New method (I think?): Hare-squared

[rob]

Never heard if this one has been proposed. I propose it here less as a serious proposal that people should adopt for real elections, and more as a hypothetical whereby we can better understand what the actual effect of IRV-Hare is, by essentially applying its improvement upon choose-one twice.

First, some background: The biggest problem with Hare (and the reason it can occasionally not select the Condorcet winner) is that its logic for eliminating candidates is based on "choose-one logic". And choose-one logic is crude: it is notoriously thrown off by irrelevant candidates because it looks only at how many ballots put that candidate above all other candidates. By repeatedly eliminating the (crudely determined) "worst" candidate rather than just going straight to the (crudely-determined) best candidate, Hare minimizes the bad effect of this. But some badness still can leak through.

Please note that when I say Hare uses choose-one logic in each round, it does so negatively. That is, it uses it to find the worst candidate, so that candidate can be eliminated. So rather than selecting the candidate with the most first place votes, it selects the one with the least first place votes.

So before getting to Hare-squared, let me define IRV-Hare in very few words. IRV-Hare can be described as selecting the candidate remaining after sequentially eliminating the candidate voted first place, least. It does this by running a series of "rounds", where the number of candidates minus one is the number of rounds. [1]

Hare-squared selects the candidate remaining after sequentially eliminating the candidate remaining after sequentially eliminating the candidate voted first place, most. It does this by running a series of rounds inside a series of rounds. So the total number of rounds is the number of candidates minus one, squared.

So Hare-squared can be described as having an inner loop and an outer loop. In the outer loop, it does the same thing Hare does: eliminate the worst candidate each time through the loop. But to find that worst candidate, instead of using "dumb" choose-one logic, it uses "smarter" Hare logic.

Here's some JS pseudocode.

var numCandidates; // number representing how many candidates are running
var candidates = []; // all the candidates in an array

// choose one

candidates = sortByFirstPlaceVotes(candidates);
var winner = candidates[0];


// IRV-Hare

for(var i=0; i<numCandidates-1; i++) {
    var sortedCandidates = sortByFirstPlaceVotes(candidates)
    var loser = sortedCandidates[numCandidates-1];
    removeCandidateFromList(candidates, loser);
}
var winner = candidates[0]

// Hare-squared

for(var i=0; i<numCandidates-1; i++) {
    var outerSortedCandidates = = sortByFirstPlaceVotes(candidates)
    for(var j=0; j<numCandidates-1; j++) {
       var innerSortedCandidates = sortByFirstPlaceVotes(outerSortedCandidates )
       var innerWinner = innerSortedCandidates[0];
       removeCandidateFromList(outerSortedCandidates, innerWinner);
    }
    var loser = outerSortedCandidates[numCandidates-1];
    removeCandidateFromList(candidates, loser);
}
var winner = candidates[0]

1. technically that's the maximum number of rounds....since it is generally defined as stopping when a candidate reaches 50%. For this discussion, we can always just assume we run it out to the end, since the result is the same and it makes the code and discussion simpler.

[Jack Waugh]

Doesn't this just produce the same result? Yes, I think so.

[rob]

@jack-waugh Nope. Just as Hare doesn't always produce the same result as choose-one, Hare-squared doesn't always produce the same result as Hare. You could say "Hare-squared is to Hare as Hare is to choose-one."

Not sure how to explain further. I'll make another try.

Hare improves on choose-one by reducing the effect of irrelevant alternatives in choosing the winner.

Hare-squared improves on Hare by reducing the effect of irrelevant alternatives in choosing which candidate to eliminate each round.

Ok, if that explanation doesn't work, here is one more attempt (slightly wordier) at explaining:

Hare "smartens" the determination of the winner by doing it in rounds, starting from the least significant (the worst candidate) and gradually homing in on the most significant (the best candidate, i.e. the winner).

Hare squared smartens the the determination of who is eliminated in each round, by doing that in rounds, starting with the least significant (the best candidate) and homing in on the most significant (the worst candidate, i.e. the one to be eliminated).

And of course you could take it further by going with Hare-cubed, etc. I have strong suspicion each time you deepen the looping, it further reduces the chance of it missing the Condorcet winner. And for elections where there isn't a Condorcet winner, I have a suspicion this approach does a very good job of making it hard to strategically manipulate..... getting better and better each time you deepen the looping.

