37 Comments

While I appreciate the topic and it's an interesting thesis, I don't buy it. One of the goals of a voting system should be to reduce the need to vote strategically, so that voters can just express their honest preferences. After this election, a lot of voters who most prefer Palin have to be asking themselves if they should rank Begich first next time around, to give an artificial sense that he has a "strong core of support". (This is analogous to how many voters in a closed primary consider "electability".) If voters get better outcomes by voting strategically as blocs, that's not going to help us move past the two-party system.

That all said, I do hope that this particular questionable outcome and the general shortcomings of instant runoff voting don't sour the public on all types of ranked voting, or more generally on structural reforms to our democracy that are badly needed.

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Hi Mike, thanks for your thoughts. Strategic voting will not help Sarah Palin or Nick Begich beat the Democrat Mary Peltola. The real problem that Republicans have, in terms of getting one of their own elected, is that Palin and Begich can't stand each other, and attacked each other continuously throughout their campaign. Consequently, in the recent special election to fill the congressional vacancy, only 50% of Begich voters ranked Palin as their second choice, while an astounding 30% of Begich voters ranked the Democrat as their second choice! That was the voters' choice. Another 20% didn't rank a second choice. So 50% of Begich voters did not pick Sarah Palin. The significance of these numbers was discussed in a previous article on DemocracySOS, see "Here’s Why Sarah Palin Lost to Alaska Native Democrat Mary Peltola", https://democracysos.substack.com/p/heres-why-sarah-palin-lost-to-democrat.

Alaska actually is far more of a CONSERVATIVE state than a REPUBLICAN state, but most of those conservatives – 60%, in fact – are registered as independents. Only 25% of Alaska's registered voters are registered as Republican. So the undoubtedly conservative majority of Alaska did not support Sarah Palin in this election, with a significant chunk of them voting for a Democrat who went out of her way to appeal to a broad spectrum of people, and actually got along with both Palin and Begich. No amount of strategic voting is going to overcome that. And among Republican voters, more of them supported Palin over Begich, undoubtedly because of Palin's greater name recognition, Trump endorsement, etc.

As a result of the previous election, some Palin voters may decide that she is toxic and can't win and switch their votes to Begich, helping him to pass Palin, who then will be eliminated. But who knows where Palin's voters second rankings will go? Would enough of them go to Begich for him to make up being 11 points behind Peltola in first rankings? That's hard to say, and again illustrates why strategic voting will not help because no one knows the outcome of such a strategy, even if enough voters could figure out how to pull it off. The best strategy with RCV is to always vote sincerely.

The only thing that could conceivably help one of the Republicans win is if Sarah Palin and Nich Begich can figure out a way to not attack each other and encourage those conservative-independent voters to "Vote Red", that is rank both Republicans on their ballot. There is a campaign encouraging that, but as long as the two candidates are attacking each other, that natural conservative majority will have a hard time coming together. So far, it appears that the moose can't change its antlers, so to speak.

Peltola continues to smartly woo those voters by taking careful positions on issues that won't alienate many of those independent-conservatives, and by taking the high road and not attacking her opponents.

I think RCV does help us move past the two-party system just by giving voters more options, more choices, at the ballot box. They can rank as many candidates as they want without fear of unintended consequences like spoilers, "lesser of two evils". It gets voters used to the idea of having choice, and also used to ranking their ballots. Once that mentality and culture is ingrained, it becomes much easier to transition to a ranked ballot system of proportional representation, such as proportional-ranked choice voting (also known as single transferable vote), which is the best method for truly opening up our political system and allowing multiple parties to run and win election. Thanks for your thoughts, all the best.

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The upcoming Alaska house election is a pretty ideal case for strategic voting, since it's basically a "do-over" of this election, which we have the results for. We don't really need to wonder "who knows where Palin's voters second rankings will go?" because we have results from this race: if Palin had been eliminated in the first round, despite 35% of her voters' ballots being exhausted, Begich would have won. (I suspect you know that, because that's implied by Begich being the Condorcet winner.)

You may be right that Alaska voters won't manage to be strategic. Maybe Peltola will reach across the aisle and convince six thousand voters who preferred Palin to switch their vote to Peltola. But she'd better not: if that happens (and no one else changes their vote), Peltola will lose to Begich.

