[EM] Proportional Representation from Ratings Ballots

[Warren Smith]

>B.Olson:
IRNR can be extended to proportional elections, and the algorithm goes
like this:

0. Ballots accept ratings >=0 for all choices. Each choice gets a
global 'weight' of 1.0
1. Sum up normalized weighted ratings ballots. Normalized means that
ratings for choices a,b,c,d scaled so that sqrt(a^2 + b^2 + c^2 + d^2)
== 1. Before normalization, each rating is multiplied by the global
weight for the choice.
2. If some choices sum up over the quota, decrease the global weight
for them such that they would sum up equal to the quota. Goto 1.
3. If not enough choices sum up equal to the quota, disqualify lowest
sum choice. Set their weight to 0.0. (No vote will go to them but be
redistributed at normalization to voter's other preferences.) Goto 1.

--WDS:
Hi Brian.  Comments and/or questions:
(1) more simply, the sum of the squares = 1.  So each ballot in an N-candidate
election is an N-vector with L2-norm=1.
(2) I assume "the quota" means, in a W-winner V-voter election, V/W?
Or V/(W+1)? Or what? And "choice" means "candidate"?
(3) I assume "not enough choices" means "fewer than W"?
(4) there is no need for "weights" since all weights are always 1 or 0 only, so
could also just talk of "surviving" versus "eliminated" candidates?
No, you really
do have weights also allowed to lie BETWEEN 0 and 1.

In (2) if you use ">V/(W+1)" as your meaning for "over the quota" that
way it is impossible for more than W candidates to ever simultaneously
have sum>quota.

Anyway, I'm not sure what your method is exactly and also not seeing
why it is "proportional" and what that means exactly.


-- 
Warren D. Smith
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