[Jack Waugh]

OK, what I didn't catch onto at first was that in the inner rounds deciding which candidacy to eliminate, ballots are being shortened when someone is eliminated from being eliminated (therefore, promoted to the next major round).

Let's see whether I can get an intuition for this and can restate the algorithm correctly.

Consider for example the first major round. It wants to promote all but one candidate.

The first inner round is going to look at the top choices on all the ballots and whoever gets the most of those is promoted.

The second inner round is interested in who remains as the top choices when the first promoted candidate is effectively not seen on the ballots. Whoever has the most count of top choices is then promoted, if she is not the last candidate unpromoted.

When one candidate remains, we leave that candidate behind and go on to the next major round.

This system does not make the voters equal in power.

I like some of your other ideas better.

[rob]

@jack-waugh said in New method (I think?): Hare-squared:

This system does not make the voters equal in power.

I don't know what you consider "making voters equal in power." I have actually pretty clearly defined what is a baseline, idealized system that comes as close as anything could at doing just that, so we have something to compare single winner elections against. I've never heard you discuss that, which makes me feel like I'm talking market economics with someone who has never bothered learning what perfect competition is. (which is a similarly hypothetical baseline)

This is a thought experiment and it has a purpose, but I think you are thinking I am proposing it as a practical method, which as I said in my second sentence, I'm not. (I'm not necessarily saying it couldn't be practical, but that is not why I am exploring it) But I think it is an important one for providing insight into IRV, including @sass and @rb-j 's arguments against IRV (which I think are WAY too strong, and are blocking progress) as well as FairVote's arguments against Condorcet (which is very flawed, but I have found challenging to explain why in a way they can't wriggle away from).

Aside from the practical issues (i.e. it is more computationally intensive than IRV, by the same ratio as IRV is more computationally intensive than choose-one), I do think this would produce good results. I have been playing around with it in code and haven't fully tested it yet. Given IRV's real world importance in this field, I can't understand why anyone would not see the value in exploring it, but then again I've never quite understood your perspective on a lot of things.

[Jack Waugh]

@rob I was wrong when I said the system would always produce the same answer as RCV IRV Hare does. My error came in my failing to take into account the fact that the inner application of the Hare method is not necessarily sorting the ballots into the same order as we would have with only the outer one, because in the process of determining the sort, we eliminate candidates from consideration and ballots transfer to the next candidate down on the ballot. Specifically for the Burlington, Vermont [0] ballots, I have not run them and I don't know.

I don't know what you consider "making voters equal in power." I have actually pretty clearly defined what is a baseline, idealized system that comes as close as anything could at doing just that, so we have something to compare single winner elections against. I've never heard you discuss that, which makes me feel like I'm talking market economics with someone who has never bothered learning what perfect competition is. (which is a similarly hypothetical baseline)

I will put that in its own topic.

This is a thought experiment and it has a purpose, but I think you are thinking I am proposing it as a practical method, which as I said in my second sentence, I'm not.

This is not the first system you have described for a thought experiment and about which you said you were not seriously proposing it for use in politics. You said that for the scheme that would take into account both the top and bottom candidate when deciding whom to eliminate from further consideration. But I think that reform could have potential, when combined with a couple of others. I will add under that topic.

This is a thought experiment and it has a purpose, . . . I think it is an important one for providing insight into IRV, including @sass and @rb-j 's arguments against IRV (which I think are WAY too strong, and are blocking progress) . . .

I look forward to hearing their response. If they ask you how this thought experiment is to shed light on the characteristics of RCV IRV Hare, I look forward to seeing how you respond to that question from them, if they do pose it.

Given IRV's real world importance in this field, I can't understand why anyone would not see the value in exploring it . . .

Yes, by all means, anything that might shed light.

---

[0] Burlington, Vermont, not to be confused with Burlington, North Carolina (which, so far as I know, has never used RCV IRV Hare).

[rb-j]

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

I don't know what you consider "making voters equal in power."

As far as I understand, this is expressed with the maxim "One person, one vote". And that cannot be satisfied outside of Majority Rule: If a simple majority of voters agree that Candidate A is a better choice for office than Candidate B, then Candidate B is not elected.

