Does this sequential variation of STAR exist?

@Keith_Edmonds this may interest you.
This is a case where monotony fails in Cardinal Baldwin; it’s not the best because it’s the first one I found, but it’s sufficient as proof:

The red value is the one that is increased, causing the defeat of D.

“Seeming sensible” is psychology issue that I am not interested in. It is fundamentally different than there being a true strategic vulnerability.

A strategic vulnerability is something where someone [1] can actually get a better outcome by voting differently than their true preferences. Generally they do so because they have some knowledge of how others are likely to vote.

That’s the definition I’m using and if you are expanding that to include the idea of someone wrongly thinking they can gain such an advantage by voting differently from their real preferences, now math can’t touch it. It’s just psychology.

And anyone who wants to complain about a method can just make up some group of voters that has some incorrect belief that causes them to use it in a way that harms their interests. Sorry, but I’m not going there.

You said you would use a min-max tactic under this system, even though you don’t even qualify your choice to do that as being if I knew who the front runners were likely to be. Really?

We can’t prevent you or anyone else from voting badly. I don’t think there should be an IQ test for voting, but if someone wants to put their least favorite candidate first because they are dumb enough to think that’s a good plan, I’m not losing sleep over that and I’m certainly not going to agree that there is a strategic incentive to do so.

First of all, you aren’t a voter, you are someone in forum about election theory. (if you are a voter and want to use a bad strategy… ok. Let us know how that works out for you.)

If you are saying a voting method has a vulnerability, you need to demonstrate that better than just saying “I’d foolishly use this system in a way that harms my interests, so this system is flawed”

I never made a claim that Cardinal Baldwin doesn’t have any vulnerabilities, and I would guess that there are some, although I think they would probably be hard to exploit in the real world.

But if you can’t show me a sample of ballots that demonstrates this (especially now that I’ve gone to the effort to make it extremely easy to test such ballots), that’s a pretty significant fact in how seriously we should take your concerns.

[1] usually, in a voting context, we say a “block of voters”, simply because a single vote rarely changes the result, or if it does, it often only changes it from a win to a tie or a tie to a win. But it’s fair to say that the hypothetical block of voters in question all have exactly the same preferences.

How does one do this?

I don’t really know what I’m looking at to be honest.

If you don’t normalise in the first round but do subsequently, I think you would be building in a failure of Independence of Irrelevant Alternatives. If you introduced a new candidate with very little support (with all other scores the same), they would be eliminated immediately, and the second round would be the same as the original first round (before the new candidate was introduced) but normalised.

It would be if there weren’t those facts I told you about before, and that you have not denied so for now they are still valid.

[1] can actually get a better outcome by voting differently than their true preferences.

I have given you a clear example where it is very good to use that strategy, while you continue to complain without showing anything.

If you are saying a voting method has a vulnerability…

You’re the one who’s saying it doesn’t have it!
There is the tactical vote min-max and I ask you why I shouldn’t use this tactic? that’s all, you have to show me that your system works, not me.

especially now that I’ve gone to the effort to make it extremely easy to test such ballots

Your simulation is good, and shows some aspects of the voting systems, but if you really think that simulation is enough to say that a voting method is valid, you are very wrong.

I made additions to that simulator and used different graphics, maybe that’s more understandable:

The Codepen allows you to easily paste in score ballot samples (in a format commonly used to describe ballot sets in this forum), and test them under various methods. Since it is a Codepen, you can tweak the ballot samples as well as the JavaScript code itself as you wish.

Here is a quick video I made explaining both the general stuff which that Codepen does, as well as this particular sample set of ballots which demonstrates a vulnerability to strategic voting under Score, STAR and STLR. Cardinal Baldwin does not show the same vulnerability, and instead picks the Condorcet winner.

@RobBrown you often say that Cardinal Baldwin would rarely fail the Condorcet criterion, which is a criterion you like, so why not go the whole way?

Elect the Condorcet winner if there is one. If not, normalise the ballots, eliminate the lowest scoring candidate, and start again.

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That’s a good question. I have suggested that method (I think it is the same) in a recent thread, here’s what I said:

“Another method that is probably nearly identical to CB would be to use score ballots, pick the Condorcet winner if there is one, if not, normalize the ballots in the Smith set (the ones who tie for most pairwise wins) and pick the score winner from those. I find Cardinal Baldwin to be a bit more elegant and easy to explain, but otherwise don’t really have a preference between them.”

I could elaborate on why I (slightly) prefer Cardinal Baldwin to this method. I first called CB “SuperSTAR” because I considered it a fairly straightforward variation on STAR. STAR uses Score to eliminate all but two candidates, then chooses the pairwise winner (which can be considered to be the Score winner with normalized ballots). CB does the same thing, but more gradually, eliminating one candidate at a time. With 3 candidates, it is identical to STAR.

So that’s kind of a selling point, that is it is simply STAR with extra layer of sophistication. I could actually see the STAR voting organization adopting it as an option, especially if a voting district considering STAR is concerned about certain weaknesses.

