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

[Kristofer Munsterhjelm]

On 10/7/23 01:44, Rob Lanphier wrote:
> 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.

That's what I'm having trouble thinking up. I would say what needs to be 
conveyed is that a method is summable if:

1. Any election can be boiled down to a summary that contains all the 
data the method requires to call the election,
2. The storage space required for the summary doesn't grow too quickly 
as you add new candidates or voters,
3. and the summaries can be combined (added up) to get the summary for 
the combined election.

That's about as short as I could make the conditions. The "grows 
polynomially" part is a formalization of the second condition; the 
"commutative and associative" part relates to the third condition.

My language is definitely far from perfect, but perhaps it'll help guide 
others who'd like to try to write a good summary of what summability means.

-km