While I agree that it's best on a societal level for everyone to vote sincerely under RCV, voting sincerely is demonstrably not always best for individual voters. See https://en.wikipedia.org/wiki/Instant-runoff_voting#Tactical_voting for more details.

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Hi Steven. I agree with your article in the main, but not your assessment of STAR Voting. Without good core support a candidate will lose in the instant runoff. The mix of the two types of support are different from RCV, but I prefer the mix in STAR.

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Thanks Alan. Reasonable people will not always agree on these finer points. For me, the fact that there is about a hundred years of election data from using IRV/ranked choice voting in places like Australia and Ireland, and now nearly twenty years of data in the US, is a comfort because we can have a pretty good idea about unintended consequences. It's all interesting to have these theoretical discussions, but the real world of politics often plays tricks in surprising ways. New electoral methods will always have an uphill battle, because without much of a track record, a number of key stakeholders will not be very comfortable with trying it out. I realize it's a bit of a Catch 22, but proponents of STAR, approval etc. have a very tall mountain to climb. For example, RCV was used first in several dozen universities before it got used in many public elections in recent years. At least there was some kind of a track record there. Though approval voting did get used by Dartmouth, and apparently was a pretty negative experience and it was repealed. Anyway, thanks for sharing your thoughts. All the best

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Approval is receiving high approval ratings in St Louis & Fargo. Not the largest cities, but much more significant than a college.

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Are you sure? I have heard the opposite. In St Louis, the city council was set repeal it and so AV advocates had to put a second ballot measure on the ballot to put AV in the city charter, so the council couldn't repeal it. And I have heard there are grumblings in Fargo too. Political reform is a tough business. Every election, a bunch of people lose, and suddenly they want to blame "the system." You need a thick skin in this business!

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A few city council members wanted to repeal it because they were afraid of losing to challengers.

It turns out they were not just ethically corrupt but legally as well.

https://news.stlpublicradio.org/2022-06-02/st-louis-board-president-lewis-reed-and-two-aldermen-indicted-on-federal-bribery-charges-13

Approval is well-liked among non-corrupt people in St Louis.

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Yes, I well know it is a steep hill. I think it is worth the climb for STAR. It stuck me how narrow the margin was in the final round of the Alaska race. That’s one reason I think we should emphasize breath of support a little more and core support a little less than in RCV. These days the candidate to the right of “centrist” candidates are all too often truly extreme. Those with intense support from a large minority but widespread dislike from other voters are dangerous.

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FWIW, if Alaska had used STAR, it's pretty likely Begich would have won.

Translating from rankings to ratings is obviously inexact, but Palin's 2nd ranked scores would need to average substantially higher than Begich's for him to end up in 3rd place.

Otherwise, Begich makes it into the ranked runoff and wins.

Hmm... 3-2-1 Voting, Borda, Bucklin, and Majority Judgement, are also Begich wins. And of course all Condorcet methods.

EDIT: Peltola wins under FPTP, RCV, and probably Score/Range.

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Sep 21, 2022·edited Sep 21, 2022Author

Frankie, you may have missed the point of my article. It's not a question of which electoral method would result in the outcome that you would like to see, or the outcome that you think is right. It's a matter of what values and principles do you want the electoral system to promote? In the case of RCV, it promotes two specific values: 1) a winner must have a fair amount of core support, and 2) a winner ALSO must have broad support. You need BOTH of these to win. These other methods that you are proposing, just like Condorcet, only value having a broad base of support. Do you see the difference? So rather than defending one system or the other, what are your thoughts about which values should be promoted as the best electoral method for electing single-winner officeholders? That should be the basis for these discussions, in my view.

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I get it, your article is post-hoc justification, i.e. why you think it's good that RCV picked Peltola.

Condorcet isn't necessarily the gold standard, but in this specific case a top-tier voting method (e.g. STAR) would have elected Begich.

FWIW I say this as a proponent of Approval Voting, which also would have elected Peltola.

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You are speculating about both Approval and STAR. Given that Palin and Begich have been fighting like cats and dogs, with none of these methods do you know if Begich voters would have approved of Palin or vice versa enough to overcome a 9 point (Palin) or 11 point (Begich) deficit with Peltola. You have no data that shows that. I believe the best single winner system elects candidates that have both core and broad support. Otherwise you end up in a situation like you apparently would be OK with, in which a third place/last place finisher in first choices ends up winning. That would thoroughly undermine the legitimacy and mandate of that officeholder.

