[EM] Linear summability

[robert bristow-johnson]

> On April 25, 2020 7:49 PM Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
> 
>  
> Some time ago I was wondering how to prove that a method is nonsummable.
> Just because we don't know of any way to make e.g. IRV summable doesn't
> mean there isn't any. I couldn't figure out how you'd definitely exclude
> every possible polyspace array.

i don't think there is a way to exclude any meaningfully different ballot ranking.  remember, every candidate unranked is the same as being ranked last.  whether you rank your least-desired candidate the lowest rank or leave that candidate unranked makes no difference.

maybe a decade ago i posted the formula and a proof that Warren Smith first did that shown the number of ballot piles that are summable as

  number of piles = floor( (e-1)×C! - 1 )

  if the number of candidates is C .

i haven't been able to grok the rest.


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