[EM] Summability criterion: do I have this right?

[Rob Lanphier]

Hi Kristofer,

Thanks for the thoughtful responses.  It was a long time ago that I learned
(not to my surprise) that most Wikipedia users only read the summary of an
article (i.e. the portion before the table of contents), and frequently
they only skim that.  So, here's the Wikipedia article about Summability:

...and here's what is stated in the summary:

> *Each vote should be able to be mapped onto a summable array, such that
> its size at most grows polynomially with respect to the amount of
> candidates, the summation operation is associative and commutative and the
> winner could be determined from the array sum for all votes cast alone.*
>

The good news: that's almost certainly more accurate than what I added to
the summary on electowiki (which apparently more accurately describes the
"Consistency criterion" than it does the Summability criterion).  The bad
news: most peoples' eyes glaze over when they hear math nerds explain the
difference between "grows polynomially" and "grows exponentially".  By the
time we start talking about big-O notation, they've already fled.

Is there a TERSE way of describing the summability criterion that is both
accurate and doesn't use jargon like "summable array", "associative and
commutative", and "grows polynomially".  It's OKAY if one uses jargon if
one can explain that jargon to a layperson in a single sentence, but it's
not great.  Just assume you're explaining the concept to someone that
barely passed American high-school algebra.

Rob

On Fri, Oct 6, 2023 at 2:19 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 10/6/23 06:45, Rob Lanphier wrote:
> > Hi folks,
> >
> > I've made a change to electowiki's "Summability criterion" article:
> > https://electowiki.org/wiki/Summability_criterion
> > <https://electowiki.org/wiki/Summability_criterion>
>
> Some further thoughts about that article: I have tried to make the
> summability criterion definition very general and information
> theoretical. For instance, the definition as listed in the article
> doesn't depend on just what the summary combination operator is, as long
> as it can't be used to cheat and turn non-summable methods summable.
>
> Perhaps this is more confusing than enlightening - particularly the
> parts about growing as log(V) in the number of voters.
>
> In practice, pretty much every summable method I can think of (even
> contingent vote, STAR, and majority judgment) use plain old addition to
> combine summaries. For instance, combining Condorcet matrices is just
> adding the cells in the two matrices together; combining Plurality
> counts is also just adding up the votes per candidate; and combining
> contingent vote summaries is just one Condorcet matrix and a Plurality
> count per.
>
> So maybe it would be better to come up with a simple idea that gets at
> the gist of it, and then have a technical nitty-gritty section to patch
> up all the loopholes... perhaps with examples for each method what their
> summaries are (Condorcet matrices, positional counts, etc). But I'm not
> sure how to do that; my prior answer is probably still a bit too
> cumbersome to give an intuitive idea.
>
> It's too bad we don't have any feedback from "mere readers" of
> Electowiki... it's hard to know what level of detail to write at.
>
> -km
>
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