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Re: paraphrased: "RCV winners must have both core and broad support"

Support or approval of various candidates by a voter cannot really be determined from a ranked ballot. In essence, a ranking method does not assess or measure support; it only measures relative preferences.

Thus the RCV method (Hare IRV for single-seat elections) does not reliably promote the two values of core and broad support, and if I'm not mistaken, I'm pretty sure Condorcet voting fails to do this as well. What Condorcet does do well is measure relative preferences. If we are going to limit ourselves to ordinal information from the voters, a Condorcet winner may be the best we can do.

If we assume we are able to measure core and broad support from the rankings of this RCV special election, and we attempt to do so in various ways, Begich is the winner (please see my Sept 26th comment). It looks to me like broad support is not actually measured by RCV, and was not measured for Begich in this election.

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Ranked Choice Voting failed in Alaska, just as we all predicted it would. It failed to elect the candidate preferred by the voters. It failed to prevent the spoiler effect. It failed to make it safe for voters to honestly rank the candidates. It failed to prevent vote-splitting.

If the voters prefer candidate A over candidate B, and your voting system chooses B, your voting system is fundamentally broken.

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Ha ha, good one, person with no name. You FAILED to make a coherent argument for your viewpoint. Instead you regurgitated a bunch of opinionated black and white statements lacking in any data or argument at all. And who exactly is the "we" that you are referring to? Not only do you have no name, but you invoke the royal "we" to buttress your wild-eyed claims? Or are you part of a group? Either way, it's pretty bad form. This is not the quality of dialogue we want to encourage on DemocracySOS, so I will give some time to put forward a real and substantive argument to back up your strongly espoused diatribe. If you don't do it, then I will delete your comment. Thank you.

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My argument is perfectly coherent, and my lack of a name is an irrelevant ad hominem.

1. "We" = critics of Hare RCV. I'm not part of any specific organization/group. I used to support RCV/FairVote, before learning more about social choice theory and realizing my error.

2. RCV advocates claim that it "ensures majority support of the winner", but Alaska's election proves this wrong. Begich was the candidate preferred by the majority, as shown in the Cast Vote Record. 52% of voters ranked Begich higher than Peltola, and 61% of voters ranked Begich higher than Palin. Hare RCV eliminated Begich first because it doesn't count all of the voters' preferences. RCV failed to elect the candidate preferred by the voters.

3. RCV advocates claim that it eliminates the spoiler effect and vote-splitting, but Alaska's election proves otherwise. Palin's presence in the race split the Republican vote and spoiled the election, causing Begich to be eliminated and Peltola to win. If Palin had strategically dropped out, or if Palin voters had strategically voted for the "lesser of two evils", the seat would have gone to a Republican. RCV failed to prevent the spoiler effect, and failed to prevent vote-splitting.

4. RCV advocates claim that RCV makes it safe to vote honestly for your favorite, because if they don't make it, your vote will transfer to your second favorite. Alaska's election proved this wrong. Palin voters were punished for voting honestly for their favorite, and many of their ballots did *not* transfer to their second favorite, because their second favorite had already been eliminated. Those preferences were discarded. RCV failed to make it safe for voters to honestly rank the candidates.

Alaska's election results show why Hare RCV is obsolete. Alaska should rule it unconstitutional and replace it with a Condorcet RCV system that actually counts all the voters' preferences (or any of a number of other systems that don't suffer from exactly the same problems as the system they're replacing).

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Broad support seems to be ignored in this case. Please consider giving each candidate some version of a score for core support and broad support. Then combine those scores for each candidate to make some version of a net score. These scores could determine the winner outright or perhaps could determine who is eliminated or who proceeds to the next round. Please see numbers below at end of this comment for three examples of various ways to create a net score.

Using only core support as a means to determine who is eliminated in a particular round appears to me to violate the criterion that both support levels should be considered. Note that Begich got 28% first ranking, which is fairly respectable in a three-candidate comparison, and Palin only did about 3% better than that. I would suggest that based on overall considerations, Palin should have been the one eliminated. To completely ignore the broad support of Begich (71.7%!) effectively exaggerates (over-emphasizes) the core support.

