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

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

To me the most fair method would give every voter equal influence on the outcome.

I am in emphatic agreement. I suspect the lack of this equality is a very key tool that the ruling class uses to keep the rest of us down. I do not know how to articulate the sufficient conditions for equality of influence. I believe that one of the necessary conditions, however, is Frohnmayer balance.

I haven’t seen a solid argument for why being “Frohnmayer balanced” automatically is better. There are many balanced methods that are terrible. But it, alone, shouldn't be the goal. A good method probably achieves it.

Vote splitting is the real enemy, and having it balanced (e.g. For and Against voting) doesn't eliminate vote splitting per se, but it tries to balance it between "clustering" vote splitting and "declustering" vote splitting. Clustering is what you get with plain old plurality, where you want to reduce similar candidates, incentivizing parties and primaries. For and against adds a declustering effect on top of that. But it's a fairly crude one, since it is still plurality.

As for recursive IRV, you could make it immediately Frohnmayer balanced simply by doing some sort of Borda count at the deepest level. I'd be willing to bet that, if you did, it would still converge to the same result. I will try it, though, it should be super easy to do.

I actually haven't “proven” anything regarding recursive IRV, but I do have it fully implemented now, thanks to a good bit of help from chatGPT, which made it so much easier. It's actually surprisingly fast, even when going way deeper than I'd expect is needed. I'd still like to build some sort of visualizer for it that's better than just a big dump of Json which is what I currently have.

However, although not a proof per se, I can walk through the logic a bit of why I think it is superior to anything else out there in terms of fairness. In general I will talk about it as if it recurses to Infinity, even though in practice, it should be completely unnecessary to go more than a couple levels deep for real world purposes.

First the background. We may all have different ideas of what fairness is, but to me it is all about removing vote splitting. Vote splitting is when irrelevant alternatives disproportionately draw votes away from relevant candidates. STAR, IRV, and Condorcet methods all attempt to remove irrelevant alternatives, but each have their flaws. With Condorcet methods, obviously there isn't always a Condorcet winner and that is the singular flaw (in that case, it “kicks the can down the road”, leaving you to find another way to settle who the winner is). With STAR, you're using score totals to guess what the irrelevant alternatives are, and that isn’t a lot more than a guess and is absolutely subject to vote splitting at stage one. With IRV you are using a process of elimination to estimate which are irrelevant. Since IRV depends on (inverse) plurality to determine who to eliminate, it also is subject to vote splitting at the elimination stage.

However, IRV, for all the complaints about it, does do one thing correctly, and that is that the process of elimination that it uses is always better than not using it, in terms of increasing the accuracy and resistance to vote splitting of the final result. That alone doesn't set it apart from other methods, but it just needs to be pointed out: process of elimination is always a good thing in terms of reducing the vote splitting effect, compared to using plurality directly.

And that last point is what recursive IRV taps into. If, in seeking a final winner, we get better results than plurality by using the process of elimination, why can’t we use the process of elimination to get better results than plurality for deciding who to eliminate? We’re always using plurality, but with each increased level of recursion, we are making it more indirect. The more indirect the usage of plurality, the better the result.

So recursive Irv, unlike every other voting method I know, can apply its effect over and over until we decide it's “good enough.” In that way, it’s analogous to how we address the computer science problem “binary representations of floating point numbers can never exactly represent certain numbers, like 1/3”. While true in theory, we can just add enough bits and the problem gets less and less significant. If 32 bit floats aren’t good enough, use 64 bit. If 64 bit isn’t good enough, use 128 bit. There is no limit to how many times you can increase the number of bits, and each time you, say, double them, the precision is increased by a predictable amount. It is a straightforward problem to increase the precision. While it has costs, obviously, you don’t need to reinvent anything if you need more precision, you just apply more of the same.

All my tests shows that recursive IRV will find a Condorcet winner, if they exist, very quickly. I’ve never seen it take more than one extra recursion level. But it doesn’t “seek out the Condorcet winner”, instead, finding the Condorcet winner is a byproduct of a process that makes the method more accurate, more resistant to vote splitting. But since that process still works in the absence of a Condorcet winner, we have something that never has to fall back on some ugly and imperfect kludge.

@psp_andrew-s

2CV now ensures, unlike any other proposed system, that the winner will, under all circumstances, be one who received at least 51% of 1st or 2nd choice votes.

A voters 2nd choice may be as good as their favorite or almost as bad as their last choice. There's no way to know, so ensuring a majority of 1st and 2nd choice votes is meaningless. Also, in any election where you can support multiple candidates there could be multiple majority supported options. The key is to find the one with the most support by looking at strength of support and/or number of voters who prefer them, ideally both.

I think we've already gone in circles about your other responses in previous conversations so I won't repeat that again here.

