I am both a supporter of the Condorcet criterion and a Hare (aka IRV)
"apologist".   Hare (properly implemented, allowing unlimited strict
ranking from the top) is a good method and so are some Condorcet methods.

I think that every voter gets a single vote that is transferable
according to the only rule that doesn't allow lower rankings to either
harm or help higher-ranked candidates is close enough to a "principle".

You are counter-posing an indecisive criterion (Condorcet) to a decisive
method (IRV/Hare).   To address your question, sometimes we should elect
B because all Condorcet methods have some Burial incentive so we can't
be confident A's pairwise victory over B is based on sincere votes.

Voters like later-no-harm for themselves and later-no-help for
rival-faction voters. Failure of later-no-harm is not nice and failure
of later-no-help is dodgy.  The Condorcet criterion is incompatible with
both LNH criteria.

I gather that in the US  there is some logistic impediment to allowing
unlimited (strict) ranking, but not to allowing unlimited equal-ranking
within a limited number of ranking positions. In that case I think the
best method is Margins Sorted Approval(implicit).

Voters rank only those candidates they approve. Initially order the
candidates according to their approval scores. Check the pairwise result
of the adjacent pair of candidates with smallest difference in their
approval scores.(If there is a tie for this then the lowest-ordered pair
among the tied pairs.) If the lower-ordered of the two  pairwise beats
the higher-ordered candidate, then those two candidates change places in
the order. Repeat this procedure to the end. The candidate at the top of
the final order is the winner.

As a voter I might be a bit annoyed that I can't rank among candidate I
don't approve and so I prefer Margins Sorted Approval (explicit) that
allows  voters to insert an explicit approval cutt-off in their rankings
(and is otherwise the same).

Chris Benham

On 22/06/2025 8:13 am, robert bristow-johnson via Election-Methods wrote:

Okay, since you're in with both IRV and Condorcet, what I want to learn from you is when it's appropriate that the IRV winner is elected, instead of the Condorcet winner when such exists.  And why?  Why is it ever a good thing to elect the IRV winner when such differs from the Condorcet winner?

The "only rule" isn't defined.  You're describing a property (or two) that this rule has (IRV has LNH) but that's not the rule.  It's a property of the rule.  MiniMax Opposition (that isn't really Condorcet consistent) also has LNH.

Some of us wonder why Majority rule (which is simply what the Condorcet criterion is) is less important than Later-No-Harm?  Majority rule is essential to valuing every voter's vote equally.  If our votes are gonna be counted equally, then I want my vote to count more than yours.

How many voters are harmed when the Condorcet winner is elected instead of Hare?  In Burlington, it was the other way around.  I need to look at Alaska August 2022.  But the number of people harmed because the IRV winner was elected is always more than the number of voters harmed if the Condorcet winner is elected, when the Condorcet winner exists and not the IRV winner.

I agree that Condorcet without a "completion method" (in case of a cycle) is not completely defined.  What Condorcet method to use is a debatable issue, and I have soft opinions about which Condorcet method.  But I still am unconvinced that any public good is served to elected the IRV winner instead of the Condorcet winner in the 99.6% of the RCV elections that occur in the U.S. (or anywhere).  We know when we don't elect the CW that IIA and favorite betrayal are violated and people are harmed for voting sincerely.  If the CW exists, comparing the CW to any other candidate, more people are harmed if the other candidate is elected than the CW.  The fewer people supporting the other candidate had votes that were more effective than the votes from the greater number of people supporting the CW.

I understand burial and how it can be a strategy in a Condorcet election when polls show that the IRV winner is different than the CW.  The IRV winner tells his/her supporters to bury the CW even if the CW is preferred over a third candidate that both groups hate.  But for it to work, they must throw the election into a cycle.  So that the mutually-hated candidate beats the former CW.  It's a dangerous game, they could get their mutually-loathed candidate elected doing that.

I know that Schulze and Ranked-Pairs were supposed to be more resistant to strategic voting like that.  But the differences exist only in the 0.4% of the time a cycle occurs.  We can adopt a second method to explicitly elect a candidate based on rules that people will generally understand and consider reasonable.

