[EM] Proportional Representation from Ratings Ballots

[Warren Smith]

On 11/5/09, Warren Smith <warren.wds at gmail.com> wrote:
>>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.

--Olson's method fails.
Suppose voter #1 votes (1,0,0,0,...0) "plurality style".
If canddt#1 is eliminated, the ballot then becomes unnormalizable.
I assume Olson deals with that by throwing it in the garbage.

More seriously:
If canddt#1 instead is declared a winner with over-quota, then Olson
reweights canddt#1
and renormalizes ballot #1 so its sum-of=squares is still 1.

However, it is impossible to do both if ALL ballots happen to be
plurality-style,
the reweighting and renormalization conflict and the conflict is
irreconciliable.

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
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and
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