@rb-j said in New method (I think?): Hare-squared:

Yes, it is. The correct time to rail is right now, with the experience in Vermont and now with the newly experienced difficulties of Maine and NYC with administering RCV elections and getting timely results.

Let's rail, but let's rail on valid grounds only, lest we attract a reputation for disingenuous propaganda. Before the first successful powered flight by humans extended with machines, all prior efforts had failed. Eventually craft work and/or engineering advanced sufficiently to overcome the problems and reach the goal. Just because NYC flubbed up with administering RCV IRV Hare, doesn't mean a method of administering it that works better couldn't be engineered. Rob is saying let the precincts publish over the Internet the counts of all the ballot types cast there. Then anyone with a computer and a little knowledge of how to use it could reproduce the tally, and it would not take days (maybe it would take me days, but lots of others would do it in two hours and that includes research and reverse engineering the format and writing scripts).

@jack-waugh said in Collaborative Coding for Simulation:

But that's not a blocking issue.

I think there are huge advantages to making stuff that runs on the front end, if you want others in the community to be able to run it. Especially if you don't have web hosting. But mostly if you want others to be able to fork your code and play with it or build on top of it, such as to build it into a voting widget, to build a simulator, etc.

But I can see why on really hard methods like Schulze (which I'm convinced was invented as a parody of improved voting methods.... "let's see if we can make something so complicated none of us even understand it" 🙂 ), it makes some sense to do it in whatever language makes it easier.

@cfrank said in Condorcet with Borda Runoff:

Can you explain why it doesn’t make sense to try to elect a candidate that is not highly divisive whenever possible?

I personally think a method should indeed do that, but trying to label that a "supermajority" might be misleading or at best, vaguely defined. Supermajority what? Supermajority might indicate something like 70%, but the other variable is "degree of approval." So does it mean something like, over 70% thinks they are pretty good, as opposed to a simple majority where over 50% thinks they are awesome? If so, I would describe that as the system "favoring moderate candidates."

Regardless, I still suspect that a Condorcet compliant method will accomplish such a goal (favoring moderate candidates) better than any given method that isn't Condorcet compliant -- at least if you also want to avoid strategic manipulation and all that ugliness.

Notice that FairVote's primary complaint about Condorcet systems seems to be almost the exact opposite of yours. They think that Condorcet systems favor moderate candidates too much. (Then again, maybe you consider "moderate" to be significantly different from "supermajority support". I am considering them roughly the same, if I properly understand what you mean by "supermajority.")

@jack-waugh The difficulty of strategically manipulating Condorcet been covered excrutiating details in numerous discussions and papers, going back decades. Don't act like this is the first time the question has been asked.

You're still doing the same annoying thing, responding with a single question, derailing the meaningful and fresh part of conversation with circular questions, while ignoring everything else.

@lime said in STLR - Score Than Leveled Runoff might not be too complex for voters:

... So then shouldn't we be encouraging voters to give preferences as close to honesty as possible, to make sure we have as little error as possible?

No, in my opinion, we shouldn't. That's asking them to play the sucker, in the presence of a voting system that can get, I think, the right answer in case no party plays sucker. The proper use of Score Voting is to apply a tactic to maximize the expected value of the outcome. And I doubt whether STAR behaves significantly differently. It's just extra complexity for no gain.

@jack-waugh said in STLR - Score Than Leveled Runoff might not be too complex for voters:

"Honest voting" is a theoretical concept that can be useful in thought experiments and reasoning and the design of algorithms, etc. However, it does not describe a phenomenon that can happen in real elections in which something important rides on the outcome of the tally.

$20 says it does.

How are we going to test that? With the voters experiencing how many elections where the outcome matters to them? And how are we going to measure the importance of an election?

@jack-waugh said in STLR - Score Than Leveled Runoff might not be too complex for voters:

What grounds do you have for coming to such an opinion? I don't think it is correct.

I think that's just the definition of the "best result" under a given metric. Regardless of what social welfare function you pick, that social welfare function will be maximized if voters are honest.

What do you care about? Electing majority winners? A Condorcet method will always elect a Condorcet winner if voters are honest (but not necessarily if they're dishonest). Maximizing social utility? Score voting does that with honest voters (but not always for dishonest voters). Maximizing the number of voters who see their favorite candidate elected? FPP does that with honest voters (but once again, can't with dishonest ones).

No matter which social welfare function you come up with, that social welfare function will do better at its job if it has accurate information than if it has inaccurate information.

The input doesn't have to be accurate information about what the voters want. It suffices, in the case of Score Voting, if it is accurate information about the voter's tactical choice. If just one side votes "honestly" and the other is trying to maximize value, the result will be wrong and will skew to the side that is using the tactic. However, I contend that when all sides are using their respective best tactic, the "pull" balances out and the result will be the same as though all were "honest". The reason to think this is that the system is additive and balanced.

