Raph Frank wrote:
Another option is to use the original ballots.  In Australia, for
their PR-STV seats, the ballots are reexamined after a vacancy and the
results calculated a second time.  However, no candidate who is still
sitting in the parliament can be eliminated (i.e. you can't lose your
seat because someone else resigns).   This has some potential problems
in the maths, but it should ensure that a candidate similar to the
outgoing member is elected, while allowing the voters' choice to
determine the replacement.

I think that is a good idea, and it encourages a party to run extra
candidates so that they have 'spares' to fill vacancies.  This can
help reduce the ability of parties to perform vote management.

Schulze's STV proposal uses a proportional completion for this purpose. As far as I understand, the proportional completion is an extension of the PR result, for more seats than really exist. If a party member quits/dies/etc, he's replaced by the highest-ranked unelected party member on that proportional completion ordering. I'm not sure how this works with independents; perhaps they should just appoint a replacement ahead of time (that is, as a precaution, like with your VP or EU Parliament examples). The risk may be too low for it to be worth the bother, in which case that seat could simply be empty.

For list PR, it would be even simpler. The next candidate on the list gets the seat. I don't think this should be used if the representative decides to vote against the party, but just if he leaves, since party list PR grants enough power to the parties as it is.

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