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. ---- Election-Methods mailing list - see http://electorama.com/em for list info
