1. Re: Summability criterion: do I have this right? (Rob Lanphier)
2. My CTE post to EM (C.Benham)

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@lists.electorama.com> wrote: > Send Election-Methods mailing list submissions to > election-methods@lists.electorama.com > > To subscribe or unsubscribe via the World Wide Web, visit > > http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com > > or, via email, send a message with subject or body 'help' to > election-methods-request@lists.electorama.com > > You can reach the person managing the list at > election-methods-owner@lists.electorama.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Election-Methods digest..." > > > Today's Topics: > > 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@gmail.com> > To: Kristofer Munsterhjelm <km_elmet@t-online.de> > Cc: James Faran <jjfaran@buffalo.edu>, > "election-methods@lists.electorama.com" > <election-methods@lists.electorama.com> > Subject: Re: [EM] Summability criterion: do I have this right? > Message-ID: > <CAK9hOY= > 7FspHB_TcmDBkpkY1Z-fQ0W2sszfmebQMvdM8dSyWDA@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@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 > > >