But I think it is an important one for providing insight into IRV, including @sass and @rb-j 's arguments against IRV (which I think are WAY too strong, and are blocking progress)

When a reform fails to do precisely what it purports to do, the thing to do is reform the reform. Reforming reform does not block progress, it diverts the direction of the progress from a direction that is not entirely progressive to another that is.

Remember RCV proponents promote RCV saying that RCV:

1. "guarantees the majority-supported candidate is elected."
2. "eliminates the spoiler effect."
3. removes the burden of tactical voting from voters, freeing them to "Vote their hopes not their fears" or "Vote for who they really like rather than the lesser of evils".

When a reform utterly fails to perform at the very core of what the reform it purports to be, ignoring or denying that failure is not conducive to the progress it purports to be.

The other important issue that is becoming even more important as statewide RCV begins to take root is the component of process transparency that we call "Precinct Summability".

For a literal "Executive Summary", read this letter I sent last spring to the governor of Vermont. (I was not successful, BTW.)

as well as FairVote's arguments against Condorcet (which is very flawed, but I have found challenging to explain why in a way they can't wriggle away from).

I would be interested in hearing what they say to you to "wriggle away". I've had multiple email conversations with Rob Richie about this and all he does and can do is deny that the facts are a problem (with nothing to support the reasoning for his denial) and dismisses the necessity to adjust course. It's simple denial and relying on their established position an momentum. He cannot wriggle away from the facts. He can only ignore and deny or poo-poo the facts.

[A Former User]

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

When a reform utterly fails to perform at the very core of what the reform it purports to be

IRV, even in Burlington

• allowed there to be a race with 3 competitive candidates (any one of whom easily could have won with small changes in public opinion). In FPTP this is almost unheard of
• Provided a ballot format which allowed voters to express richer preference than a single name
• Selected a better winner than choosing the candidate with the most first-place votes would have

Now, can we please stop bringing up Burlington.

[rb-j]

@andy-dienes said in New method (I think?): Hare-squared:

IRV, even in Burlington

allowed there to be a race with 3 competitive candidates (any one of whom easily could have won with small changes in public opinion). In FPTP this is almost unheard of

That's bullshit. You can have a race with 3 or more competitive candidates with FPTP. It happens all of the time. This issue is preventing the election of a candidate without majority support of the electorate. FPTP often fails to do that. And IRV failed to do that "even in Burlington".

Provided a ballot format which allowed voters to express richer preference than a single name

Fine, no one is disputing the value of the ranked ballot (well, opponents of RCV do, like these guys). But what good is using a ranked ballot if you ignore the content of the ranked ballot and elect a candidate that does not have majority support.?

Selected a better winner than choosing the candidate with the most first-place votes would have

Big fucking deal! FPTP can make a similar claim: *Selects a better candidate than choosing the candidate selected by sortition or selected by military support."

IRV can and does ignore the express preferences that voters put on their ranked ballots and can and does elect the non-majoritarian candidate as a result. This means that the fewer voters that saw their candidate elected had cast votes that had more juice, more power, than the larger number of voters that had cast votes for the majority candidate.

Now, can we please stop bringing up Burlington.

Denial ain't just a river in Egypt.

And you cannot get past the problem of lack of process transparency because Hare IRV is not precinct summable. And also, because Hare is not precinct summable, you cannot get past the problem of election night results for statewide or large city betraying the label Instant Runoff Voting.

And do you want the Write-In option to be meaningful? What if, for a statewide race (like what happened with Lisa Murkowsky in 2010 FPTP), that Combined Write-In actually wins an RCV election? How are you gonna deal with that?

With Hare it's a terrible fucking mess. With Condorcet, all you need to do is split each precinct into two sub-precincts, separate the Murkowsky write-ins from the others, tabulate both sets of ballots separately with the tabulator machines (clearing the counters in between) and then ADD the results for each pairing, except for the Write-In category). You can do this decentralized on the same evening of the election.

[A Former User]

@rb-j

You can have a race with 3 or more competitive candidates with FPTP. It happens all of the time

No, it doesn't. It happens sometimes, but given how many more FPTP elections than IRV that's not saying much.

