Symmetrical IRV
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In standard Instant Runoff voting, there is a process of elimination in which we count the number of "first choice" votes at each stage, and eliminate the candidate with the lowest score. This is done over and over till we have a single candidate left.
What about a variation where, rather than just counting the first choice votes, we count the first choice votes minus the last choice votes, and use that at each stage to eliminate the lowest scoring candidate.
Notice that when only two candidates are left, these methods are the same.
How would this change the dynamic? Would it eliminate any center-squeeze effect?
(Has this been given a name? I'm calling it "symmetrical" because it equally favors first choice and last choice in the tabulation, unlike regular IRV which is biased toward top choice)
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IRV usually allows a limited number of rankings and the unranked candidates on a ballot are in effect equally ranked to each other in a rank below the lowest explicit rank (I think). I think of these candidates as the "sludge" at the bottom. An asymmetry of IRV can be seen in the lack of "cream" at the top to balance the "sludge" at the bottom. A "cream" would consist of any number of candidates ranked equally at the top. A way to allow cream would be to allow equal ranking in general. So, I think that if you are looking to modify IRV to achieve symmetry, changes to make the constraints on voting symmetric between the top and bottom of a voter's ranking should accompany the change you already described.
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@jack-waugh Yes, this method could deal with that in a couple ways.
One is to simply require all candidates be ranked. That probably wouldn't fly in the real world.
Another would be to simply say that all candidates you refer to as "sludge" (all unranked candidates on a single ballot) would have a fraction of a point subtracted. So if there were 5 candidates that a voter left unranked and therefore in last place, each would have 0.2 points subtracted.
You are right that even that doesn't make it perfectly symmetrical, but having it treat "dislike" as equal and opposite of "like" is a big step in that direction.
I'll admit I'm posting this as mostly a hypothetical method, not one I'm seriously proposing for the real world. I'm mostly interested in exploring just what it is about IRV that is problematic.
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All systems that split votes exhibit inequality of power between the voters. The converse has not been proven, but out of caution, I want to treat it as under suspicion of being true. And any system that doesn't provide an antivote for every possible vote exhibits inequality of power at least between some voters. And the system you have described doesn't provide the antivote. I think that is part of what makes IRV problematic.
Maybe an interesting hypothetical for moving away from the problems: allow equal-ranking (but don't count skipped ranks). In every elimination round, as you say, use the number of top rankings minus the number of bottom rankings. Bottom would include sludge except on ballots that rank all the candidates, which are sludge-free ballots, and in those cases, the bottom is the bottom explicit ranking.
These changes would make a symmetric IRV.
But another problem remains in that there can be more than two rounds of tallying. I believe Sara said all these are nonmonotonic (particularly Cardinal Baldwin).
Maybe a solution can be found by eliminating half the candidates in one round and find the winner in the second round.
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@jack-waugh said in Symmetrical IRV:
And any system that doesn't provide an antivote for every possible vote exhibits inequality of power at least between some voters. And the system you have described doesn't provide the antivote.
You don't think ranking them in opposite order is an antivote under this? Or are you just saying that because the typical rules allow incomplete ballots, and you can't really make an opposite ordered ballot to an incomplete ballot without equal rankings, that means there is no antivote?
I can agree it is imperfect but I can't agree with considering this, or regular IRV, to be worse than choose one, which you say in your signature (regarding regular IRV). You seem to be concentrating on the binary question "is it perfect (according to X criterion)?" rather than "to what magnitude is it imperfect?"
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@rob said in Symmetrical IRV:
Or are you just saying that because the typical rules allow incomplete ballots, and you can't really make an opposite ordered ballot to an incomplete ballot without equal rankings, that means there is no antivote?
Yes, that's why I'm saying that. In the hypothetical where complete rankings are guaranteed, there is an antivote, and it is indeed produced by reversing the ranking of the vote. Or if cream at the top is allowed, that opens up all votes to having an antivote. If say you and I are in total disagreement as voters and you are going to submit a ballot without a complete ranking, my vote has cream to balance your sludge.
