STAR-like method ("reverse STAR"?)

Marylander

@jack-waugh said in STAR-like method ("reverse STAR"?):

Can we show that reverse STAR never provides an incentive to invert ranks?

Never? No, because it isn't true. The following example is effective at showing this for many Condorcet methods. (Not all, but many.)

40 A5 > B3 > C0
25 B5 > A3> C0
35 C5 > B3 > A0
A 275; B 350; C 175
B60-A40; B65-C35; A65-C35
B is a Condorcet winner and a score winner.
If 26 A voters lower B to 0, A will win the score vote, but B will still be a Condorcet winner. (At least 30 A voters must bury B to 0 to make B not a Condorcet winner just by burying B.)
However, if these 26 A voters also give C a point, then there is a Condorcet cycle, and so A wins.

26 A5 > C1 > B0
14 A5 > B3 > C0
25 B5 > A3 > C0
35 C5 > B3 > A0
A 275; B 272; C 201
B60-A40; C61-B39; A65-C35

However, I don't think this example is terribly damning because B voters only have to reciprocate a little to get back to winning. Although I do wish sorted margins was easier to explain because it is quite strong against this kind of strategy.

Edit:
@rob said in STAR-like method ("reverse STAR"?):

(BTW you made an error on the second line, you meant C0 not A0)

Fixed.

rob

@marylander It's an interesting example, although I agree it isn't "terribly damning" because, well, I just can't imagine anyone in a real world election trying to use that strategy because they'd have to be extremely knowledgeable about how others are going to vote, to not risk doing more harm than good. (i.e. giving the election to C, who they like the least)

In theory, we could alter the method to (after narrowing the field to the ones that have the most pairwise wins) then narrow it to the top two score winners, then choose the pairwise winner from those two. So then it would be even more like STAR, but with the pairwise step at the beginning.

26: A[5] C[1] B[0]
14: A[5] B[3] C[0]
25: B[5] A[3] C[0]
35: C[5] B[3] A[0]

****** Pairwise wins ******
A: 1
B: 1
C: 1
****** Score ******
A: 275 (2.7500)
B: 272 (2.7200)
C: 201 (2.0100)
****** STAR ******
B: 60
A: 40

This would give it to B, which would be the Condorcet winner if everyone voted sincerely. In this case it is basically STAR (since the pairwise step didn't actually narrow it down at all), but of course most of the time it's just gonna pick the Condorcet winner.

(BTW you made an error on the second line, you meant C0 not A0)

culi

@rob Very late to this conversation but what you're describing is exactly the Dasgupta-Maskin method[1] which is just Copeland with a Borda tie breaker. This method has actually been used in figure skating competitions under the name of "one by one"[2]

There are different version of Copeland depending on how you wanna score wins, ties, and losses. Most commonly used is probably the 1/½/0 (1 point for wins, 0.5 points for ties, 0 for losses) method but Lull proposed a 1/1/0 method and 3/1/0 is commonly used in sports. But it seems like you're just using a 1/0/0 Copeland here

This system can also be compared to Black's which is essentially just Condorcet with Borda tiebreaker

[1] https://scholar.harvard.edu/files/maskin/files/voting.pdf
[2] https://sci-hub.se/10.1287/opre.2014.1269

culi

Perhaps we can differentiate them like so:

star: top two runoff based on borda score and pairwise winner for the second round
dasgupta_maskin/one_by_one: 1/0.5/0 copeland with borda tiebreaker
reverse_star: 1/0/0 copeland with borda tiebreaker
black: simple condorcet with borda tiebreaker

Jack Waugh

@culi In Borda, you can't skip ranks, but in reverse STAR (which could be called RATS), you can.

rob

@culi Well it isn't a Borda tie breaker, it is a Score tiebreaker. This method uses Cardinal ballots.

Jack Waugh

This may be the fairest system I have ever heard of for a single winner.

rob

@jack-waugh Cool I'm not sure whether it is the absolute fairest but I like its balance of fairness (i.e. "one person one vote" or more accurately described as "everyone has equal voting power") and simplicity.