But what good is using a ranked ballot if you ignore the content of the ranked ballot and elect a candidate that does not have majority support.?

Placebo effect is real and important. Even just feeling like you get to express your true opinion is important, even if the rest of the rankings were entirely thrown away. I would also prefer the ability to rank candidates on the ballot with choose-one too, even if it just elects the one with the most first-place votes.

Big fucking deal! FPTP can make a similar claim: *Selects a better candidate than choosing the candidate selected by sortition or selected by military support."

yeah, and if I lived in a country where the winner was chosen by military bureaucracy I would prefer FPTP a hell of a lot more.

Denial ain't just a river in Egypt.

Fatigue ain't just a mountain in Canada. And I'm incredibly fatigued of the same tired talking points about one specific, and ultimately pretty inconsequential, election.

[rb-j]

@andy-dienes said in New method (I think?): Hare-squared:

You can have a race with 3 or more competitive candidates with FPTP. It happens all of the time

No, it doesn't. It happens sometimes, but given how many more FPTP elections than IRV that's not saying much.

Sure it does. Nothing about FPTP that stops anyone from having an election with more than 2 candidates. The problem is electing the correct candidate. FPTP sometimes fails to do that. And so does Hare IRV.

But what good is using a ranked ballot if you ignore the content of the ranked ballot and elect a candidate that does not have majority support.?

Placebo effect is real and important.

So you're promoting dispensing placebos instead of medicine that actually has physiological effect?

Even just feeling like you get to express your true opinion is important, even if the rest of the rankings were entirely thrown away.

And when the election results are reported and you discover that you were robbed from having your candidate (or your second-choice candidate) elected because the method ignored the second-choice votes of 1/6th of the electorate, despite the promise that it does not, I don't think you'll be "just feeling like you get to express your true [vote]".

I would also prefer the ability to rank candidates on the ballot with choose-one too, even if it just elects the one with the most first-place votes.

This is so stupid and irresponsible. And disingenuous.

Big fucking deal! FPTP can make a similar claim: *Selects a better candidate than choosing the candidate selected by sortition or selected by military support."

yeah, and if I lived in a country where the winner was chosen by military bureaucracy I would prefer FPTP a hell of a lot more.

But FPTP ain't good enough, is it, Andy?

[A Former User]

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

This is so stupid and irresponsible. And disingenuous.
But FPTP ain't good enough, is it, Andy?

I feel like you are getting pretty abrasive and personal, so I am going to step away from this discussion.

[rob]

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

As far as I understand, this is expressed with the maxim "One person, one vote".

Yeah that is a very vague saying. I get the concept, but many people interpret it very literally, such as saying that ranking or approving doesn't qualify simply because they are doing more than checking a single box.

I've used the example of people voting for a number (say an office temperature or the amount of monthly dues) and choosing the median, which is as close to everyone having "equal voting power" as anything I can imagine.

I tend to think Condorcet systems most closely approach that in elections with human candidates and a single winner.

And that cannot be satisfied outside of Majority Rule: If a simple majority of voters agree that Candidate A is a better choice for office than Candidate B, then Candidate B is not elected.

I've never been big on the use of the word "majority" when there are more than two candidates. Especially if combined with the word "support", which seems so artificially binary. If I vote for someone over another person, that is no indication that I "like" them in any everyday sense of the word, only that I prefer them over someone else.

I agree that Condorcet is best (it seems to meet my idea of "game theoretically stable," which is important to me but not necessarily a priority for others), but I just don't like using the concept of "majority." And again, I refer back to the "voting for a number" thing.... my vote might pull the vote from 69.2 degrees to 69.3 degrees, when I preferred 72 degrees. That can be perfectly fair and equitable, but the word "majority" doesn't in any way apply.

[rob]

@rb-j Please dial back the aggression, it is unhelpful and against the spirit of this forum. I agree with many of your goals, but attacking people isn't the best approach. We are trying to make this a welcoming forum, such as to newcomers.

Thanks.

[rob]

@jack-waugh said in New method (I think?): Hare-squared:

I look forward to hearing their response. If they ask you how this thought experiment is to shed light on the characteristics of RCV IRV Hare, I look forward to seeing how you respond to that question from them, if they do pose it.

