[EM] A family of easy-to-explain Condorcet methods

[Daniel Carrera]

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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20210630/5b35318e/attachment.html>