Filling Vacancies in PR Systems

When a vacancy occurs in a single member district, it is often filled through a special/by election. In a PR system, this might break proportionality unless all the seats in a district or cluster go vacant at once. Giving some official the power to fill vacancies also may not maintain proportionality, and worse, this power is ripe for abuse (see: Rod Blagojevich).
One way of filling a seat could be to rerun the election on the original ballots with the departing representatives disqualified and the other original winners assured election (this has been done with non-list STV.) For an optimization method, this would be easy: limit the possible winner sets to those that contain the remaining reps. For methods such as RRV, where the order in which the previous candidates were elected has no effect on a given round, the remaining reps could be declared already elected, and the election would be rerun from there. For methods such as Sequential Monroe where the order of election matters, the two best options seem to be:

  • Declare the order of election of the remaining reps in the rerun to be the same as that of the original election. So in the early rounds of the rerun, declare the winner to be the remaining rep who was seated earliest in the original election, (ignoring who the method actually says to seat, but using its reweight step.) Repeat until all of the remaining reps have been seated. Then use the method normally to fill the remaining seats.
  • Rerun the election normally, but disqualify all candidates except the remaining reps until all remaining reps have been seated. The candidates seated after the remaining reps fill the vacancies.

For Sequential Monroe, you can also just elect the candidate with the highest average score among the hare quota of votes belonging to the candidate that last held that vacant seat.

1 Like

Also, one interesting scenario that would break all of these vacancy filling procedures would be when all the candidates ran uncontested (the number of candidates equaled the number of seats). When a candidate steps down in that scenario perhaps an actual election (where new ballots are used and the other candidates can lose their seats) should be held in that multiwinner district.

1 Like

The departing representative might have been from a small party that only fielded one candidate because they thought they had no chance of getting two. So under a system that uses the old ballots, that party is now excluded, arguably unfairly.

1 Like

It’s a wild idea, but maybe you could require a 2/3rds majority for any candidate to be seated in a vacancy by-election? That mostly ensures they have the support necessary to avoid majoritarianism in the legislature.

If everyone knows that this is the rule beforehand, this could be less likely to happen. When this sort of replacement system has been used with STV, for example, candidates often had a couple of “running mates” who their supporters were to rank just below them. Then if someone had to leave their seat, it would go to a running mate.

That could get cumbersome if you have about 10 real candidates in the race, and maybe 10 to 20 more running mates, no? Though with vote management strategies in the mix, maybe not as many would need to be ranked.

1 Like

What do you do if no one gets the required level of support?

First off, I’d suggest this as a last resort if no other ways of filling the seat are possible. Second, I might even support the by-election being optionally called, only if government ministers think someone can win that level of support. Third, if nobody wins, here’s an idea: any legislators who voted with the vacant seat at least 90% of the time are given a vote. All those with votes decide who the new legislator should be. If nobody voted 90% of the time that way, then leave the seat empty. After all, this is a rather long list of measures to go through. Also, I’d suggest maybe a quality tiebreaker: if the original ballots suggest a replacement shim voters barely liked, meanwhile there were a significant number of legislators who voted in line with that person 95%+ of the time, perhaps we ought to trust the legislators to pick the most satisfying replacement. One potential problem I see is people starting to vote in line with others on uncontroversial votes to gain power, so maybe only close legislative votes (some option won with <5%/7% margin) ought to count for deciding who gets to fill the vacancy.

Leaving the seat vacant has to be a temporary solution; you can’t just fill it in the next election when the next election isn’t for more than another year or so. This is especially true for smaller assemblies like a city council. Giving the vote to a member with a similar voting record would also be harder for smaller assemblies since the chance of finding someone who votes very similarly to the departing rep is smaller.

Another temporary way of addressing the problem might be to put a 2/3rds majority requirement in the legislature itself to fill the vacancy. That way, there is a lot of time for the members to find a compromise legislator. Could sortition play some role here as well? Either pick the new members randomly from the population if a few spots are open, or, more preferably (but still problematic), assemble a Citizens’ Assembly which picks the new seats, and perhaps has a 2/3rds majority requirement there as well to decide who should fill the seats. A combination of all these various ideas ought to yield solutions a large portion of the time. One other idea I have heard in the context of California, where I believe voters keep their ballot stubs from their mail-in ballots, is to somehow track how much voting power each voter’s ballot has, then ask them to bring that stub to a Recall election. Perhaps the same can be implemented for byelections, though not without strenuous objection.

I previously mentioned that choosing a successor based on the previous ballots has been used with STV. Here is an example (although arguably a poorly implemented one):
Cambridge, MA, which uses STV to elect its city council fills vacancies by running IRV on the ballots that were credited the departing councilmember at the end of the original election.
Source: https://www.opavote.com/methods/cambridge-stv-rules