[EM] Preferential voting system where a candidate may win multiple seats

Chris Benham cbenhamau at yahoo.com.au
Sat Jun 29 18:02:26 PDT 2013

Kristofer Munsterhjelm  wrote (29 June 2013):
"The combined method would go like this:

1. Run the ballots through RP (or Schulze, etc). Reverse the outcome ordering (or the ballots; these systems are reversal symmetric so it doesn't matter). Call the result the elimination order.
2. Distribute seats using Sainte-Laguë.
3. Call parties that receive no seats "unrepresented". If there are unrepresented parties, remove the unrepresented party that is listed first in the elimination order.
4. Go to 2 until no party is unrepresented.

This should help preserve parties that are popular as second preferences but not as first preferences, because the elimination order will remove parties that hide the second preferences before it removes the party 
that is being hidden, thus letting the second-preference party grow in support before it is at risk of being eliminated.

Note that this doesn't solve the small-council problem. If we have:

46: L > C > R
44: R > C > L
10: C > R > L

1 seat,

then the first seat goes to L just like in Plurality. The elimination order never enters the picture."
I don't see this. Your elimination order is obviously L, R,C.  R and C are "unrepresented" so we eliminate R.
Then we have
46: L 
54: C 

Then we redistribute the seat to C and then eliminate L and confirm the final redistribution.
But I'm not on board with the spirit of this method, because it seems to give a say to voters who are efficiently represented a say in which party/candidate will represent other voters.
Chris Benham
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