To paraphrase WDS: consider a voting system in which a vote consists of 32 bits. The tally takes the XOR of the ballots and then takes the result modulo the count of candidates to get the index of the winning candidate. How do I cast an "honest" vote in this system?

@Keith said in S-TM:

If there was two candidates supported by the largest bloc of about 40% of the voters they would still fight with eachother.

Yes, but they would still both be supported by that 40% because they both don't want to do things that make them lose that block.
Positive the fact that they try to have the block bigger and bigger, but if the block is for example "Republican", it will remain "Republican" (as well as the 2 candidates who then end up in the automatic runoff).

Also, falling back to score is not something I would view as a problem

The problem is that if you end up in Score Voting then you might as well use Score Voting from the start, which is simpler (but has its downsides).

@A Former User said in What level of PR do different systems get?:

I assume nothing about the distribution. I speak of the average s/v, over all possible numbers of quotas in an interval (as defined above).

The bias that I speak of is differing s/v averages over low & high intervals.

Nothing whatsoever to do with a distribution.

In this post on Election Methods, you wrote:

Here is what I mean by "bias". I claim that my meaning for bias is consistent with the usual understood meaning for bias::

For any two consecutive integers N and N+1, the interval between those two integers is "Interval N"

If it is equally likely to find a party with its final quotient anywhere in interval N, then determine the expected s/v for parties in interval N.

Compare that expected s/v for some small value of N, with the expected value of s/v for some large value of N.

If the latter expected s/v is greater than the former, when using a certain seat allocation method, then that allocation method is large-biased.

If the opposite is true, then the method is small-biased.

I have bolded and italicised part of your quote. It is an assumption about the distribution. You might think it's a fair assumption. But it is an assumption, something you've been denying. So I'm glad that's clarified.

[quote]

And while that might seem unrealistic, we can see the case of very small parties that never get enough votes to win a seat. A particular party might be due about 0.1 seats at every election but never win one under a particular method. Is that bias?
[/quote]

Sure, but it’s not the kind that has always been meant when speaking of bias. Fractional-quota small parties were traditionally never really wanted in PR countries.

It seems we're changing the subject here. This is about a method being objectively unbiased. We are not talking about practicalities at all and what is wanted. So do you admit to bias in the "Bias-Free" method then?

[quote]
(Michael's method involves a 0^0 in the 0 to 1 seat range, so appears to break, so I'm not sure how it is supposed to handle this case.)
[\quote]

No, it still works, though the usual formula doesn’t work. There’s a way to do the integral from that 0^0 point. It’s an exception that has to be separately integrated as a separate problem.

The answer to that problem is a rounding point equal to 1/e.

To clarify then, those parties consistently getting fewer votes than 1/e of a quota of votes are the subject of systematic bias, under the "Bias-Free" method.

[quote]
(after all Sainte-Laguë simply returns the most proportional result)…
[/quote]

…according to the difference measure of s/v-variation. …which doesn’t make as much sense as ratio. But of course your preference is entirely your business. …but if you’re going to say that Professor Huntington was wrong, you’ll need more than an assertion. You’ll need to say where you think he was wrong. Help that mathematics professor out by explaining where he made his error.

…& as I‘be explained to you many times, if by “most proportional” you mean “ having least maximum variation in s/v, that’s an entirely different matter from bias, whose meaning I’ve already told you several times.

Well, I've discussed Huntington's paper in the previous post, so that's sorted now. And you agree that Sainte-Laguë magically gives less bias than Huntington-Hill despite being worse. I also explained in a previous post why minimising the variance of s/v measured arithmetically is the best measure. s/v adds to a set number (s in fact). It is, in essence, an arithmetic sample, not a geometric one. Using geometric variance breaks if a party has zero seats. If you had a sample that multiplied to a set number, then use the geometric variance. It would make most sense. (Edit - is you were looking at v/s instead of s/v it would make sense to use the harmonic mean and variance.)

[quote]

The only way to get rid of bias under any assumptions…
[\quote]

BF has no bias.

As pointed out above, it only has no bias under certain assumptions. I could devise a voting distribution of voting behaviour (that could exist in a possible world) where it has either small or large party bias. The only way to eliminate any possibility of this would be to use a non-deterministic method. However, "Bias-Free" does have a small-party bias relative to Sainte-Laguë, which by the most sensible measure gives the most proportional result. This is itself a form of bias. But anyway, I'm repeating myself. I think we're probably done because you're not going to reply. But it's a shame. I think "Bias-Free" probably has some interesting theoretical properties, and it would be interesting to see them explained. But you asserted too much about it, and were unable to discuss it in a reasonable manner.

Well, I wanted to check this forum out, & there was talk about doing a lot of polling, which I consider very useful to demonstrate how the methods work.

But the amount of participation in the recent poll wasn’t very promising.

Because as I pointed out in one of the threads about it, it wasn't run very well.