Method 1:

Percentage ballots with 1st or 2nd place votes (in essence, a combined measure of core support and broad support):

Begich Palin Peltola

71.7% 48.0% 50.2%

Method 2:

Begich Palin Peltola

% score for 1st place votes 28.5 31.3 40.2

% broad support: % 2nd place votes* 60.4 24.4 16.9

Combined score 88.9 55.7 57.1

( * What % of remaining ballots besides those with first place votes did a candidate receive 2nd place votes?)

Method 3:

Borda count scores:

Begich Palin Peltola

189332 149715 170750

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Dec 13, 2022·edited Dec 13, 2022Liked by Steven Hill

One thing that I haven’t seen in any of the comments or analysis yet is: if a different type of election system is implemented, wouldn’t the type/mix of candidates likely change as well?

Assuming that a different system (~especially~ once established for several cycles) would result in similar candidate behavior/ positions, let alone similar lists of candidates, seems … rather imprecise.

- - - -

(Perhaps considering that could make it hard to sustain arguments for/against any particular system.)

People who might ~never~ consider running for office in ‘first-past-the-post’ or RCV environments, for example, might be willing to run under another scheme such as ‘approval voting’. Likewise, divisive candidates who currently do well in FPTP-style elections might moderate themselves or choose a different career path altogether.

Any recommendations for existing writings comparing different electoral systems ~without~ assuming that candidate pool would remain relatively equivalent?

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I've written an in-depth response on my blog: https://voting-in-the-abstract.medium.com/rcv-and-core-support-e0d1780a9184

Some of my main points:

1. "Core support" is a concept that hasn't been properly defined. To define it such that it can be intrinsically important we must define it in terms of cardinal preferences, not just in terms of how many voters ranked a candidate first.

2. Condorcet does value both core support and broad support - it's just more flexible about it than RCV is. Under Condorcet methods, a candidate still benefits from having a lot of core support - but if they don't, they can still make up for it by having a lot of extra broad support. Under RCV, if a candidate lacks enough core support then their broad support is ignored altogether.

3. Condorcet embodies simple and intuitive values: that all voter's preferences should matter equally, and that candidates should be incentivized to care about all voters equally. The values of RCV ("A candidate who has virtually no core support, even though the candidate did have broad support, that candidate should not win. You need BOTH core and broad support to win an election under RCV.") are incompatible with values of Condorcet.

4. When I say that I prefer the values of Condorcet to the values of RCV, you don't need to "make a dash for the rest room". I prefer the values of Condorcet because I believe that incentivizing candidates to care about all voters equally will make a wide range of polarization-induced disasters, such as a civil war or democratic backsliding, less likely. If you convinced me that necessitating core support (rather than merely valuing it) leads to better consequences for society than optimizing for depolarization, that would convince me to endorse RCV values over Condorcet values.

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I am really on board with Marcus here. "Core Support" is just a "value" that FairVote concocted to justify their failure to sometimes value votes equally, which results in a minority ruling instead of majority rule, which results in a spoiled election (the spoiler is the candidate who loses in the final IRV round), and results in a bunch of voters getting punished for voting sincerely because their favorite candidate could not get elected and their second-choice vote was never counted.

FairVote also is trying to change the definition of what it means to be a "spoiler" or for an election to be "spoiled".

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Jul 31, 2023Liked by Steven Hill

What doesn’t make sense is to use two totally different and arbitrary methods for a post-hoc evaluation of the candidates, and then to likewise arbitrarily decide which of those two methods is a priori superior as an argument against the other one.

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I couldn't agree more. Each electoral system has its own values and internal logic, so judging one method by the values and internal logic of a different method makes no sense. The optimal approach is to first decide which values and principles you want incorporated into your democracy and elections -- which values and principles you think are best for your democracy -- and then it is possible to design a method that will fulfill those values and principles. This approach is a basic precept of the field of electoral system design.

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Aug 1, 2023·edited Aug 1, 2023

I believe my meaning was lost to you. Firstly, you are wrong that Condorcet methods would require multiple elections, as voters can easily indicate their ranking of any number of running candidates on a single ballot. You state, “According to the rules of this Condorcet simulation, the true winner of the congressional election in Alaska was not Democrat Mary Peltola, who had a nine point lead in first rankings over the nearest candidate and defeated leading Republican Sarah Palin in the final instant runoff. No, they claim it was the third place finisher, Nick Begich, Palin’s fellow Republican.” But your very notion of what constitutes the “third place finisher” is exactly the subject of my previous post. Therefore if you do agree with me as you say, then you surely must have some cognitive dissonance on this point, yes? Or do I misinterpret you somewhere?