Condorcet-Plurality (which is also what BTR-IRV will result in for 3 significant candidates) may be more gameable than something like Condorcet-Borda or Condorcet-IRV.  I worry more about how the actual legislative language will look.  And we found that Condorcet-TTR (top-two runoff) has concise and understandable language and elects the IRV winner in the case of three significant candidates and a cycle.

I had learned in the past couple years that in selecting a Condorcet-consistent method for legislation, that it's best that the law simply says what it means and means what it says.  So that led us to a Two-method system.  So it's straight-ahead Condorcet, like a Round-robin tournament, and if there is no unbeaten champion, the top-two 1st-choice vote getters run against each other.

Voters also like majority rule and knowing that their vote counts equally to every other voter.  Voters like knowing that if their first-choice candidate cannot get elected, that their second-choice vote will be counted.

I know that.  "Later-No-Harm" is sorta a play on words.  Strictly defined, it means that your choice of 2nd-ranked candidate will never harm the chances of your 1st-ranked candidate to be elected.

But voters also worry about their 1st-choice harming the chances of their 2nd-choice candidate in the case that their favorite is defeated.  It's a different sort of "later no harm".  It's swapping the role of the two candidates.  Voters don't want either their 1st or 2nd ranked candidates to harm each other except in the contest between the two (then they want their 1st choice to harm their 2nd choice).

Well, different states operate elections independently (it's one reason the stupid-ass electoral college came into being) but with optical scan and programmable election software, there is no logistic difference between any RCV method.  Condorcet is no more difficult than Hare for Dominion Voting Systems or some vendor like that.

I think "unranked" should mean nothing other than "tied for last place".  A lower preference than any ranked candidate.  It shouldn't mean anything else.

The ranked ballot should only mean this: If a voter ranks A higher than B, then in the contest between A and B, this voter votes for A.  (And their vote counts as one vote, independent of the number of ranking levels separating A and B.)  The ranked ballot should not mean anything more than that.

--

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

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Robert,

In the case where all the voters give their sincere full rankings, it is
possible that the Hare winner will have much higher Social Utility while
the CW has zero or next-to-zero real support:

49  A|>>C>B>D
48  B|>>C>A>D
03  D>>C>A|>>B

(The | indicates approval cutoff and >> means extra strong preference,
but neither Hare or the Condorcet criterion has any use for that
information).

C>D  97-3,   C>B  52-48,   C>A 51-49  so C is the CW. Hare eliminates C
and then D and then B and elects A.

A is the top choice of nearly half the voters and is approved by more
than half the voters.   C is the top choice of none of the voters and is
approved by 3% of them.

Now take the case where there are two large factions of voters and a
third much smaller one. Many of the supporters of the large factions
mistakenly assume that it is safe to bury the rival large faction's
candidate under the small faction's candidate:

11  A
35  A>C  (sincere is A or A>B)
44  B>C  (sincere is B or B>A)
05  C>A
05  C>B

C>A  54-46,  C>B 45-44  so C is the voted CW, but with sincere votes
A>C  46-10 or 90-10 and A>B  51-49 so A is the sincere CW.   Hare
eliminates C  and then B and elects A.

So Hare can do a better job of electing the sincere CW than a method
that meets the Condorcet criterion.

Yes it is.  The "rule" is the Hare algorithm.

No Condorcet method meets Favorite Betrayal or IIA.  It is true that
good Condorcet methods are somewhat less vulnerable to Compromise than
Hare, but on the other hand all Condorcet methods (some more than
others) are vulnerable to Burial and Hare isn't.

MinMax (Pairwise Opposition) is nether a Condorcet method or any version
of the single transferable vote and doesn't meet Later-no-Help. So why
mention it?

https://votingmethods.net/em2005.html

Other algorithms (or "rules") have been suggested that involve
eliminating candidates one-at-a-time until one candidate is (among
remaining candidates) is top-voted among remaining candidates on more
than half the ballots, but none of them meet both Later-no-Help and
Later-no-Harm.

In that case if you don't like Margins Sorted Approval (explicit) for
some reason I don't understand what your problem is with the "Benham"
method, which is like Hare except that before any and each subsequent
elimination it checks for a pairwise-beats-all candidate among remaining
candidates (and elects the first such candidate).  It resists Burial
better than Schulze or Ranked Pairs and is generally much better than
those awful other methods you mentioned.

