BTR-score
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@chocopi Sorry, it was @Lime https://www.votingtheory.org/forum/post/3716
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In this new ordering, Paper Jr. takes out Rock early, preventing Rock from taking out Scissors. Now Scissors wins.
This is, of course, an extremely specific scenario--and a good illustration of why focusing on absolute criteria is misleading. No one should care that something like BTR or Stable Voting are non-monotonic one-in-a-gazillion elections.
Thank you. I missed that case. In the list I provided this corresponds to [B]CAD turning to B[A]CD.
Smith-Score would be ok but re-normalization would need to be explained.
There might be a misunderstanding. The normalization of ballots is an assumptions of voter behavior, not part of the method. Smith//plurality misses that paragraph because it uses a ranked ballot instead of rated like Smith//score.
@casimir you indicated that the second-highest score winner in the cycle will be elected in a 4-cycle. This means that lowering the score of a candidate can cause them to win in such a case, which practically speaking is a very rare case.
Take a look at the list I provided. It has some cases where the second highest candidate wins, but no case where lowering the score of a candidate causes them to win instead of someone else. Likewise, raising someones score won't cause them to loose. The case that @chocopi pointed out is one where changing the order of the other candidates causes someone to loose. It's weird, but it's no reason to not give your favorite candidate full support (except for the favorite betrayal case, which comes with being a Condorcet method).
Because I'm from Germany, monotonicity is somewhat relevant, but it's not that all non-monotonic methods are banned.
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@casimir what I mean is that, in the realm of score perturbations that keep a given 4-cycle in tact, the ultimate goal would be to have given your favorite candidate a score such that they receive the second-highest sum of scores, not the first-highest. Does that make sense?
Again, it’s a weird, seemingly irrelevant edge case. But as you mention, it might not be irrelevant in situations where there are strict laws about monotonicity.
For the record, I really like BTR. It’s one of my favorite methods. It’s highly efficient to say the least. And your claims about how well it conforms to monotonicity make me like it even more, since my main concern about it from the beginning has been monotonicity.
I consider it a “cardinal-Condorcet” method, which I rate a 9 out of 10. It can be made even more monotonically robust by extending from “eliminate the bottom 2 Condorcet loser” to “eliminate the bottom N Condorcet loser” for N>2.
I’m not sure if N=K (the number of candidates) succeeds in full monotonicity, but I wager it does.
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I'm not sure I understand the question. In which case would it be beneficial to have your favorite placed second by score?
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@casimir suppose you submit your ballots, and then A,B,C,D are in the top 4-cycle. If your favorite is A, maybe you reasonably gave them your highest score. Now suppose A also has the highest aggregated score among the 4. Then, they will lose to the second-highest scoring candidate X≠A. So perhaps if you had lowered the score of A (without going below your second favorite among the 4–B, say), maybe A would have won instead of X.
Also, as you mention, it’s possible that by being dishonest about preferences below A, one could avoid the top cycle situation and lean on the highest score angle. I don’t have the details fleshed out.
Super niche and a really improbable situation. And maybe even an impossible situation, but I’m not sure it’s actually impossible.
Last note is that finding a single Condorcet loser is also generally more efficient than computing the entire preference matrix. With dynamic programming, taking the bottom N>2 may also be fairly efficient.
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Here are all the permutation of a 4-cycle:
C[A]BD B[A]CD C[A]DB B[A]DC [A]CBD [A]BCD [A]CDB [A]BDC [A]DCB [A]DBC C[B]AD [D]CAB C[B]DA [D]CBA [B]CAD [D]ACB [B]CDA [D]ABC [B]DAC [D]BCA [B]DCA [D]BAC [C]DBA [C]DABOut of these there are six cases where the second highest candidate wins.
C[A]BD B[A]CD C[B]AD C[A]DB B[A]DC C[B]DAFor this to be a problem there should exist an alternative where the first and second placed candidates swap, but the new second place wins. But looking at the options above, there is non where C wins in second place. Also, for the B first cases, swapping B and A still leaves A winning. So, at least in a 4-cycle, this is not an issue.
As for FB, it fails the same way as this example with for example candidates ordered form high to low score as D A B C.
All that said, I'm mostly concerned with practicality. For me the purpose of BTR-score is to be an as-simple-as-possible Condorcet method. Any way to make it compliant with more criteria would also make it more complex. It's good to know what properties it has, but I have no strict requirements. If it is non-monotonic in some rare cases, so be it - as long as it has no overt issues like Copeland does.
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If a court wishes to "ban non-monotonic voting methods", they would first have to declare all partisan primaries illegal.
I'd agree with you. In practice, partisan primaries determine which candidates you can actually vote for (because of the two-party system). But from a purely legal point of view, a partisan primary isn't "part of the election"; it's just a private association making a decision about who to support.
