[EM] A family of easy-to-explain Condorcet methods (Daniel Carrera)

Fri Jul 2 03:16:54 PDT 2021

Daniel,  The method you proposed, in cases where there is no Condorcet
winner, has the same flaws as the IRV method of counting rank choice votes
- easily can eliminate a majority favorite candidate in the first round and
still has the property of any higher ranked candidate hurting the chances
of winning of any lower ranked candidate....  There's got to be a way to
use Condorcet without adding in the worst features of IRV method of
counting rank choice ballots.

On Thu, Jul 1, 2021 at 4:02 PM <
election-methods-request at lists.electorama.com> wrote:

>
>    1. Re: A family of easy-to-explain Condorcet methods (Daniel Carrera)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Wed, 30 Jun 2021 16:09:29 -0500
> From: Daniel Carrera <dcarrera at gmail.com>
> To: Kristofer Munsterhjelm <km_elmet at t-online.de>
> Cc: election-methods at lists.electorama.com
> Subject: Re: [EM] A family of easy-to-explain Condorcet methods
> Message-ID:
>         <
> CAEaabNh_ykt4BxWjmwFhTf+nRoRd2qMF5uuSqGvY2QvMOoc0ag at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> On Wed, Jun 30, 2021 at 11:25 AM Kristofer Munsterhjelm <
> km_elmet at t-online.de> wrote:
>
> > > Aha! I'm learning, I'm learning...
> > > https://electowiki.org/wiki/Dominant_mutual_third_set
> > > <https://electowiki.org/wiki/Dominant_mutual_third_set>
> > >
> > > I couldn't find a page for "Plurality Benham". Let's see...
> >
> > Yeah, I might need to contribute more to Electowiki again. I kind of
> > stopped after I disagreed with another contributor on how certain
> > political positions were portrayed, and I couldn't be bothered to find
> > the proper sources to back my response with, so I didn't do anything at
> > all.
> >
>
> Well, I hope you contribute to Electowiki again. I've learned a lot from
> it.
>
>
>
> > > It wasn't obvious to me at first that taking Behman and replacing "do
> > > IRV" with "sort by plurality" and replacing "eliminate" with "remove"
> > > makes it equivalent to the proposed method. But after thinking about it
> > > for a bit, I *think* I see it. But I need to think more about this.
> >
> > Suppose that in some round you're going to check if A, the bottom
> > candidate on the list, wins. If nobody else on the list beats A
> > pairwise, then A is by definition a Condorcet winner among the remaining
> > candidates. And that's the criterion Benham uses to select its winner.
> > Thus looking for a pairwise loss against any candidate is the same as
> > finding the Condorcet winner (up to tie situations).
> >
>
> Yeah. I was a bit stuck because it wasn't obvious to me that the sequence
> of removals or eliminations would happen in the same order. But they do:
>
> Benham/Pb: ... Check to see if there is a CW. If not, eliminate the bottom
> candidate.
>
> Me: ... On each round check to see if the bottom candidate is the CW,
> otherwise eliminate them.
>
> It took me a moment to prove to myself that these are identical (mine is
> just slower). If there is no CW winner on this round, both methods
> eliminate the same candidate. If there is a CW in this round, Benham finds
> them immediately while my version wastes a few rounds ditching candidates
> before it arrives at the CW. My version is also more convoluted to explain.
> Pb allows for a particularly easy explanation because you don't have to
> talk about sorting, ranking, etc. Here is the simplest way I've found to
> express Pb:
>
> PB:  "*If there is a CW, elect them. Otherwise, remove the candidate with
> the fewest first person votes and repeat.*"
>
> A poster on Reddit just gave me a layman's version:
>
> PB:  "*If someone would win against every other guy in a 1 vs 1 matchup,
> they win. Otherwise we kick out the guy that the fewest voters picked as
> their first choice and repeat*"
>
> I've even toyed with the language for the Burlington mayoral election. Back
> in 2019 rb-j posted the language from the pro-IRV group. It's 169 words:
>
> -------
> All elections of mayor, city councilors and school commissioners shall be
> by ballot, using a system of ranked choice voting without a separate runoff
> election. The chief administrative 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.
>  (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, an instant
> runoff re-tabulation shall be performed by the presiding election officer.
> The instant runoff re-tabulation shall be conducted in rounds. In each
> round, each voter?s ballot shall count as a single vote for whichever
> continuing candidate the voter has ranked highest. The candidate with the
> fewest votes after each round shall be eliminated until only two candidates
> remain, with the candidate then receiving the greatest number of votes
> being elected.
>  (4) The city council may adopt additional regulations consistent with this
> subsection to implement these standards.
> -------
>
> For reference, rb-j's text for BTR-STV was 343 words. I can write Pb in
> similar language in 148 words:
>
> -------
> All elections of mayor, city councilors and school commissioners shall be
> by ballot, using a system of ranked choice voting without a separate runoff
> election. The chief administrative 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.
>  (2) A candidate ?A? is said to win against another candidate ?B? if more
> voters rank ?A? above ?B? than rank ?B? above ?A?. If there is a candidate
> that wins against every other candidate, that candidate is elected.
>  (3) If no candidate wins against every other candidate, the presiding
> officer shall remove the candidate with fewest first place votes, in
> rounds, until one of the remaining candidates wins against every other
> candidate. That candidate is elected.
>  (4) The city council may adopt additional regulations consistent with this
> subsection to implement these standards.
> -------
>
> This makes Pb a very realistic proposal for the very real decision next
> year in Burlington, when the city council will decide whether to adopt some
> kind of ranked ballot system again.
>
>
>
> > > Alright. Overall it sounds like PB is doing really well. To me it looks
> > > easier to explain than BTR-STV and it has several nice features on top.
> > > Even if it's not monotonic, well, neither is IRV and IRV is starting to
> > > get adopted. If monotonicity means that the method is too complicated
> > > for any city council to adopt and they just end up choosing IRV, then
> > > monotonicity is not worth it.
> >
> > It's a bit of a tradeoff. Going from Benham to Pb gives you summability
> > and a somewhat simpler description of the method, but you lose clone
> > independence.
> >
>
> Is clone independence a big problem in Pb? This is an intentionally vague
> question. I'm trying to distinguish between problems that are very likely
> to happen very often in real elections and theoretical problems that are
> unlikely to show up often. Split votes in FPTP is by far the world's best
> known example of electoral failure, whereas my understanding is that
> Minimax is only affected by clones if you have three clones in a cycle in
> the Smith set.
>
>
> Agenda methods might in general have an additional advantage: that they
> > mirror parlaimentary procedure, and thus council officials should be
> > more familiar with the logic -- at least in assemblies that handle the
> > agenda that way.
> >
>
> I hope you're right. I hope council officials find Pb intuitive.
>
>
> Cheers,
> Daniel
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-- 
Kathy Dopp, Natick, Mass., MS mathematics
http://www.kathydopp.info/COVIDinfo
SSRN: http://ssrn.com/author=1451051
Science is my passion, politics my duty (Thomas Jefferson, paraphrased)
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