[EM] Election-Methods Digest, Vol 231, Issue 19

Mon Oct 9 16:30:43 PDT 2023

The lay-person definition of summability is "can be tallied locally in
practice". That's the thing we actually care about. Technically, then, that
definition does not describe summability but rather a thing that is
effectively mutually inclusive with summability, so it's a perfectly
reasonable lay definition in my opinion. I think that's why we've been
struggling to create a technical definition: we're trying to objectively
describe a thing that's naturally a bit subjective. Or at least I am. Mabe
the person who originally asked is not concerned with protocols for public
elections ¯\_(ツ)_/¯

On Sat, Oct 7, 2023 at 11:15 PM <
election-methods-request at lists.electorama.com> wrote:

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> Today's Topics:
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>    1. Re: Summability criterion: do I have this right? (Rob Lanphier)
>    2. My CTE post to EM (C.Benham)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Sat, 7 Oct 2023 20:17:16 -0700
> From: Rob Lanphier <roblan at gmail.com>
> To: Kristofer Munsterhjelm <km_elmet at t-online.de>
> Cc: James Faran <jjfaran at buffalo.edu>,
>         "election-methods at lists.electorama.com"
>         <election-methods at lists.electorama.com>
> Subject: Re: [EM] Summability criterion: do I have this right?
> Message-ID:
>         <CAK9hOY=
> 7FspHB_TcmDBkpkY1Z-fQ0W2sszfmebQMvdM8dSyWDA at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Thanks everyone for weighing in on this topic, and thanks Kristofer for
> fixing up my previous inaccurate summary on electowiki.  After Kristofer
> made his changes, I followed up with some shuffling of the prose in the
> body of the article.  It's far from perfect, but I think the article is
> better than it was last week:
> https://electowiki.org/wiki/Summability_criterion
>
> We should also consider making similar changes over on English Wikipedia,
> since that article hasn't gotten a lot of love since I restored it in
> January 2022.
> https://en.wikipedia.org/wiki/Summability_criterion
>
> I suspect I'm not the only one who has conflated the "Summability
> criterion" and the "Consistency criterion".  Here's a link to the latter:
> https://electowiki.org/wiki/Consistency_criterion
> If I'm right, it may be useful to explain the relationship between
> "consistency" and "summability" to electowiki readers.
>
> Even as a longtime advocate for Condorcet compliance, I have to concede
> that approval voting beats strict Condorcet winner compliance with regards
> to consistency and simplicity.  It's much easier to imagine real-time
> results consumable by mainstream voters from talking-head newscasters as
> they report on election night than it is to imagine what this looks like
> with methods that fail the consistency criterion.
>
> Rob
>
> On Sat, Oct 7, 2023 at 2:51?AM Kristofer Munsterhjelm <
> km_elmet at t-online.de>
> wrote:
>
> > On 10/7/23 06:26, James Faran wrote:
> > > I'm not certain about the second item.  My worry is the following
> method
> > > that someone must have thought of before me and rejected.
> > >
> > > Given any single ballot, we can use it to create the pairwise matrix.
> > > The entries will be +1, 0, or -1. From that pairwise matrix we can
> > > reconstruct the preference order given on the ballot. Concatenate all
> > > such pairwise matrices. This "summary", an n by n by v array, has size
> > > on the order of n^2*v, where n is the number of candidates and v the
> > > number of voters. The combination of these is by concatenation in the
> > > "v" direction of the array.  This is quadratic in n (just as good as a
> > > pairwise method) and linear in v (pairwise methods are logarithmic in
> > > v). Plurality is linear in n and logarithmic in v (when v gets bigger
> we
> > > just have to increase the number of digits used to describe the
> totals).
> > > The point is that this method transfers complete ballot information,
> yet
> > > clearly is not a method one would want to use.  And we certainly, in
> > > avoiding discussion of polynomial growth, don't want to suddenly need
> to
> > > explain logarithmic growth.
> > >
> > > As v has a tendency to get bigger than n, I think "polynomial in n" and
> > > "logarithmic in v" might be a good standard.  (A rough calculation
> leads
> > > me to believe this method beats just listing the number of ballots of
> > > each of the n! types when (n-2)! > v, so is only really a help when n
> is
> > > large.  For 10^7 voters, I think n=14 might do it.)  All in all, as it
> > > stands the second point is good enough. We'd just want to avoid
> > > responding to a "What does that mean?" question with "You don't want to
> > > know," or "You wouldn't understand." However, for studying the
> question,
> > > a more precise definition is needed, lest every method be "summable".
> > > Should the amount of calculation time needed to analyze the "summary"
> > > come into it?
> >
> > Yes, the current mathematical standard defined in the Electowiki article
> > is "polynomial in candidates, logarithmic in voters" for just the reason
> > you mentioned: the number of voters increases much more quickly than the
> > number of candidates. Strictly speaking, I suppose polylogarithmic could
> > also work, but nobody has ever made such a summary so I shouldn't
> > complicate matters too much.
> >
> > Perhaps something like "should grow slowly in the number of candidates
