[EM] How to make a summable version of STV

[fsimmons at pcc.edu]

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.]

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.

Now for the frosting on the cake:

Since PR elections generally have an electorate in the tens of thousands, we can make the following 
simplification:

Instead of using range ballots on a scale of zero to six, have the voters fill out range ballots on a scale of 
zero to one (i.e. approval ballots) with the aid of a fair die:

If the desired rating is r, toss the die, and if the value that "shows" is r or less, then rate the candidate 1, 
else rate the candidate zero

With more than ten thousand voters the resulting factions will be statistically indistinguishable.from the 
ones gotten by use of seven levels.