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

[Chris Benham]

Vidar wrote:
"If I'm not to use a quota, but rather something like Sainte-Laguë as it's done today, how would I know when to start excluding the smaller parties?"
 
When one (or more) of them doesn't have a seat according to the initial (trial) apportionment.
 
*Use the best formula for apportioning seats in List PR 
(based on first preference votes).
If every list/party has at least one seat, finish.

Otherwise, eliminate the party voted top on the fewest ballots and promote the next most preferred uneliminated candidate on those ballots to top. (In other words transfer the vote, Alternative Vote/IRV style).

Based on the updated tallies (that include votes transferred from eliminated parties) repeat until the final apportionment leaves no party without a seat.*

"As for eliminating the party voted top on fewest ballots, that does seem to have a weakness I'm trying to mend. For example, take the following votes:

7 A,B,E,C,D
9 C,B,D,E,A
6 B,D,E,A,C

Here B would be eliminated first, even though B is popular among all these voters, where as A and C are popular among fewer voters. I believe Ranked Pairs & Beatpath would rank B above A & C in this scenario.
This is why I'm contemplating on rather eliminating the candidates that are least represented on the ballots regardless of rank, and rather fall back to eliminate the candidate with least first preference votes if
there are multiple candidates least represented on ballots. I'm not entirely certain of the implications of such a change, though. And for it to have any effect, you would have to limit the amount of preferences instead of listing all candidates as I did in the example above."

I think it is desirable that voters are free to rank as many candidates as they wish. My suggestion is simpler and meets the Later-no-Harm criterion. 

The "problem" you allude to I am sure would affect very few seats. 

Chris Benham
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