Jack Waugh

@rob OK, I'll bite -- what do you think is fairer, and on what grounds?

rob

@jack-waugh My primary criteria for fairness is that each voter has equal pull. As you know, I've said the nearest to perfect example of this is voting for a number (such as temperature) and picking the median. If you translate that to single winner elections with a finite number of candidates, you want to make it "as Condorcet as possible." That is, you want to -- as much as possible -- ignore strength of preference. (because factoring in strength of preference incentivizes exaggeration, etc)

I have a suspicion, but I haven't confirmed it, that the "most Condorcet" method is the recursive IRV one I proposed. (https://www.votingtheory.org/forum/topic/276/recursive-irv) The deeper you recurse, the better. If you only do it one level deep, it is plain old IRV. Go one level deeper and it will make it Condorcet compliant. Go 3 or 4 levels deep, and, well, it will just keep getting more and more Condorcet-ish.

That said, this reverse STAR one is plenty good, simply by virtue of being Condorcet. A simple improvement (based on what I said above) would be to normalize the ballots of the members of the Copeland set prior to calculating scores, but that makes it more complicated and I think it is unnecessary.

Toby Pereira

@jack-waugh said in STAR-like method ("reverse STAR"?):

@rob OK, I'll bite -- what do you think is fairer, and on what grounds?

You're saying it's the fairest. I think the onus is on you to justify that!

Jack Waugh

This post is deleted!

Jack Waugh

Paul Cohen comments on this method (I had brought it to his attention (writing under my real name, William Waugh)). One can reply in the publication he uses if one is fast enough. After a certain timeout period, it becomes impossible to add a comment to a given article without supporting the publication with money. I don't know how many or few people read his posts.

Jack Waugh

Maybe it should be called "LLull Then Score", abbreviated LLTS.

rob

@jack-waugh He doesn't seem to understand the basics.

He says "it seems quite likely that Condorcet scoring would only result in the continuation of two-party politics," but doesn't really give any reason for coming to this conclusion.

He previously noted "Consider that in a contest between only two candidates, it is unclear what advantage Condorcet voting might have, even over plurality voting." Well, yeah, of course. If only 2 candidates, making it ranked or Condorcet or anything else won't improve it.

But the point is that, under a better system (which could be this one, IRV, Approval, STAR, or whatever), the incentives change, especially in the long term. People more in the middle have far more incentive to run. There is less incentive to eliminate similar candidates via primaries or other party nomination mechanisms. Meaning it is far more likely to have more than two viable candidates.

Parties, and especially the two major parties, will remain an important force in political elections as long as there are plurality elections. Even if the current election is done via Condorcet, you can't 100% escape the influence of parties that are mostly incentivized due to the plurality elections that are still happening. But the more you have Condorcet elections (or STAR or IRV or whatever), the less the influence by the major two parties will be.

I believe this "vote splitting resistant" effect is strongest on Condorcet methods, but it is true for all of the above methods. If he doesn't understand how this would reduce two-party domination, I would suggest he needs to do some reading before he give hot-takes.

Jack Waugh

@rob, yes, I started to argue with him in the same direction as yours, but instead of carrying the argument all the way through, I paused in the middle of it to see whether he was following me so far. He evidently has family trouble and has had to throttle his level of attention on my responses.

Jack Waugh

@rob I repeat, however, that there is a time limit for appending comments.

rob

@jack-waugh yeah I started to reply there but it has a weird registration process that annoyed me. (it had a "register and post" button, but then complained I wasn't registered when I tried to use it). Also just an old site that looks like it's hardly used anymore. So I didn't bother.

Feel free to direct him here if you want to. (not that there's been a lot of activity here either)

Jack Waugh

@toby-pereira said in STAR-like method ("reverse STAR"?):

You're saying it's the fairest. I think the onus is on you to justify that!

Compared to which alternative?

rob

@jack-waugh The "-est" suffix means compared to all alternatives.

But if you want a specific alternative to compare it to, I'd suggest recursive IRV, at a depth of at least 3.

All this hinges on a definition of "fair." To me the most fair method would give every voter equal influence on the outcome. But of course that's tricky to quantify as well.