[EM] How to make a summable version of STV

[Kristofer Munsterhjelm]

fsimmons at pcc.edu wrote:
> This is to illustrate a point that Warren has recorded on his website
> somewhere (I don't remember exactly where); namely that lack of
> summability is not insurmountable.
> 
> We start with the assumption that the voters have range style ballots
> on a scale of zero to six.  [Seven levels are about optimal according
> to the psychometrics experts.]

I thought five was, not seven. Do you have any papers?

> At each precinct the ballots are sorted into n piles, one for each
> candidate.  The ballots in each pile are averaged together to get a
> rating vector for each candidate.  [At this first stage if a
> candidate shares (with k-1 other candiates) top rating on a ballot,
> then a copy of that ballot is sent to each of those candidate's
> piles, along with a weight of 1/k .]
> 
> The precincts send the n candidate vectors, together with their
> respective totalweights to the counting center.  For each candidate a
> weighted average of the vectors for that candidate from all of the
> precincts is computed, and the total weight is taken as the size of
> that candidate's faction.
> 
> The STV computation is then based on these n almagamated factions.

That would fail the Droop proportionality criterion. Just take your 
favorite example where Range fails it, then stick an universal favorite 
candidate X in front of every voter's vote. Now, there's only one rating 
vector - X's - and the averaging will smooth out any structure beyond X.

This is an extreme example, but the averaging could hide detail in more 
realistic ballot sets, too.