There are some other things I think are cool about Cardinal Baldwin, which I am working on but will probably save for the new forum. I will say that I have long been working on trying to express “Condorcet-like behavior” with actual numerical scores, that can be shown in a bar chart. It is a hard problem, but I think it has immense value to be able to see results in a reasonable, meaningful bar chart, while preserving the best things about Condorcet compatibility.

And while the algorithm for computing those scores shown above was written 15 years ago (and I’m not sure I even understand it when I look at it now), it occurred to me recently that Cardinal Baldwin lends itself very well to produce very similar scores but in a much more elegant way.

OK, fair enough, but I don’t really see STAR as having gained so much traction in the general scheme of things that one would want to base a method on it for that reason.

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I can’t really argue with that. However, there are a fair number of people who are on this forum that are big advocates for STAR.

The fact that STAR is actually used within the 2020 US Presidential race counts for something – even though it is in a very minor way (“The Independent Party of Oregon used STAR voting in their 2020 primary election. The Democratic Party of Oregon used STAR Voting for their 2020 Presidential Delegate Elections.” - https://en.wikipedia.org/wiki/STAR_voting )

Was it you that commented that the vote for domain names was not “in STAR’s wheelhouse”? (edit: actually that was @Marylander ) I agree with that, and think we should prefer methods that work in a generalized sense. Like, if you can’t use them for little votes like this (with lots of candidates and very few voters), doesn’t that reveal a general flaw with them?

So, do you know a name for the method (or methods) that we are speaking of? I.e. that use Score ballots, and either choose the Condorcet winner, or if none exists resolve it using normalized Score ratings of the candidates in the Smith set? If not, we should probably come up with a name.

I talk up Cardinal Baldwin partly just because it has a name. :slight_smile:

It might be a good idea, but I don’t know of any name at present!

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I sort of named it so it having a name does not count for much. It is just the cardinal version of Baldwins method so the name seemed to fit. I think we should really start putting more systems in to electowiki. It will save confusion in the end.

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We should come up with a name if one doesn’t exist. (as well as clarifying whether the “Smith set runoff” is done sequentially, or simply as a single Score tally on the normalized votes).

I propose “Stella voting.” Stella is Italian for star (the system can still be presented as having similar usage to Amazon/Yelp star ratings system), and has a nice ring to it.

But ultimately (again, if there is no name for this method), we should have a vote for the name. Using this method, of course. :slight_smile: I think it is worth having an agreed upon name since it is one that will continue to come up.

Regarding Cardinal Baldwin, yeah, well I have something to refer to it by, and we’ve been doing so since I stopped calling it “SuperSTAR”… (after I embarrassingly created a second thread asking if such a method existed!)

Agree, both of these should be in there. Maybe we can make contributing to Electowiki a category on the new forum, so we can have good discussions around adding new ones, etc. Electowiki isn’t great for discussion (although technically there are talk pages, but they are awkward).

Looking at this again, this is different from what I suggested. My suggestion was in a way more similar to Cardinal Baldwin in that you eliminate one candidate at a time (only stopping when you have a Condorcet winner among the remaining candidates) and don’t use the Smith set. Like a cardinal version of Benham’s method.

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Oh sorry I misinterpreted.

I built mine out, and it was pretty simple. Eliminate all candidates not in the Smith Set, normalize ballots, use the one with the highest score. Seems really straightforward, and as best I can tell no one has suggested it (which surprises me).

Yours seems like it would almost always produce the same result, although I could be wrong. Do you code JavaScript? Should be easy to code yours up.

Regardless, I think it was a good idea to keep searching for a good method that uses Score ballots but always picks the Condorcet winner. I’m pretty happy with the one I got, but it would be interesting to compare it to yours.

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Ok @Toby_Pereira, I implemented your method, or at least I think I did. I called it TobysCSHybrid, but you can give it any name you want. (or we can do a vote for a name, using it for tabulation, which is of course my suggestion :slight_smile: ) Let me know if you think I got it right. I didn’t attempt to deal with tie situations, which I probably should. https://codepen.io/karmatics/pen/ExKZVjM

It’s actually one of the shorter methods codewise, although of course it calls into other functions (tabulateScore, tabulateCondorcet, and eliminateCandidateAndNormalize).

With the ballot data supplied at the CodePen, it got the same result as CardinalBaldwin and STAR, e, while all the others got c. Remember this is on an election that is extremely close and had three candidates in the Smith set, so not super surprising that some methods produce a different result.

In addition, I made a hybrid of yours with my “Stella” method. Yours doesn’t always meet the Smith criterion (as you note it ignores the Smith set), while the Stella method does. So I made a variation that uses the same logic to narrow it down to the Smith set and normalize, but then calls into your method for the last phase, rather doing a Score tabulation on those remaining candidates. Codewise, it worked pretty nicely because a bit of reorganization allowed me to reuse code, so most of this comes for free. (I called it “Stella Toby Hybrid” for lack of a better name) This one also picked e.

