<div dir="ltr">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)_/¯</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Oct 7, 2023 at 11:15 PM <<a href="mailto:election-methods-request@lists.electorama.com">election-methods-request@lists.electorama.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Send Election-Methods mailing list submissions to<br>
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Today's Topics:<br>
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1. Re: Summability criterion: do I have this right? (Rob Lanphier)<br>
2. My CTE post to EM (C.Benham)<br>
<br>
<br>
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<br>
Message: 1<br>
Date: Sat, 7 Oct 2023 20:17:16 -0700<br>
From: Rob Lanphier <<a href="mailto:roblan@gmail.com" target="_blank">roblan@gmail.com</a>><br>
To: Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de" target="_blank">km_elmet@t-online.de</a>><br>
Cc: James Faran <<a href="mailto:jjfaran@buffalo.edu" target="_blank">jjfaran@buffalo.edu</a>>,<br>
"<a href="mailto:election-methods@lists.electorama.com" target="_blank">election-methods@lists.electorama.com</a>"<br>
<<a href="mailto:election-methods@lists.electorama.com" target="_blank">election-methods@lists.electorama.com</a>><br>
Subject: Re: [EM] Summability criterion: do I have this right?<br>
Message-ID:<br>
<CAK9hOY=<a href="mailto:7FspHB_TcmDBkpkY1Z-fQ0W2sszfmebQMvdM8dSyWDA@mail.gmail.com" target="_blank">7FspHB_TcmDBkpkY1Z-fQ0W2sszfmebQMvdM8dSyWDA@mail.gmail.com</a>><br>
Content-Type: text/plain; charset="utf-8"<br>
<br>
Thanks everyone for weighing in on this topic, and thanks Kristofer for<br>
fixing up my previous inaccurate summary on electowiki. After Kristofer<br>
made his changes, I followed up with some shuffling of the prose in the<br>
body of the article. It's far from perfect, but I think the article is<br>
better than it was last week:<br>
<a href="https://electowiki.org/wiki/Summability_criterion" rel="noreferrer" target="_blank">https://electowiki.org/wiki/Summability_criterion</a><br>
<br>
We should also consider making similar changes over on English Wikipedia,<br>
since that article hasn't gotten a lot of love since I restored it in<br>
January 2022.<br>
<a href="https://en.wikipedia.org/wiki/Summability_criterion" rel="noreferrer" target="_blank">https://en.wikipedia.org/wiki/Summability_criterion</a><br>
<br>
I suspect I'm not the only one who has conflated the "Summability<br>
criterion" and the "Consistency criterion". Here's a link to the latter:<br>
<a href="https://electowiki.org/wiki/Consistency_criterion" rel="noreferrer" target="_blank">https://electowiki.org/wiki/Consistency_criterion</a><br>
If I'm right, it may be useful to explain the relationship between<br>
"consistency" and "summability" to electowiki readers.<br>
<br>
Even as a longtime advocate for Condorcet compliance, I have to concede<br>
that approval voting beats strict Condorcet winner compliance with regards<br>
to consistency and simplicity. It's much easier to imagine real-time<br>
results consumable by mainstream voters from talking-head newscasters as<br>
they report on election night than it is to imagine what this looks like<br>
with methods that fail the consistency criterion.<br>
<br>
Rob<br>
<br>
On Sat, Oct 7, 2023 at 2:51?AM Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de" target="_blank">km_elmet@t-online.de</a>><br>
wrote:<br>
<br>
> On 10/7/23 06:26, James Faran wrote:<br>
> > I'm not certain about the second item. My worry is the following method<br>
> > that someone must have thought of before me and rejected.<br>
> ><br>
> > Given any single ballot, we can use it to create the pairwise matrix.<br>
> > The entries will be +1, 0, or -1. From that pairwise matrix we can<br>
> > reconstruct the preference order given on the ballot. Concatenate all<br>
> > such pairwise matrices. This "summary", an n by n by v array, has size<br>
> > on the order of n^2*v, where n is the number of candidates and v the<br>
> > number of voters. The combination of these is by concatenation in the<br>
> > "v" direction of the array. This is quadratic in n (just as good as a<br>
> > pairwise method) and linear in v (pairwise methods are logarithmic in<br>
> > v). Plurality is linear in n and logarithmic in v (when v gets bigger we<br>
> > just have to increase the number of digits used to describe the totals).<br>
> > The point is that this method transfers complete ballot information, yet<br>
> > clearly is not a method one would want to use. And we certainly, in<br>
> > avoiding discussion of polynomial growth, don't want to suddenly need to<br>
> > explain logarithmic growth.<br>
> ><br>
> > As v has a tendency to get bigger than n, I think "polynomial in n" and<br>
> > "logarithmic in v" might be a good standard. (A rough calculation leads<br>
> > me to believe this method beats just listing the number of ballots of<br>
> > each of the n! types when (n-2)! > v, so is only really a help when n is<br>
> > large. For 10^7 voters, I think n=14 might do it.) All in all, as it<br>
> > stands the second point is good enough. We'd just want to avoid<br>
> > responding to a "What does that mean?" question with "You don't want to<br>