Here's why IRV is worse than FPtP, and I get this argument from @Sass .
- In FPtP, your entire vote is always counted.
- Election security -- FPtP is tallied by the precincts and summed over their reports. The tallying point for IRV is a single point of failure and is vulnerable to a secret, scaled-up attack.
- Monotonicity.
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@jack-waugh said in Symmetrical IRV:
In the hypothetical where complete rankings are guaranteed, there is an antivote, and it is indeed produced by reversing the ranking of the vote.
Gotcha. I guess I am most interested in analyzing that hypothetical situation then, since my point here is less about pitching a new method, and more about determining exactly what it is about IRV that people complain about.
@jack-waugh said in Symmetrical IRV:
In FPtP, your entire vote is always counted.
Election security -- FPtP is tallied by the precincts and summed over their reports. The tallying point for IRV is a single point of failure and is vulnerable to a secret, scaled-up attack.
Monotonicity.I have thoughts on all of these, but will save them for another post to avoid straying off topic.
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. . . since my point here is less about pitching a new method, and more about determining exactly what it is about IRV that people complain about.
I think that this idea when combined with a couple of other tweaks, could make an interesting system to consider proposing seriously for use in politics. However, I would still wonder whether it guarantees monotonicity.
So, starting with RCV IRV Hare, tweak zero is the idea you raised in this topic, "rather than just counting the first choice votes, we count the first choice votes minus the last choice votes, and use that at each stage to eliminate the lowest scoring candidate.
Tweak one is permitting equal rankings.
Tweak two is bottom-two runoff.
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@jack-waugh Ok but those tweaks don't, to me, help with clarity. They may be improvements, but they aren't pure situations that help people wrap their heads around the concepts at hand.
I'm not sure what equal rankings provide except making it a bit easier on voters. To me it is a minor issue. One way of looking at it is this:
What if an online vote allowed you to rank the candidates by operating a slider?
And what if those sliders didn't round the values? So the only way you are going to get "equal rankings" is if you get it exactly the same to the pixel.
Does it matter? If you put one of them a tiny fraction above another, the system is basically saying "if it is a perfect tie otherwise, so you get to make the choice between these two candidates, which do you pick?"
What do you gain from being given the option to refuse to choose one?
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@rob said in Symmetrical IRV:
I'm not sure what equal rankings provide except making it a bit easier on voters. To me it is a minor issue.
No. You can't force the voters to rank all the candidates; they won't. The only reasonable way to treat the candidates they don't rank is as ranked below the others. The unranked candidates are therefore equal ranked. So what is in question is not whether to allow equal ranking, but whether to allow it everywhere. If your ballot can have sludge at the bottom, my ballot must be allowed to have cream at the top to counter your ballot. If your stance is honored in the tally but mine is breached, you are being given a special privilege on account of your stance toward the candidates, and my political right to equality as a voter is being violated.
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@jack-waugh said in Symmetrical IRV:
No. You can't force the voters to rank all the candidates; they won't.
Actually that is exactly what Australia does in many elections, force you to rank all of them.
But I don't think I ever suggested that, I simply said disallowing equal rankings is not particularly harmful, and is unrelated to the other issues I am speaking of.
If your stance is honored in the tally but mine is breached, you are being given a special privilege on account of your stance toward the candidates, and my political right to equality as a voter is being violated.
What are you talking about? I've never heard of an election where some people get to do equal rankings or leave unranked candidates at the bottom, and some don't. So why are we discussing this?
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If your ballot can have sludge at the bottom, my ballot must be allowed to have cream at the top to counter your ballot.
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@jack-waugh said in Symmetrical IRV:
If your ballot can have sludge at the bottom, my ballot must be allowed to have cream at the top to counter your ballot.
If you are simply talking about fairness, I'm not sure I see how that applies. It seems fair enough that you can counter that by simply having sludge at the bottom of your own ballot.