I would describe this one as “aggressively Condorcet”. The scores (beyond simple rankings) are used to the absolute minimum possible… simply to eliminate members of the Smith set, and of course even then they are normalized.

I think you’d have to have God-like omniscience to be able to gain any benefit from knowing how others will vote and exaggerating or whatnot.

At bottom are full results. Notice that, if no Condorcet winner, your method has the most bulky results here, since it alternates between doing Condorcet (producing a list of pairwise wins) and Score (producing a list of scores), so there’s a fair amount of meaningful data to dump out. Stella output is shorter because it skips straight to the Smith set.

First, though, each round looks something like this:

***** round 2 *****
  *** scores ***
    c: 2.4804
    e: 2.4390
    f: 2.3606
    d: 2.2968
    b: 2.0414
    a: 1.9574
  *** pairwise ***
    c: 3
    d: 3
    e: 3
    f: 1
    b: 0

That shows that after the score comparison, a is eliminated, then a Condorcet round is done, which results in 3 candidates in the Smith set.

While this is the whole thing (showing all the methods’ output)

****** Pairwise wins ******
c: 4
d: 4
e: 4
f: 2
a: 1
b: 0

****** Score ******
c: 2215 (2.4804)
e: 2178 (2.4390)
f: 2108 (2.3606)
d: 2051 (2.2968)
b: 1823 (2.0414)
a: 1748 (1.9574)

****** Stella  ******
c: 2537.5
e: 2440
d: 2047.8333

****** Stella Toby Hybrid ******
 ***** round 1 *****
  *** pairwise ***
    c: 1
    d: 1
    e: 1

 ***** round 2 *****
  *** scores ***
    c: 2.8415
    e: 2.7324
    d: 2.2932
  *** pairwise ***
    e: 1
    c: 0

****** STAR ******
e: 413
c: 405

 ****** Cardinal Baldwin ******

 ***** round 1 *****
    c: 2.4804
    e: 2.4390
    f: 2.3606
    d: 2.2968
    b: 2.0414
    a: 1.9574

 ***** round 2 *****
    c: 2.5555
    e: 2.4409
    d: 2.2724
    f: 2.2417
    b: 2.0764

 ***** round 3 *****
    c: 2.8415
    e: 2.4253
    d: 2.0784
    f: 1.9825

 ***** round 4 *****
    c: 2.8415
    e: 2.7324
    d: 2.2932

 ***** round 5 *****
    e: 2.3124
    c: 2.2676

****** TobyCSHybrid ******

 ***** round 1 *****
  *** pairwise ***
    c: 4
    d: 4
    e: 4
    f: 2
    a: 1
    b: 0

 ***** round 2 *****
  *** scores ***
    c: 2.4804
    e: 2.439
    f: 2.3606
    d: 2.2968
    b: 2.0414
    a: 1.9574
  *** pairwise ***
    c: 3
    d: 3
    e: 3
    f: 1
    b: 0

 ***** round 3 *****
  *** scores ***
    c: 2.5555
    e: 2.4409
    d: 2.2724
    f: 2.2417
    b: 2.0764
  *** pairwise ***
    c: 2
    d: 2
    e: 2
    f: 0

 ***** round 4 *****
  *** scores ***
    c: 2.8415
    e: 2.4253
    d: 2.0784
    f: 1.9825
  *** pairwise ***
    c: 1
    d: 1
    e: 1

 ***** round 5 *****
  *** scores ***
    c: 2.8415
    e: 2.7324
    d: 2.2932
  *** pairwise ***
    e: 1
    c: 0

****** STLR ******
c: 2898.25
e: 2463.75
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Thanks for doing that. I’ll have a look over it. To answer your question from earlier, I don’t do any coding - maybe it’s a skill I’ll have to acquire!

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No problem. Definitely check out the CodePen video in the other thread. If you haven’t tried yet, the CodePens are usable by non-coders (you can type/paste in sample ballots to tabulate under a variety of methods, do the “blurred ballots” thing to mix things up a bit, etc), but if you’d like to try your hand at tweaking the code, let me know and I’d be glad to help you get started. You seem like you’d have the aptitude for it, and it should get a lot more interesting once the new forum is here if things go as planned.

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In terms of measuring the “Condorcet compliance” of a method, why not simply measure the frequency with which the method complies with some range-analog of Condorcet, given that there is a Condorcet winner? Obviously there is a problem with scope, since the frequency is context-dependent, i.e there is no fixed frequency that can be expected to apply well to every case. Much like it is questionable what is meant by a “random triangle.” It reminds me of this:


But as long as you think you are addressing the pool of reasonable or expected situations within your simulations, that measure of compliance should still be fine. Hopefully this isn’t off base too much, but since one major component of a voting system is essentially a compression algorithm, I think the proof that there is no universal compression scheme is something people concerned with voting theory ought to see:


This is good evidence that the choice of voting system should be optimized depending on context, and that it cannot be optimized universally. Which in my opinion makes this whole discussion easier in some ways and harder in others.
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