[EM] Quotaless STV-PR suggestion

[Chris Benham]

I'd like to propose an STV-like PR method that does without a quota.

Here is the procedure for filling 3 seats:
 
*Voters rank from the top however many candidates they wish.
 
To fill the first seat, one-at-time 'eliminate' the candidate highest-ranked
(among remaining candidates) on the fewest ballots until 4 candidates
remain. The candidate A that is then top-ranked on the highest number of
ballots is elected.
 
A is dropped from the ballots and the 'eliminated' candidates are restored.
Ballots that contributed to A's winning tally are now given a weight of 2 and
all the other ballots a weight of 3.
 
To fill the second seat, one-at-a-time 'eliminate' the candidate that is highest 
ranked on the smallest total weight of ballots until 3 candidates remain.
The candidate B that is then highest ranked on the greatest total weight of
ballots is elected.
 
B is  dropped from the ballots and previously 'eliminated' candidates are restored.
Ballots that contributed to both A's  and B's winning tallies are given a weight of 1.
Ballots that contributed to the winning tally of a single candidate (A or B) are given
a weight of 2.  All the other ballots are given a weight of 3.
 
To fill the final seat, one-at-a-time eliminate the candidate that is highest ranked 
on the smallest total weight of ballots until 2 remain. The candidate C that is then
highest ranked on the greatest total weight of ballots is elected.*
 
So initially each ballot is given a weight that is equal to the number of seats to be filled, and then they reduce in weight by 1 for each candidate they've helped elect.
 
The number of candidates the field is reduced to in each round is equal to the numbers of seats not-yet-filled plus 1.
 
I am sure this meets Droop Proportionality for Solid Coalitions. 
 
At least some versions of STV-PR  have the problem that adding or removing
a few ballots that vote for nobody (say just plump for some X that is ignored
or voted no higher than equal-bottom on all the other ballots) can change at
least one of the winners by changing the size of the quota.

It is much simpler than Meek to explain and operate, but seems (from some 
examples I've seen) to give Meek-like results.
 
Chris Benham
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