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Aug 3, 2023·edited Aug 3, 2023

I personally take your speedy response to what you interpreted as an agreeing viewpoint contrasted with your silence in response to this challenge as a concession. But a more mature response would be to acknowledge your error and retract your article.

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Aug 6, 2023·edited Aug 6, 2023

You haven't explained why you prefer Hare to bottom-two runoff or why you want to forbid equal-ranking except at the bottom.

Failing to elect the Condorcet winner when there is one is manifestly minority rule in a circumstance wherein majority rule instead would have been possible.

Failure of Frohnmayer balance opens up a crack into which capital can insert its wedge and thereby continue to prevent democracy and enforce the GHG emissions associated with endless war, as a consequence of which, humanity shan't have many more generations to survive.

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Steven,

Do you believe that it is the "most democratic" practice to take the candidate that would win the most votes in an election against Peltola AND win the most votes in an election against Palin and NOT elect that candidate? That sounds contradictory to democracy. In each of those pairwise elections among the entire voting population, Begich would have been chosen by more people.

Primaries let partisan diehards narrow the field before the rest of us get to weigh in. So does RCV/IRV. In each round of an IRV election, ONLY the 1st place votes are taken into consideration. Giving special significance to that "core" of support means that divisive candidates (including ones that would actively harm large subsets of the population) could win based on the fervor of their base. If everyone's vote is equal, why are the people in that "core" given more weight than the rest of us?

RCV is no antidote to partisanship.

Dems are happy with the Alaska result, but this can cut both ways.

In proportional representation IRV/RCV works better. More than one voice represents everyone. But if we are going to have a single politician represent the views of everyone in a geographical district, they should reflect consensus and broad support, not a "core" of supporters.

If we really want diverse, representative views present in policy making, we should use Citizens Assemblies (sortition) wherever feasible.

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LOL, in the Final Word category: here is a tweet storm about results from a new study from Nicholas Stephanopoulos, Kirkland & Ellis Professor of Law at Harvard Law School, putting a cherry on the cake. Real world data bests public choice theory bunkum!

https://twitter.com/ProfNickStephan/status/1769752230012272691

@ProfNickStephan

Mar 18

"I just posted this paper, written for a symposium at Washington & Lee, on the real-world record of instant-runoff voting. A key question about any voting method is how often it elects the "Condorcet winner," favored by voters over any other candidate. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4763372

In American IRV elections, the Condorcet winner was elected in 181 of 183 races over the last couple decades. Examining foreign IRV elections in Australia and Scotland, I find that the Condorcet winner was elected in 191 of 193 races.

These are very high rates: about 99%. The gains from switching to a Condorcet-consistent method that's guaranteed to elect the Condorcet winner are therefore small. From a Condorcet efficiency perspective, IRV is already excellent.

The paper also tackles the related question of how often there's a Condorcet winner in the first place. The answer is almost always: in 183 of 185 American IRV elections and 193 of 193 foreign IRV elections.

Contrary to the fears of public choice theorists, then, voters' candidate preferences are almost never cyclical. There's almost always a single candidate whom most voters prefer to any other candidate (in a head-to-head matchup). From this standpoint, voters look pretty rational."

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This is such a paradoxical argument. If electing the Condorcet winner is important, then we should use a Condorcet system.

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It's not paradoxical if you realize that: 1) it's not important to prioritize electing the Condorcet winner over all other democratic values and goals when the Condorcet winner is already being elected 99.99999% of the time, and 2) it's not important when you realize that a distant third place finisher could actually win when using the defective Condorcent method (like Nick Begich in Alaska being initially 12 points behind the RCV winner Mary Peltola and even 2.7 points behind second place Sarah Palin), and 3) not important when you come to grips with the fact that Condorcet winners do not always meet the equally important democratic criteria of having some degree of core support, and 4) esp not important when you realize that Condorcet does not even really exist except in the mind of its zealots, since no public elections anywhere use that method, there is no voting equipment anywhere to tally such a system, and trying to count such ballots by hand in large public elections would be such a laughable farce that it would not survive even a single election.