> > know," or "You wouldn't understand." However, for studying the question,<br>
> > a more precise definition is needed, lest every method be "summable".<br>
> > Should the amount of calculation time needed to analyze the "summary"<br>
> > come into it?<br>
><br>
> Yes, the current mathematical standard defined in the Electowiki article<br>
> is "polynomial in candidates, logarithmic in voters" for just the reason<br>
> you mentioned: the number of voters increases much more quickly than the<br>
> number of candidates. Strictly speaking, I suppose polylogarithmic could<br>
> also work, but nobody has ever made such a summary so I shouldn't<br>
> complicate matters too much.<br>
><br>
> Perhaps something like "should grow slowly in the number of candidates<br>
> and even more slowly in the number of voters". But even that's adding<br>
> more detail to a brief summary.<br>
><br>
> In any case, my idea was that the summary should be brief, and then<br>
> questions like "what does *slow* mean" can be answered by pointing at<br>
> the mathematical definition, or by a longer elaboration that first<br>
> explains the justification (e.g. "there will be more voters than<br>
> candidates"), and then does a rigorous definition.<br>
><br>
> -km<br>
><br>
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Message: 2<br>
Date: Sun, 8 Oct 2023 16:45:19 +1030<br>
From: "C.Benham" <<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>><br>
To: "<a href="mailto:election-methods@lists.electorama.com" target="_blank">election-methods@lists.electorama.com</a>"<br>
<<a href="mailto:election-methods@lists.electorama.com" target="_blank">election-methods@lists.electorama.com</a>>, Michael Ossipoff<br>
<<a href="mailto:email9648742@gmail.com" target="_blank">email9648742@gmail.com</a>><br>
Subject: [EM] My CTE post to EM<br>
Message-ID: <<a href="mailto:4d5e2a8b-5bd5-46d6-dd40-3b3857edfc5e@adam.com.au" target="_blank">4d5e2a8b-5bd5-46d6-dd40-3b3857edfc5e@adam.com.au</a>><br>
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<br>
<br>
Michael,<br>
<br>
> ... there's no offensive strategy for changing the winner from the CW<br>
> to one's own favorite,<br>
<br>
Say sincere is<br>
<br>
46 A<br>
44 B<br>
10 C<br>
<br>
A is the CW (as well as being every other type of winner).<br>
<br>
Now suppose the B voters all decide to bury against A by ranking C second:<br>
<br>
46 A<br>
44 B>C<br>
10 C<br>
<br>
Now? C has the lowest Borda score and the lowest "top count", so if we <br>
are using<br>
IRV/RCV or Baldwin? C is eliminated, "taking down" A and leaving B elected.<br>
<br>
The "offensive strategy" has succeeded. This is the same outrageous <br>
failure of<br>
the Later-no-Help and Plurality criteria that we see with Margins.<br>
<br>
I'm not clear how Coombs (or your preferred version of it) handles <br>
truncation.<br>
<br>
Is the "bottom count" Fractional (in other words based on the <br>
symmetrically completed ballots)<br>
or Whole (so that truncated ballots give a whole vote to each of the <br>
bottom-counts of the truncated<br>
candidates)?<br>
<br>
In this case neither version eliminates C, but I'd be surprised if <br>
examples couldn't be made of<br>
them also failing those criteria.<br>
<br>
You implied that you are a fan of Later-no-Harm.? If that is the case I <br>
don't think you will find a better<br>
method than plain IRV/RCV<br>
<br>
Chris B.<br>
<br>
> Here are 3 elimination-methods that eliminate 1 candidate at a time:<br>
><br>
> ?<br>
><br>
> RCV/IRV: Eliminates lowest topcount<br>
><br>
> ?<br>
><br>
> Coombs: Eliminates highest bottomcount<br>
><br>
> ?<br>
><br>
> Baldwin; Eliminates lowest Borda-score.<br>
><br>
> ?<br>
><br>
> Any one of those can be the ?base-method? .<br>
<br>
<br>
<br>
<br>
<br>
> *Michael Ossipoff*email9648742 at <a href="http://gmail.com" rel="noreferrer" target="_blank">gmail.com</a> <br>
> <mailto:<a href="mailto:election-methods%2540lists.electorama.com" target="_blank">election-methods%40lists.electorama.com</a>?Subject=Re%3A%20%5BEM%5D%20My%20CTE%20post%20to%20EM&In-Reply-To=%3CCAOKDY5CU-zc3Y%3DC%3DrFWagy3zVw5Px6KPaULqW89gHdxshRZh8A%<a href="http://40mail.gmail.com" rel="noreferrer" target="_blank">40mail.gmail.com</a>%3E><br>
> /Fri Oct 6 14:33:40 PDT 2023/<br>
><br>
><br>
> ------------------------------------------------------------------------<br>
> When I said:<br>
><br>
> "There?s no offensive strategy for changing the CW to one?s own favorite."<br>
><br>
> I meant, there's no offensive strategy for changing the winner from the CW<br>
> to one's own favorite.<br>
><br>
> On Fri, Oct 6, 2023 at 5:21?PM Michael Ossipoff <email9648742 at <a href="http://gmail.com" rel="noreferrer" target="_blank">gmail.com</a> <<a href="http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com" rel="noreferrer" target="_blank">http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com</a>>><br>
> wrote:<br>
><br>
> >/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 <br>
> 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 <br>
> 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 <br>
> 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 <br>
> the />/rankings before any eliminations." />//>/? />//>/Michael Ossipoff/<br>
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