[EM] Legislative language for Condorcet RCV

Sun Apr 13 09:17:27 PDT 2025

On 2025-04-04 17:34, robert bristow-johnson wrote:
> I'm changing the title of the sub-thread.
> 
>> On 04/03/2025 4:51 PM EDT Kristofer Munsterhjelm <km-elmet at munsterhjelm.no> wrote:
>>
>>   
>> On 2025-04-03 21:58, robert bristow-johnson wrote:
>>
>>> About "Ranked Robin" that's seems to me to be a Sass invention and I
>>> don't understand why they tepidly promote that instead of just Condorcet
>>> RCV in general.  I have become convinced that for Condorcet RCV to ever
>>> be adopted in legislation, it will have to be either
>>> 1. BTR-IRV which requires only a small change to the existing IRV language or
>>> 2. a Two-method "straight ahead" Condorcet method.  Probably
>>> either  Condorcet-Plurality or Condorcet-TTR.
>>>
>>> The reason I came to this position was from discussions with friendly
>>> legislators and legislative counsel here in Vermont.  We need for
>>> "The law should say what it means and mean what it says."  The
>>> Two-method straight-ahead Condorcet is simply that.  Any other
>>> Condorcet-consistent method seems to obscure what it's doing.  What
>>> we want the law to do is to insure that if more voters mark their
>>> ballots that Candidate A is preferred to Candidate B, that Candidate
>>> B is not elected.  That's the only way that ensures that our votes
>>> are valued equally (as in "Equal Vote Coalition") and for the
>>> election to not be spoiled and for voters to not be punished for
>>> voting sincerely (which disincentives tactical  voting).
>>
>> What do you think of minmax? One possible way to put it is "in the
>> absence of a Condorcet winner, elect the candidate who would need the
>> fewest additional top votes to become one".
>>
> 
> Is that language sufficiently *procedural*.  Like spelling out the
> step of exactly how to count the votes and declare the winner?

No, that's the disadvantage. I guess you could make a verification 
process at the end that verifies that candidate A's score is n by adding 
(n-1) first preferences, counting again, seeing that A is not a CW, then 
adding n first preferences and confirming that A is now a CW. But it 
feels pretty ugly.

>> As for the others, I would much prefer C-TTR to C-Plurality; I suspect
>> the latter would be too easy to manipulate.
>>
> 
> Remember that it's only in 0.5% of the RCV election that this
> opportunity to manipulate would exist.  For me, thinking about
> legislative language, it's about persuading legislators (and voters)
> that the law is reasonable and reflects their collective vote.  They're
> not going to like any obscurity or opacity.  They may suspect something
> sneaky that benefit some group (like "liberals") might be slipped in
> underneath obscure language.  Anti-RCV people already suspect that.

Center squeezes don't occur that often with IRV, either, but when they 
do, it's pretty damaging. My concern with C-Plurality is that the way to 
strategize is so transparent, compared to something that's either more 
IRV-like or thoroughly pairwise, that it would tempt people to use 
strategy more often.

I could be wrong, of course; but it would suck if I were right.

> I have a document of templates for legislative language here:
> https://drive.google.com/file/d/1DGvs2F_YoKcbl2SXzCcfm3nEMkO0zCbR/view .
> Even though the legislative language they came up with is different:
> https://legislature.vermont.gov/Documents/2024/Docs/BILLS/H-0424/H-0424%20As%20Introduced.pdf
> I still consider the templates sufficient to explain clearly the
> essential components of the law.
> 
> Anyway, using the template, how compact can you get the Minimax or
> Copeland language to look?  And, to the pedestrian voter (or
> legislator), how to we persuade them that this law is transparent and
> that it truly reflects the voters' collective will?
> 
> Condorcet-Plurality is in the template.  Condorcet-TTR wouldn't be much worse:
> 
> _______________________________________________
> 
> All elections of [office] shall be by ballot, using a system of
> ranked-choice voting without a separate runoff election. The presiding
> election officer shall implement a ranked-choice voting protocol
> according to these guidelines:
> (1) The ballot shall give voters the option of ranking candidates in
> order of preference. Lower ordinal preference shall be considered higher
> rank and the candidate marked as first preference is considered ranked
> highest. Equal ranking of candidates shall be allowed. Any candidate not
> marked with a preference shall be considered as ranked lower than every
> candidate marked with a preference.
> (2) If a candidate receives a majority (over 50 percent) of first
> preferences, that candidate is elected.
> (3) If no candidate receives a majority of first preferences, a
> Condorcet-consistent retabulation shall be performed by the presiding
> election officer. The retabulation shall examine every possible pairing
> of candidates. Given N as the number of candidates, then the number of
> possible pairings of candidates is N(N-1)/2. In each pair, if the number
> of ballots marked ranking a selected candidate over the other candidate
> exceeds the number of ballots marked to the contrary, then the other
> candidate is declared defeated. After all candidate pairings are
> examined, the candidate who remains not declared defeated is the
> Condorcet winner and is elected.
> (4) If no Condorcet winner exists in subdivision (3), then the
> prevailing candidate of the pair involving the two candidates having the
> most first preferences is elected.
> (5) The [governing jurisdiction] may adopt additional regulations
> consistent with this subsection to implement these standards.
> _______________________________________________
> 
> So, in subdivision (4), how would the language look like for Minimax? >
> For a single-method system like Ranked Pairs, how would subdivisions
> (3) and (4) be replaced?

Copeland should be pretty easy:

(3) If no candidate receives a majority of first preferences 
[...language omitted, same as above...] In each pair, if the number of 
ballots marked ranking a selected candidate over the other exceeds the 
number of ballots marked to the contrary, then add one to the selected 
candidate's tournament victory count.

(4) The candidate with the highest tournament victory count is elected. 
In the case of a tie, then the tied candidate having the most first 
preferences is elected. (alternatively: prevailing candidate of the pair 
involving the two tied candidates having the most first preferences is 
elected.)

Copeland,Plurality is somewhat better than Condorcet-Plurality because 
it passes Smith. The Plurality tiebreak must choose between candidates 
in the Smith set, as they all have higher Copeland scores than 
candidates outside it. So if, e.g. a burial spree goes wrong, you don't 
get a candidate who's pairwise beaten by a lot of other candidates 
elected just because he has a high first preference count.

Still, it's somewhat limited, because if there are three strong 
candidates and one of them engineers a cycle, then the Copeland set will 
contain the three candidates who are part of the cycle. So it's not very 
decisive in that respect.

As for minmax, you could write out an algorithm, but the problem is that 
it wouldn't look anything like the phrasing. E.g.

- If no candidate receives a majority of first preferences ... mark each 
candidate's worst victory margin as undefined.
- Examine each pair of candidates. Let the pair's margin be the number 
of voters who marked a ranking preferring the first candidate over the 
other, subtracted by the number of voters who marked a ranking 
preferring the second candidate to the first. If the first candidate's 
worst victory margin is undefined or greater than the pair's margin, 
update the first candidate's worst victory magnitude to equal the pair's 
margin.
- The candidate with the highest worst victory magnitude is elected.

The intuition of the algorithm is more like "the candidate who survives 
the best/takes the least beating no matter who he's paired up with wins".

(I wonder how computationally complex methods are defined in legislative 
language where they are used... for instance, it would be a nightmare to 
write down a hand-count algorithmic procedure for Meek STV.)

-km