Cool. I haven't necessarily fully formulated it.

I will say, very briefly, this:

The general effect Hare-IRV has on an election, when compared to choose-one (*), can be described as the "Hare effect." As Hare-squared (and Hare-cubed, etc) show, this effect can be applied more than once. Doing so helps clarify what the effect actually is.

Each time it is applied, it moves the method along a spectrum toward some imagined "ideal" method that is immune to strategy, gives each voter equal pull, etc. (Hare-IRV might move it 80% toward that goal. Hare-squared might be more like 95%, Hare-cubed 99.5%, etc. These are just estimates, and I'm not sure it will ever be directly measurable)

If it can be shown that applying Hare multiple times will make it that much less likely to have Burlington-style "misses", or can otherwise remove instability, reduce strategic incentives, etc, it can be strongly argued that "the Hare effect" is a good thing, even if normal Hare-IRV simply doesn't apply the effect as much as we'd like. The problem is that the choose-one logic that Hare uses in determining who to eliminate is crude and encourages strategic voting. It pollutes the method, so to speak. Each time the Hare effect is applied, that pollution is diluted.

So to the IRV bashers, my message is: IRV is good (compared to choose-one), it just isn't as good as it could be. To the IRV but not Condorcet people, my message is, stop being p*ssies and just own what you are doing rather than shying away from taking it that one extra step (i.e. Condorcet).

And of course, other methods (bottom two runoff being a good example), might be a far more efficient way of doing this. It may not be as good as Hare-to-the-20th-power, but it is very likely good enough that any "choose-one pollution" is so diluted as to be insignificant.

That is a good part of the argument. I started to build out the method (starting with regular IRV, but then reusing the same code to allow applying the effect as many times as I want), and will continue as I have time. I'll wait until I have a better presentation to, for instance, take this to EndFPTP where there is a larger audience.

* if it helps, imagine a method that ranks the candidates, but simply elects the candidate that gets the most first choice votes. Since all methods we are comparing use identical ballots, it is an apples to apples comparison.

[A Former User]

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

Each time it is applied, it moves the method along a spectrum toward some imagined "ideal" method that is immune to strategy

I know I have linked it before, but I really think you would enjoy reading about Stable Voting. It kind of does exactly this and is a recursive method asking "if this candidate were not in the election who would have won?" and the result is a method which makes a very strong case for being the "best" (on theoretical grounds) deterministic Condorcet method.

Also, I just find the paper exceptionally well-written; it manages to go into a lot of detail while maintaining a conversational style. This paper by the same authors is also excellent and is on my favorites list.

[rb-j]

Yes. You are exactly correct, @rob.

Besides RCV, I am involved in a sorta complex multi-directional "discussion" in Vermont about the nation's most successful third party, about the effect of party crossover in primaries, and of the value of the "open primary" (not to be confused with what California, Washington, or Alaska are doing, where there is no party primary).

Someone is systemically taking undeserved advantage of someone else. And there is a lotta disingenuity tossed around. It's:

1. the Center Squeeze of Hare RCV and who, in Vermont, benefits and who loses.

2. "clone" party crashing another party's primary.

3. single-member vs. two-member vs. mixed different-sized districts in a legislative body (how well constituents are served by each) and the political effect of switching one to another - who benefits and who loses (and remember, elections are a zero-sum game),

And I'm drawing maps for ward redistricting in Burlington and we're getting in crunch time. Big decisions being made soon about what map the voters will get to see on the ballot next town-meeting day. And some, not-entirely-transparent reasons for preventing voters from seeing more than one plan.

So I'm kinda grumpy. I'm sorry.

[rob]

@andy-dienes Thanks, I will read it when I get time. (I have been spending way too much time on this forum recently!)

I'm all into "game theoretical stability", and finding ways to visualize what a "perfect" method would be, even if it is impractical (and unnecessary) to have such methods in the real world. But I find them valuable as an exercise, and hopefully in terms of minimizing some of the ugly back and forth that can happen when discussing things like IRV.

[rob]

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

So I'm kinda grumpy. I'm sorry.

We all get grumpy sometimes.

[rb-j]

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

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

As far as I understand, this is expressed with the maxim "One person, one vote".

