 = R:5, CR:4Lets say this was the 2016 presidential race and R=Trump while L=Hillary. A system that could find the CR candidate would have been better. Many people would see that immediately. Furthermore, you would only get such candidates in such a system. People often assume that you get the same candidates when you have different systems but this is false. Unviable candidates do not even show up.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
We just don't know - approval voting has never been used in a major election where campaigns would put significant funds into saying "bullet vote or I might lose."
Exactly. In all the real Approval elections that happened recently, that would have ruined their campaign. Running that campaign would make them look like a jerk
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
Then in fact CR does win (with IRV-Prime), even though only 2 voters ranked them as #1; these 2 voters seem like dictators, as far more voters ranked L as #1 & R as #1
This is a good example since there will always be a few voters of all orderings. I would make this point on your electowiki page.
In summary, you have made a better IRV at the cost of some complexity. I do not study ranking systems for reasons that should be clear by now so I cannot speak with any authority on how it compares to other ranking systems. IRV is likely one of the worst so I would not celebrate yet. Also, I would not make the bold claims about strategy or monotonicity without talking to a proper expert on such systems.
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@Keith-Edmonds said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
It depends on who you ask. In this situation
49 = L:5, CR:4
51 = R:5, CR:4Lets say this was the 2016 presidential race and R=Trump while L=Hillary. A system that could find the CR candidate would have been better.
Better for the country, agreed; but look at the state things are in now, does it seem like people care what's better for the country?
That 51 majority would be pissed & immediately vote to outlaw the voting system; the question is: how can we get those 51 people to think "oh yeah it's clear CR is the winner & we lost" (ok, you'll never get that with all 51; you'll always have the sore losers)
I think IRV Prime might be that, because that center sucks away that majority - i.e. I think in practice, it will get the results you expect while at the same time getting everyone supportive of the voting system instead of against it.
Many people would see that immediately. Furthermore, you would only get such candidates in such a system. People often assume that you get the same candidates when you have different systems but this is false. Unviable candidates do not even show up.
Completely agree - I think that's actually the beauty of IRV Prime, it'll change the parties. Do you believe the major parties would continue to be polarizing when they see that's a losing strategy in the general election? I highly doubt it.
This is a good example since there will always be a few voters of all orderings. I would make this point on your electowiki page.
Will do.
In summary, you have made a better IRV at the cost of some complexity. I do not study ranking systems for reasons that should be clear by now so I cannot speak with any authority on how it compares to other ranking systems. IRV is likely one of the worst so I would not celebrate yet. Also, I would not make the bold claims about strategy or monotonicity without talking to a proper expert on such systems.
Completely agreed - I've been reaching out but have been having a tough time finding the right folks! I think I may have finally gotten in contact with some so we'll see where it goes.
Thanks so much for the views/thoughts, very much appreciated!
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@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
Better for the country, agreed; but look at the state things are in now, does it seem like people care what's better for the country?
That 51 majority would be pissed & immediately vote to outlaw the voting systemI strongly disagree with your interpretation of the game theory here. If the 51% knew they were going to be 51% then sure but they do not. in any given election they could be the 49%. What people want is a system where independent of which side they are on they will get a good winner. This is a concept put forth by John Rawls called "the Veil of Ignorance".
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
Do you believe the major parties would continue to be polarizing when they see that's a losing strategy in the general election?
No but I think this is still a polarizing system relative to neutral. Score is balance and Approval is antipolarizing or centerist.
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@Keith-Edmonds said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
I strongly disagree with your interpretation of the game theory here. If the 51% knew they were going to be 51% then sure but they do not.
But they will after the election results - and when they see the election results showing that 51% of them gave CandidateR the highest score, the cardinal system will be vetoed in an instant - that, or everyone will switch to bullet voting so it never happens again.
The beauty of IRV Prime is that'll never happen - like you said, they don't KNOW that they have 51%, but they'll hope they do; so they'll rank #1 their favorite but #4 a safe compromise.
If it turns out that they really did have 51%, they'll win & it'll be a vote of confidence for the voting system.
On the other hand (as will frequently happen) if they only have 48% & the center has the remaining 3% & the center candidate wins, they'll see very clearly in the results why center won.
in any given election they could be the 49%. What people want is a system where independent of which side they are on they will get a good winner. This is a concept put forth by John Rawls called "the Veil of Ignorance".
I don't think people want a good winner - people are selfish, they want the winner that best represents them.
Nothing will piss off a democracy more than a majority candidate losing (in spite the fact that a more representative candidate would actually be better for the country).
Each individual voter, in general, cares about themselves, not the general good.
No but I think this is still a polarizing system relative to neutral. Score is balance and Approval is antipolarizing or centerist.
IRV-Prime is a forceful unpolarizing system - as long as a polar side doesn't have the majority (which is almost certain most of the time), it pushes voters towards a compromise.
Approval & score would be the best if people voted "for the greater good" & weren't so easily manipulated by campaign ads.
But do we want the system that works best with humans (selfish & easily swayed)? Or the system that works best in a utopian society?
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@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
and when they see the election results showing that 51% of them gave CandidateR the highest score, the cardinal system will be vetoed in an instant
No, I do not think so. If the system is fair they will be happy. What prevents them from choosing a sytem which polarizes is that the other side may get their polarized winner next time.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
everyone will switch to bullet voting so it never happens again.
In score voting yes but that is why STAR was in vented
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
Each individual voter, in general, cares about themselves, not the general good.
They key is to choose a system where everybody's selfishness works to reinforce the system. Like in economics. As stated by Nobel laureate F. Hayek “Planning and competition can be combined only by planning for competition, not by planning against competition.” The system which is best under strategy is best
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
IRV-Prime is a forceful unpolarizing system - as long as a polar side doesn't have the majority (which is almost certain most of the time), it pushes voters towards a compromise.
It is less polarizing than regular IRV but I have quite sure it will have a polarization bias. You should make some Yee diagrams to see for yourself.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
Approval & score would be the best if people voted "for the greater good" & weren't so easily manipulated by campaign ads.
False. You need to back up a bold claim like that.
@marcosb said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):
But do we want the system that works best with humans (selfish & easily swayed)? Or the system that works best in a utopian society?
Exactly, want the system which is best given all the strategic consideration s in the real world. That is either STAR or STLR
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@Keith-Edmonds Thanks! Unfortunately it doesn't send me any form of notification, will respond.
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My first impression is that it is too difficult to understand and explain.