[EM] New simple kind of party-based proportionality, avoiding deweighting, and using range-style ballots

[Warren Smith]

As input, every voter submits a rating-type (range-voting-style) ballot scoring
all N candidates on some fixed allowed-score-interval say [0, 999].
(It will be important that the min score be 0.)
Also, each candidate has a publicly-known party affiliation.

The goal is to produce W "winners" (0<W<N) in a "proportional
representation" manner.

Compute the average rating for each candidate, which (via sorting)
yields an ordering of all candidates. Scan through it from top to
bottom, declaring each candidate a "winner" or "not" as you go; a
candidate is a winner unless prevented from being so by a
proportionality condition (in view of the previously-declared
winners).

Note that this is fast (low order polynomial time)
and simple.  And "precinct summable" too.
Also note that there is no ballot "deweighting" going on.  Every
ballot is used with
"full weight."

The problem is the proportionality condition -- what should it be?  If
we know party affiliations this is no problem:  each party is granted
a share of the number of seats.
You can't get (much) more than your share (that's our definition of
"violation of proportionality").

Party X's share could be proportional to score for a party-X candidate
summed over all voters, and averaged over all candidates in X.  This
definition has the property that if voters score their party's
candidates max and all other parties min, then party X's share will be
proportional to the voter-population that wants party X.

Parties will have incentive to run their best candidates and ONLY their best
(since otherwise their avg score and hence share decreases), but not so few they
cannot win all the seats they will deserve.  That ought to control ballot bloat.
There are senses in which the method is "cloneproof" and "monotonic."

Voters who wish not to provide a score for some candidate (e.g. they
feel ignorant about him) can do so, and then only his genuine scores
affect his average (and ditto for the party-wide average).   There
could be a fixed initial number of artificial all-0 votes to
bias averages a little toward 0 (or all-K to bas toward K).

I dislike all methods (including this) that use party-affiliations as
input, but aside
from that it looks good to me
(pending all the criticisms and comments that may soon arrive :)

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html