But other than that, it sounds like a GREAT system, LOL. "Other than that, how was the play Mrs. Lincoln?"

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> it's not important to prioritize electing the Condorcet winner over all other democratic values and goals

What other values and goals would conflict with it?

> it's not important when you realize that a distant third place finisher could actually win when using the defective Condorcent method

What do you mean by "distant third place finisher"? What's "defective" about Condorcet?

> (like Nick Begich in Alaska being initially 12 points behind the RCV winner Mary Peltola and even 2.7 points behind second place Sarah Palin)

As you know, first round tallies are meaningless when there are more than two candidates. If there are many candidates from Party A vs 1 candidate from Party B, for instance, B can get the most first-round votes, even if a majority of voters would prefer any of the A candidates over B.

When the majority can only express support for one candidate at a time, and there are multiple similar candidates on the ballot, the majority's votes get split between them. Adding more and more A candidates to the ballot reduces the votes that each gets in the first round, but doesn't change the fact that voters prefer Party A over Party B.

> not important when you come to grips with the fact that Condorcet winners do not always meet the equally important democratic criteria of having some degree of core support

What does "core support" mean?

> Condorcet does not even really exist except in the mind of its zealots

"Zealots"? o_O Why so hostile?

> since no public elections anywhere use that method

It's been used in plenty of places: https://en.wikipedia.org/wiki/Schulze_method#Usage https://en.wikipedia.org/wiki/Condorcet_method#Use_of_Condorcet_voting

> there is no voting equipment anywhere to tally such a system

Aren't there many jurisdictions that use ranked ballots? Alaska and Maine use them statewide…

> and trying to count such ballots by hand in large public elections would be such a laughable farce that it would not survive even a single election

How so? Wouldn't it be faster and cheaper to count? It's precinct-summable, unlike Hare RCV, so the ballots don't need to be transported to a central location; they can be counted in each district and then report only the totals.

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"... when the Condorcet winner is already being elected 99.99999% of the time."

geez I wish you guys were capable of being truthful.

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"Condorcet advocates use the wrong standard for evaluating Ranked Choice Voting elections"

The standard is that:

When more voters mark their ballots that Candidate A is preferred to Candidate B then Candidate B is not elected.

Now tell us, why *should* Candidate B be elected when more voters prefer A?

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Let's imagine an election with five candidates, A, B, C, D and E. Candidate E is included on EVERY ballot, but in 3rd place on all those ballots. Meanwhile, Candidate A is ranked FIRST on 45% of those ballots, and is ranked in 4th place -- behind Candidate E -- on 55% of the ballots. Do you think Candidate E should be declared the winner over Candidate A?

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Assuming voters voted sincerely (and I cannot figure out how to *not* take voters at their word, even thought we do know tactical voting occurs, we just will never know which votes were not sincere), then yes, if when asked, *more* voters say that E is better than A than the number of voters that say A is their choice over E, then to elect A, those 45 voters have cast votes that are more effective than the 55 voters that had said that E is better. Without majority rule, we don't value the votes equally, we don't have One-person-one-vote.

If B, C, and D hadn't run and the voters held their same preferences with the remaining candidates (which are now just A and E), we don't want the election to turn out differently. Whether A is better for office or E is better for that office, does not depend on whether B or C or D run or not. If more voters want E in office than the number who want A in office, you are devaluing the value of the votes from E voters to below the value of the votes from A voters if you elect A.

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Here's a recent study from Harvard Law prof Nicholas Stephanopoulos using real world data: https://twitter.com/ProfNickStephan/status/1769752230012272691

@ProfNickStephan

"I just posted this paper, written for a symposium at Washington & Lee, on the real-world record of instant-runoff voting. A key question about any voting method is how often it elects the "Condorcet winner," favored by voters over any other candidate. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4763372

In American IRV elections, the Condorcet winner was elected in 181 of 183 races over the last couple decades. Examining foreign IRV elections in Australia and Scotland, I find that the Condorcet winner was elected in 191 of 193 races.

These are very high rates: about 99%. From a Condorcet efficiency perspective, IRV is already excellent....Contrary to the fears of public choice theorists, then, voters' candidate preferences are almost never cyclical. There's almost always a single candidate whom most voters prefer to any other candidate (in a head-to-head matchup). From this standpoint, voters look pretty rational."

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