Chris Benham

On 24/06/2025 1:24 pm, robert bristow-johnson via Election-Methods wrote:

Okay, Chris, I'm gonna do one issue at a time, and I'll start top-down.  And I will actually refuse to go down rabbit holes.

So here, it appears that you're changing the semantics of the game, and I won't go there.

The whole point of choosing the ranked ballot over the scored ballot is that there is no ">>".  Just ">" and "=".  Ranked ballot voting does not provide for ">>".  Nor does it provide for "|" either, although I'll grant that a natural place to put "|" is at the unranked level.  But it's not the point of the ranked ballot.

The only information we get from the ranked ballot and the only information we want from the ranked ballot is A>B>C.  All this means is that if the choice was between A and B, the vote is for A.  If between A and C, the vote is for A.  But if the choice was between B and C, the vote would be for B.  In any case, the vote counts as exactly one vote.  Degree of preference does not matter.  And it should not, because people will just be incentivized to exaggerate their degree of preference to make their vote count more.  Borda conceded as much when he answered a point from Condorcet: "My system is only intended for honest men."  The system, whatever it is, should be resistant to attempts by dishonest voters to game it.  It can't be done, perfectly.  But we shouldn't set up a utilitarian ranking or rating system that will incentivize either strategic or tactical voting (and I differentiate a little between the two, but they're both bad).

So, I am not going down the utilitarian rabbit hole in this.  I'm just for the strict equality of our votes to the degree possible.  It must not matter how enthusiastic or passionate our support is for the candidate we vote for.  Our votes should be counted equally anyway.

Okay, I'll dabble in one more thing, and then I'm leaving this alone.

I know that.  It wasn't my point.  I meant only what I said.  Just take the sentence for precisely what was written.

Yes, the incentive to compromise comes from spoiled elections.  There were 4 spoiled RCV election in the United States that we know of because no CW was elected.  Two of which could have been unspoiled (Burlington 2009 and Alaska 2022).  The other two are good examples of Impossibility a.la. Arrow.  I have always been clear that changing from Hare to Condorcet only fixes the first two.  And any Condorcet will fix it, not just the "good Condorcet" methods.

But as RCV is adopted more and more, this failure will occur more often than once per decade, it will happen every year (if RCV is widespread and IRV is the method).  Then there will be trouble.  We should make course corrections now and not wait for that day.

That's right.  But the vulnerability to burial requires the Condorcet election to either be in a cycle or to push it into a cycle.  If we're not in a cycle, nor even close to a cycle, burial will do nothing to help the side doing it.  Burial cannot make a non-CW into a CW.  All burial can do is toss it into a cycle and hope that your non-CW is elected with how the Condorcet-consistent method elects in a cycle.

Because you said something about "the only rule that doesn't allow lower rankings to either harm or help higher-ranked candidates".  Hare isn't the only rule that does LNH.  I don't like MinMax (Pairwise Opposition) because it's not Condorcet.  I'm just saying that your "simple principle" is not yet well-defined.

But the Condorcet criterion is well-defined.  Not complete, but well-defined.  And it's simple.  Very simple.  And hard to argue with.  At least you haven't brought up the contrived bullshit about "core support" that we read from the likes of Deb Otis and other IRV apologists.

bestest,

robert

--

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

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Going by the returns from last night, it looks like there was probably a
Center Squeeze in NYC, although it might not be visible on the ballots
since presumably lots of people probably only ranked either Cuomo or
Mamdani out of laziness.

On Tue, Jun 24, 2025 at 8:24 PM robert bristow-johnson via Election-Methods
election-methods@lists.electorama.com wrote:

Plausible but I’m not convinced. I think Mamdani genuinely won over a lot
of center-left voters — at least speaking anecdotally from conversations
I’ve had with folks in that sphere in NYC — on the merits of his platform
rather than strategic considerations.

It seems to me that both:

(1) More voters preferred Mamdani to Lander head-to-head.

(2) More voters opposed Mamdani than Lander.

On Wed, Jun 25, 2025 at 3:52 PM Closed Limelike Curves via Election-Methods
election-methods@lists.electorama.com wrote: