[EM] Proportional Representation beyond STV?

[Chris Benham]

I  have two main ideas on this subject. It seems to me that  STV  is 
impeccable in principle, EXCEPT for  the horrible, arbitary feature it 
has in common with  IRV of  eliminating the candidate who happens to 
have the lowest total at the time it is convenvenient to eliminate a 
candidate. So why not eliminate the Condorcet loser instead?
 Here is a specific proposal:  Ranked ballots, equal preferences and 
truncation allowed. Quota is (1/n+1)+ 0.0000001. Equal first preferences 
are split into fractions of a vote. All candidates with a quota of first 
preferences are elected, and overflow lower preferences are distributed 
. The part of the overflow consisting of "exhausted" ballots can just be 
treated as equal preference for the unmarked candidates and distributed 
fractionally  (This seems correct in principle and saves mucking around 
with having to change the quota.)  After the overflow any candidates who 
now have a quota are elected.  If there are any seats now left 
vacant,then counting all the votes at full value, of  the remaining 
candidates eliminate the Condorcet loser (using I'm-not-sure-what 
completion method).  Distribute this candidate's preferences and elect 
any candidate who now has a quota. If any seats are still vacant, 
repeat, etc.
My second idea is this:  Elect the CW (completed however), and then 
depending on how many seats there are to be filled, fractionally mark 
down some of the ballots according to their contribution to electing the 
winner, and taking into account the "wasted" vote. Repeat  until the 
desired number of candidates are elected. The details of  exactly which 
ballots to mark down by exactly how much  I haven't yet thought about, 
but I shouldn't think it is a huge problem.

Chris Benham