@rob Thanks Rob, the plain English is just what I needed. I will think about it

@andy-dienes Awesome. Pandas definitely can make things concise if done right. There are lots of functions.

I have advanced the code from where it was crashing every time to where it gives wrong answers, so that's progress.

@culi The forum is not dead. It's not the most active forum, but it's definitely not dead.

@cfrank I'll make sure to include Bucklin.

@cfrank said:

The book "Economics and Computation" (edited by J. Rothe) suggest that it "may also be appropriate to not implement a specific tie-breaking rule, but to randomly choose one from several 'reasonable' tie-breaking rules

Ewwww. 🙂 Not a fan of random anything.

My current thinking on Condorcet is that, preferable to finding the Condorcet winner directly and then doing something else if there is none, is to have a singular mechanism that determines the winner (always, unless there is a "true tie" which becomes less and less likely with large numbers of voters), that just happens to be Condorcet compliant. BTR-IRV is a good example. My intuition is that it is less likely to provide an incentive to strategically try to create a cycle, if a cycle isn't really a major "thing".

Anyway, that's probably just semantics (as to whether it is a tie breaker) and straying a bit from voting on voting methods.

Just bumping this again. Since cycle removal works quite cleanly for 3 candidates, you could have a STAR-type method where the top 3 by score go into the run-off instead of 2, and with the top 3, you then remove cycles and find the Condorcet winner.

Alternatively you might want to come up with a cloneproof measure to find the top 3, perhaps similar to the score excess method that I posted here, based on Chris Benham's approval opposition.

@psephomancy sorry for tangent, I won't continue discussion here on this.

But quickly: you're first person to emphasize this. "Choose any" only makes sense in contrast to "choose one". I suppose indeed totally out-of-context it could be misinterpreted, and your point is valid, and it does make me less totally confident about the label. Thanks

I believe this is resolved.

@Jack-Waugh, Thanks for working through all these examples. I, too, had some questions about the GF vote, or the more general instructions regarding always voting for every alternative subjectively preferred over the focus. For a GF vote to be instrumental in impeding termination, the G vote total would have to be at least a strict majority (that is: F > half, because equal to half is not sufficient), and the F vote total would have to be the maximum vote count and exactly equal to the G vote total. Thus it is possible for a GF vote to hinder termination. However, in addition to G blocking termination, G is preferred by the voter over F, so G blocking theloop termination with F as the final winner is also indicating the possibility for G to be a later focus and possibly a better final outcome.

For testing purposes I wrote voter-agent code for voting to stop the loop. This strictly speaking is not part of SAVE, but it does indicate what I think voters might do. Each voter-agent has a property called indifference, which is a fraction between 0.0 and 1.0. At 0.0 the slightest difference matters, while at 1.0 the voter is totally indifferent to the alternatives. All voters start at 0.0 and increment their indifference value (1) every time the focus is a Condorcet winner (because if we cannot improve upon a Condorcet winner we will eventually accept it), and (2) whenever the focus subjectively improves after having first moved away (when the focus move away, such as when in a majority cycle, we also want to be more accepting, but only as we're coming back). These are the five basic reasons for an agent to vote for the focus:

Ideal - the focus is close to the voter's subjective ideal alternative. Cluster - the best and the worst of the most recent focus alternatives are really close together. Top-half - the spread between the best and the worst is moderately close (3x indifference) and the focus is in the top half of that spread. Limited-gain - the focus is close to the upper limit to any potential future gains. Peak - the focus is as good or better than a focus that was followed by a movement away from the agent's idea.
All of these conditions except Peak use the indifference value. The conditions are ordered from most difficult to satisfy to the easiest to satisfy.

The reason I bring this up is because I think voters might well vote for loop termination on the off-chance they can get a better result more quickly. Which implies a vote to terminate usually does not mean "I really want to terminate now" but instead is the kinder and gentler "it is okay to terminate now". Under those circumstances, the GF vote is perfectly reasonable, and supports the possibility of termination without foregoing the chance to influence the next focus choice.

@jack-waugh At the bottom of all my projects is a "Steal This" button that takes you to the source code. It's up on GitHub:

https://github.com/tif-calin/votevote/

Though I must warn you I haven't yet cleaned it up to make it easy to contribute to (planning on it when I get some free time).

All the logic happens inside this SuperElection class. The main motivation behind this is making a lot of use of cacheing to optimize these calculations. I.e. why calculate the borda score twice for Borda and for STAR when you can just calculate it once and reuse it.

So it's quite tangled up right now and not as documented as it should be

another way to look at the difference between EPA and AS (at least, on approval ballots) is that EPA spends ballot power such the variance in amount spent per utility gain is exactly minimized, and AS spends ballot power such that the variance in amount spent per utility is exactly maximized. Despite their similarities, in that respect they represent two ends of an extreme.