For one thing, having sludge at the bottom of a ballot (i.e. equally ranked candidates) is not giving the voter any advantage in IRV or Condorcet methods, other than saving them some time.
I can see some value in handling things symmetrically in that sense (which is the reason I proposed the above system for IRV) , but it isn't really about fairness per se, but about avoiding vote splitting and strategic incentives.
By the way, STAR voting claims to be all about that sort of symmetry (i.e. "equal vote"), but if they really wanted it symmetrical, they should say that if you don't give a candidate a rating, it will default to the middle rating.
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@rob said in Symmetrical IRV:
It seems fair enough that you can counter that by simply having sludge at the bottom of your own ballot.
Not unless you had cream at the top of your ballot.
To counter your sludge, I need to move your sludge candidates up to my cream.
All my ranks have to be your ranks, but reversed.
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@jack-waugh This is an property you (and some others) have expressed a desire for, but I've never heard the case for why it is important other than it sounds good. It's more "equal" but not in a way that directly translates to "fair." Both sides are playing by the same rules
I can understand why this property you want can reduce vote splitting. But the whole "it's not fair if it doesn't do this" doesn't really register for me. Why does voting require that each voter must be able to do something that is exactly the inverse of what someone else can do?
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@rob said in Symmetrical IRV:
Both sides are playing by the same rules
This is true of Choose-one.
Systems that split votes do not provide equality. I don't know whether all systems that do not provide equality split votes, but out of suspicion, fear, and caution, I want to assume so until it is proven otherwise.
And as discussed elsewhere on this forum, systems that pass Frohnmayer do not necessarily provide equality (such systems can be constructed with rules involving finding matching pairs of votes and throwing them out). However, systems that fail it definitely do not provide equality.
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@jack-waugh said in Symmetrical IRV:
This is true of Choose-one.
Systems that split votes do not provide equality. I don't know whether all systems that do not provide equality split votes, but out of suspicion, fear, and caution, I want to assume so until it is proven otherwise.Right, and that's why I think the whole "equal vote" thing is misleading.
If you are against vote splitting, more power to you. I'm on board.
But when you try to position one sort of equality (being able to cast a ballot that directly negates another person's ballot, i.e. the system is symmetrical in a negative-to-positive sense) as meaning that it will be equal in the "all people should have equal voting power" sense, It think it is misleading and obfuscates your goals.
Score voting is "equal" in your way, but it can disadvantage those who prioritize honesty, so it is unequal in that way.
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It'd be great if we could design a system where the best that voters could do (individually) is vote their wishes, without taking into account any estimate about the other voters' affinities, and there'd be no vote splitting. However, Gibbard disproved this.
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@jack-waugh said in Symmetrical IRV:
However, Gibbard disproved this.
You keep saying this, while ignoring the fact that the degree of vulnerability matters.
Do you accept that it is a fact that if you go for a walk in the park, a tree branch can fall on you and kill you?
Do you still go for walks in parks?
It sucks when it happens, but it is generally considered a "freak occurrence":
https://nypost.com/2022/08/15/nyc-park-goer-struck-by-tree-dies-at-hospital-police-source/If you answered yes to both, you are well on your way to understanding that the best way to evaluate problems is not to simply consider the binary question of whether or not the problem exists, but that you should instead be considering the magnitude of the problem.
I believe that you can reduce the concerns that Gibbard/Arrow noted to be so small that they effectively don't exist. Any reasonable Condorcet method does this.
I'd really love to hear you actually address this, you've expressed your concern over Gibbard etc so many times, and just ignore when we point out that the degree of concern can be reduced such that it is insignificant. But it is still non-zero, which you continue to dwell on.
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@rob How can the degrees of vulnerability to Gibbard be characterized? At this point, I'm not even asking how it could be estimated of a given voting system. Just, on what sort of a scale could the result of such an estimation be placed.
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