> > and even more slowly in the number of voters". But even that's adding
> > more detail to a brief summary.
> >
> > In any case, my idea was that the summary should be brief, and then
> > questions like "what does *slow* mean" can be answered by pointing at
> > the mathematical definition, or by a longer elaboration that first
> > explains the justification (e.g. "there will be more voters than
> > candidates"), and then does a rigorous definition.
> >
> > -km
> >
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> ------------------------------
>
> Message: 2
> Date: Sun, 8 Oct 2023 16:45:19 +1030
> From: "C.Benham" <cbenham at adam.com.au>
> To: "election-methods at lists.electorama.com"
>         <election-methods at lists.electorama.com>, Michael Ossipoff
>         <email9648742 at gmail.com>
> Subject: [EM] My CTE post to EM
> Message-ID: <4d5e2a8b-5bd5-46d6-dd40-3b3857edfc5e at adam.com.au>
> Content-Type: text/plain; charset="utf-8"; Format="flowed"
>
>
> Michael,
>
> > ... there's no offensive strategy for changing the winner from the CW
> > to one's own favorite,
>
> Say sincere is
>
> 46 A
> 44 B
> 10 C
>
> A is the CW (as well as being every other type of winner).
>
> Now suppose the B voters all decide to bury against A by ranking C second:
>
> 46 A
> 44 B>C
> 10 C
>
> Now? C has the lowest Borda score and the lowest "top count", so if we
> are using
> IRV/RCV or Baldwin? C is eliminated, "taking down" A and leaving B elected.
>
> The "offensive strategy" has succeeded. This is the same outrageous
> failure of
> the Later-no-Help and Plurality criteria that we see with Margins.
>
> I'm not clear how Coombs (or your preferred version of it) handles
> truncation.
>
> Is the "bottom count" Fractional (in other words based on the
> symmetrically completed ballots)
> or Whole (so that truncated ballots give a whole vote to each of the
> bottom-counts of the truncated
> candidates)?
>
> In this case neither version eliminates C, but I'd be surprised if
> examples couldn't be made of
> them also failing those criteria.
>
> You implied that you are a fan of Later-no-Harm.? If that is the case I
> don't think you will find a better
> method than plain IRV/RCV
>
> Chris B.
>
> > Here are 3 elimination-methods that eliminate 1 candidate at a time:
> >
> > ?
> >
> > RCV/IRV:  Eliminates lowest topcount
> >
> > ?
> >
> > Coombs: Eliminates highest bottomcount
> >
> > ?
> >
> > Baldwin; Eliminates lowest Borda-score.
> >
> > ?
> >
> > Any one of those can be the ?base-method? .
>
>
>
>
>
> > *Michael Ossipoff*email9648742 at gmail.com
> > <mailto:election-methods%40lists.electorama.com
> ?Subject=Re%3A%20%5BEM%5D%20My%20CTE%20post%20to%20EM&In-Reply-To=%3CCAOKDY5CU-zc3Y%3DC%3DrFWagy3zVw5Px6KPaULqW89gHdxshRZh8A%
> 40mail.gmail.com%3E>
> > /Fri Oct 6 14:33:40 PDT 2023/
> >
> >
> > ------------------------------------------------------------------------
> >   When I said:
> >
> > "There?s no offensive strategy for changing the CW to one?s own
> favorite."
> >
> > I meant, there's no offensive strategy for changing the winner from the
> CW
> > to one's own favorite.
> >
> > On Fri, Oct 6, 2023 at 5:21?PM Michael Ossipoff <email9648742 at
> gmail.com  <
> http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com>>
> > wrote:
> >
> > >/Name of Method: />//>/? />//>/CW,Takedown-Elimination (CTE) />//>/?
> />//>/or />//>/? />//>/Simmons-Ossipoff Method />//>/? />//>/Okay yes, I
> like the 2nd one. />//>/? />//>/It adds an enhancement to any of several
> already-existing />/elimination-methods. />//>/? />//>/Here are 3
> elimination-methods that eliminate 1 candidate at a time: />//>/?
> />//>/RCV/IRV: Eliminates lowest topcount />//>/? />//>/Coombs: Eliminates
> highest bottomcount />//>/? />//>/Baldwin; Eliminates lowest Borda-score.
> />//>/? />//>/Any one of those can be the ?base-method? . />//>/?
> />//>/Method rule: />//>/? />//>/Ranked balloting. Equal-rankng &
> truncation allowed. />//>/? />//>/1) Check for a CW & elect hir. />//>/?
> />//>/2) If none, do the base-method. />//>/? />//>/3) During the doing of
> the base-method: />//>/? />//>/When the base-method?s rule eliminates a
> candidate, eliminate
> > additionally />/anyone who is pair-beaten by that candidate. ?&
> additionally any />/candidate beaten by that 2nd candidate. />//>/?
> />//>/That?s takedown & secondary takedown. />//>/? />//>/4) If anyone
> becomes un-pairbeaten due to elimination of who beats hir, />/s/he wins.
> />//>/? />//>/5) Continue till only one candidate remains uneliminated.
> />//>/? />//>/[end of count-rule definition] />//>/? />//>/Though it was
> Forest who introduced the unprecedentedly gamechanging />/Takedown, &
> applied it to Coombs & Baldwin, the bombast in this post
> > is all />/mine. />//>/? />//>/Obviously a CW wins if voting is sincere.
> />//>/? />//>/There?s no offensive strategy for changing the CW to one?s
> own favorite. />//>/? />//>/There?s no need for defensive strategy to
> protect the win of a CW. />//>/? />//>/While MinMax(wv), Schulze, RP(wv) &
> Smith//MinMax(wv) require defensive />/truncation to deter burial strategy
> against the CW, the above-defined />/method requires no such defensive
> strategy, & voters can rank all the
> > way />/down to the bottom if they want to. />//>//>/PS. I added a
> statement that, for the purposes of takedown & secondary />/takedown,
> "pair-beaten" should probably mean "pairbeaten according to
> > the />/rankings before any eliminations." />//>/? />//>/Michael Ossipoff/
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