[EM] Better Choices for Democracy

Tue Jun 24 18:34:49 PDT 2025

Robert,

> Why is it *ever* a good thing to elect the IRV winner when such differs from the Condorcet winner?

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.

> The "only rule" isn't defined.
Yes it is.  The "rule" is the Hare algorithm.

> We *know* when we don't elect the CW that IIA and favorite betrayal are violated and people are harmed for voting sincerely.

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.

>   MiniMax Opposition (that isn't really Condorcet consistent) also has LNH.

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.

> 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.

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:
>
>> On 06/23/2025 6:55 AM EDT Chris Benham <cbenhamau at yahoo.com.au> wrote:
>>
>>   
>> 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.
> 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?
>
>>> So IRV is a procedure without a principle.  It just says "Count the highest-ranked votes for candidates that have not yet been defeated, then defeat the candidate with the least votes.  Rinse and repeat."  That's simple, but not a principle.
>> 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".
> 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.
>
>>> Condorcet says "When more voters rank A over B than than to the contrary, B is not elected."  That's also simple.  The procedure is derived from that principle.  The thing that IRV apologists have to justify is why *should* B be elected?  Why is it a good thing that B is elected?  What principle or what public good is it?
>> You are counter-posing an indecisive criterion (Condorcet) to a decisive
>> method (IRV/Hare).
> 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.
>
>>     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.
> 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 like later-no-harm for themselves and later-no-help for
>> rival-faction voters.
> 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.
>
>> 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 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).
>
>> 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.
> 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.
>
>> 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).
>>
> 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 at audioimagination.com
>
> "Imagination is more important than knowledge."
>
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