Yeah that is a very vague saying. I get the concept, but many people interpret it very literally, such as saying that ranking or approving doesn't qualify simply because they are doing more than checking a single box.

I understand that, and it's essentially where we RCV advocates disagree with detractors who insist on FPTP.

What they don't want to understand is the notion of the Single-Transferable Vote. It's one vote, but it gets shifted around in such a manner that best benefits the political interest of the enfranchised person who is voting. They get only one vote.

The difference between the Hare advocates and the Condorcet folks are that the former says that some of us cannot transfer our vote from our higher-ranked candidate, that was just eliminated, to the contingency candidate of our choosing as expressed on our ballots. The Condorcet advocates say we can. When you promote your product saying *"You can vote for the candidate you really want and need not choose between the lesser of evils. If your favorite candidate cannot win election, then your vote counts for your second choice." Howard Dean (whom I was fortunate enough to introduce to a big crowd in NH in 2004) made that claim ignorant of the fact that it's demonstrated false in the experience of his very own home town.

When you make that claim (which is Property 4 in this), you should mean it.

In order to allow voters to vote their hopes instead of their fears, the election should not punish (or disincentivize) voters from voting their hopes. It does that by actually preventing the spoiler effect (an oft advertized feature of RCV). And it does that by making sure that the majority candidate is elected and not blocked from election because of the spoiler.

I've used the example of people voting for a number (say an office temperature or the amount of monthly dues) and choosing the median, which is as close to everyone having "equal voting power" as anything I can imagine.

The median helps block the effect of exaggeration of one's preference in order to unfairly increase the effect of one's expression of their preference.

But so does One-person-one-vote. Unlike Score Voting or Borda RCV, it doesn't matter if I prefer A enthusiastically and you prefer B only tepidly, your vote for B should count just as much as my vote for A.

The median thing is a mathematical tool to prevent outliers from changing the measure of how the middle of the spectrum affects a composite measured property (like median income vs. mean) or in social choice.

I tend to think Condorcet systems most closely approach that in elections with human candidates and a single winner.

And that cannot be satisfied outside of Majority Rule: If a simple majority of voters agree that Candidate A is a better choice for office than Candidate B, then Candidate B is not elected.

I've never been big on the use of the word "majority" when there are more than two candidates. Especially if combined with the word "support", which seems so artificially binary.

Between two candidates there is an unambiguous notion of majority support if we agree that every voter's expression of support (that's what a vote is) is counted equally.

The fact that there always exists a simple majority between two candidates (unless they tie) is misconstrued by naive (or disingenuous) RCV advocates to claim that RCV is "guaranteed to elect the majority-supported candidate" because it boils the election down to two candidates in the final round, in which there is always a simple majority.

Of course that Hare final-round pair of candidates is not the only way to pair two candidates and examine which one is supported more than the other. Everyone, other than the Condorcet loser, is a "majority candidate".

If I vote for someone over another person, that is no indication that I "like" them in any everyday sense of the word, only that I prefer them over someone else.

That's correct. And that preference of yours counts just as much as my preference for the "someone else". Doesn't matter how much more I prefer my candidate vs. how much you prefer yours. Our votes should count equally.

I agree that Condorcet is best (it seems to meet my idea of "game theoretically stable," which is important to me but not necessarily a priority for others), but I just don't like using the concept of "majority."

Simple majority and Absolute majority have dictionary definitions that are reasonably concise.

And again, I refer back to the "voting for a number" thing.... my vote might pull the vote from 69.2 degrees to 69.3 degrees, when I preferred 72 degrees.

And a good and fair social choice system should not incentize you from expressing your preference in any manner other than sincere. Express your sincere preference and rely on the method to respect your preference, as a person holding equal rights and equal franchise, equally as much as any other person's preference.

That can be perfectly fair and equitable, but the word "majority" doesn't in any way apply.

That's right. And if we were voting for an alternative that is an ordered quantity, Score Voting using median score rather than plurality score, seems very fair and equitable to me. Maybe use this for a public vote on the city's budget cap or tax-base percentile. But not people or maps or discrete alternative plans that are not an ordered quantity. Then the only fair thing is valuing each voter's vote equally.