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@jack-waugh said in BTR-score:
it's just a private association making a decision about whom to support.
If it is a private decision, then why does the public have to pay for it (in the US)?
Good question. You can ask the Supreme Court.
https://en.wikipedia.org/wiki/California_Democratic_Party_v._Jones -
@jack-waugh said in BTR-score:
If it is a private decision, then why does the public have to pay for it (in the US)?
The justification for taxpayer funded closed primary elections is the theory that a even a closed primary offers more voter participation than nomination by caucus or party leadership.
Primaries, open, semi-open, and closed, provide free publicity to major political parties and establish a certain legitimacy to the major parties.
I am weird, I think we should offer each and every party the choice of an open, semi-open, closed or no primary elections. This would help third parties. This will also never happen.
One alternative is let parties nominate candidates as they see fit. If their are more than seven candidates, hold a blanket primary to narrow the field to three or four candidates, two candidates if plurality voting will be used.
The leading purveyors of RCV, the Top Four & Final Five folks, want to do this in a manor to screw political parties and help unaffiliated candidates. What they call "nonpartisan"; party nominations are not listed on the ballot but party affiliations of each candidate (from voter registration records) are listed on the ballots. This are "confused partisan" rather than "nonpartisan" elections.
They want to the nominees of political parties to be subject the same signature requirements as unaffiliated candidates. Unaffiliated candidates would have the advantages of not having to qualify for party status and not be responsible to party members.
All this signature gathering would drive up the cost of nomination signatures. Wealthy independents and major parties would get their signatures, more difficult for third party and independents who are not wealthy .
The dream of the Top Four and Final Five leaders is to elect a small squad of "moderate" (wealthy, donner class light) independents that would seize the balance of power in America.
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In summary, does anyone have a serious objection to the idea of all of us promoting this system for all cases where there isn't already a big investment in Score (including Approval) or STAR?
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@jack-waugh I like the system in theory, it’s a pretty conservative cardinal Condorcet method. I’d like to see more examples of how it resolves when there is no Condorcet winner. I also think it can be improved to Bottom N Runoff (BNR) and made more conservative, although BTR has a simpler description.
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@jack-waugh
It might still be too complex for voters without prior education. As someone immersed in these discussions, it is easy to loose sight of how little people know about voting and how many conceptual steps people have to take before understanding the method. I've argued here that it might be more useful to promote a spectrum of compatible methods (approval, score, STAR and BTR-score in this case). -
@casimir, thanks, that's a very interesting write-up.
At the end, you suggest that the equal-vote criterion would be too restrictive as a minimal standard. But all four of those systems pass it, I believe. They are additive and Frohnmayer-balancing.
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@casimir just a suggestion for your article, you might like to name the systems at the top as well and possibly give a very brief description of each. In my view you’ve addressed probably the most promising systems for reform efforts (although I personally don’t endorse STAR).
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@jack-waugh
Balance is one feature that the four methods share, but as a general minimal requirement for me to support a voting system it's to restrictive. It might exclude methods that are reasonable. On the other hand, it does even include some that are not so good in my opinion. A for-or-against variant of plurality, where you can either vote for only one, or against only one candidate, would still pass balance, but would be hardly better than plain plurality.
There has been a quite elaborate discussion about this on /r/endfptp which convinced me to remove that paragraph.@cfrank
Thanks for the feedback. I will add that to the article.
What is your reason against STAR? -
@casimir hmm I think it’s interesting as a system from the standpoint of tactical voting when nominations aren’t “adversarial,” but I worry how robust it is against strategic nominations—if parties nominate two clone candidates at a time, then it basically just becomes score with an added inefficiency. And I think score itself is fine, why not just do score? Parties are virtually guaranteed to engage in strategic nominations, because they already do right now.
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@cfrank
That's the issue that prompted me to think about related methods like BTR-score. Later however, I came across a good argument that convinced me this isn't so much of a problem. STAR becomes like score with strategic nomination, but that is the expected behavior. The main election is the score part, the runoff is there as a safe-guard and to make it compliant with laws that require a majority. Basically, the difference between score and STAR isn't that big, but practically it's easier to get STAR implemented. In the VSE simulation by John Huang, they even perform the same under "honest" and "two-sided strategic" assumptions. -
@casimir sure that makes some sense, but it also seems peculiar. STAR would double the number of candidates running, making it more difficult for voters to come to an informed understanding of the platforms of those candidates. At the same time, it would introduce a competition between the top two candidates for any party throughout the election, and who knows what kind of insanity that might induce: "We're both great, but I'm better" seems like an odd conflict to me. Or it could even be a good thing but it isn't clear.
Anyway, that's probably a conversation for a different thread, but essentially why I don't support STAR. I think BNR-score or BNR-approval would be preferable.
