Splitting seats

I remember hearing about a variant of plurality voting where you vote for candidates in an IRV format until the amount of support for the lowest ranked candidate is above a certain threshold. At this point, all the people on the ballot go to the legislative body and proportionally share the seat, each of them casting a partial vote based on how much of a vote they received in the election.

The idea would work as follows:

After the runoff phase,
A won 50% of the vote
B won 30% of the vote
C won 10% of the vote
D won 10% of the vote
E was eliminated in an earlier phase for having less than 5% support and votes for him were redistributed.

When candidates A-D arrive at the legislature, they split the seat so that A can cast 0.5 votes on any legislation, B casts 0.3 votes, and C and D can cast 0.1 votes each. As a whole, the “seat” casts a full vote. (Note that this is simplified. It might be that candidate A has 0.534 votes.)

I like this idea because it completely removes jerrymandering as a threat (at least as far as I can tell) and potentially breaks two party domination, while still allowing people to vote for candidates rather than parties. I also feel like this might increase voter turnout because, no matter how the election turns out, your vote counted for something.

Does this approach have a name? It’s related to STV, but I feel like its not the same.

Parts of your idea resemble Reweighted Representative aka Direct Representation or Weighted Congressmen. You can find some discussion of that system in this article: https://www.rangevoting.org/Asset.html

Maybe there is a way to do a Condorcet PR version of your proposal as well i.e. instead of eliminating and transferring, somehow pairwise comparing winner sets, like in CPO-STV.
A cardinal PR version would also be interesting, especially if the partial support information shown on a rated ballot could be made relevant to deciding how much vote power each winner has. One system that might be useful as a template for designing such a method is Sequential Monroe Voting.

The weighted congressmen sounds like the idea, but I feel like the issues they are talking about are not as hard to deal with than they make it out to be.

I’m not super attached to the IRV approach to eliminating people, but I don’t like the idea of the candidates deciding where their votes should go. There may be a strong reason you didn’t select his choice. I feel like this diminishes the agency of the voter to decide where their vote goes.

I like the way IRV ballots are designed from an understandability perspective. I consider it important for people to understand HOW their ballot is used. I also think that the vote-splitting and spoiler effects that occur in IRV is diminished by not reducing the vote to two candidates, as the issues only occurs between candidates with less than (in my example) 5% of the vote.

I am actually fairly suspicious of Condorcet enforcing schemes, as they can lead to fairly obvious insincere voting by their very nature. But perhaps a bit of Condorcet-inspired ideas could be useful.

It is possible to do Condorcet-IRV methods where some form of IRV is used if no Condorcet winner exists; these tend to enjoy similar strategy-resistance properties as IRV, such as, IIRC, “if the Condorcet winner is honestly ranked 1st by 1/3rd of all voters, no rational strategy can defeat them”
One such method is Benham’s method “sequentially eliminate candidates IRV-style and transfer ballots until someone is a Condorcet winner among the uneliminated candidates”, another is Smith-IRV which is, IIRC, “eliminate all candidates outside of the Smith Set, then run IRV”

Also, here is a further link to the Reweighted Representative system: https://www.kialo.com/reweighted-representative-gives-representatives-unequal-vote-strength-in-the-house-proportional-to-the-share-of-the-vote-5589.50

I like seeing “if the Condorcet winner is honestly ranked 1st by 1/3rd of all voters, no rational strategy can defeat them.” But I don’t see how that works if Condorcet criteria are used to determine who gets removed or who gets selected. If I know the biggest challenger to A is B, and I know that A is close to being the Condorcet Winner, then I would always vote B lowest to attempt to remove them via Condorcet regardless of how I feel about B with respect to other candidates.

I feel that a feature of a good voting system would include the fact that voting sincerely is a strong and viable strategy to get your favorite candidate in to office, and getting the 2nd place candidate in to office if the 1st place loses, etc. Ideally, the order of lower rankings on the ballot should not effect whether the higher level candidates get in (in a ranked system), while also not having spoiler effects. This would mean that voting sincerely would be the strongest strategy. (Of course, this is an ideal, so this is not necessarily possible). I believe this would improve enthusiasm for voting by allowing them to vote their conscience. Some people don’t want to vote because they can’t stomach the dishonesty required to have utility (e.g. voting for Clinton over Trump when you really want someone else like Stein). Enforcing Condorcet winners opens a system up to strategies to change the Condorcet winner, therefore I am suspicious of such systems.

But, in this context, it probably doesn’t matter as much. It might be a good idea to make sure a Condorcet winner gets in as a moderating voice within the body. Perhaps a variant of BTR-IRV to remove lower ranked candidates? That way, you don’t remove someone with a lot of secondary support easily. This could result in a compromise member of the seat being elevated above the rest, where most people agree that this person is OK whereas the other’s they might not. But when lower ranking start effecting upper rankings, I start getting nervous.

Thank you for this link. I feel like one of the cons about the system, namely that the legislature may be too large to fit in the room, is less of an issue than people might think. If we use this system, there could be fewer districts, so a 200 district area may be reduced to 50 without loss of representative power of the voters. This would allow there to be, on average, 4 people per district without increasing the size of the “room.”

Similarly, there could be rules of the house that control who can speak. Just because an extremist gets in with 5% of the vote doesn’t mean they should be allowed to address the legislature. I don’t want literal KKK members or nazis speaking before the legislature as members. To prevent things like could be a rule that a seat, when given the chance to speak as a legislator can speak now before the legislature, only one member of the “seat” may speak, as determined by a voting process within the seat (using their portion of the vote). This can happen off the floor to save the legislatures time, and perhaps could enforce stipulations, like if A is the speaker of the seat, he might have an enforceable agreement to bring up a concern of seat member B or a talking point of seat member C in exchange for their support, with a potential for written rebuttals from dissenting members to be put on the record and only spoken aloud at the request of enough members of the legislature (based on their proportion of the vote, of course).

The elimination of candidates is done based on 1st choice votes.

I think BTR can actually elect a candidate X when voters unanimously preferred candidate Y over X, similar to this example for random pairwise elimination:

For weighted power within parliament, I would advocate the following (that I’ve posted elsewhere before). This is the approval voting version:

Work out the probability of each candidate being picked given the following algorithm:

Pick a ballot at random and list the candidates approved on this ballot. Pick another ballot at random, and strike off from the list all candidates not also approved on this ballot. Continue until one candidate is left. If the number of candidates goes from >1 to 0 in one go, ignore that ballot and continue. If any tie cannot be broken, then elect the remaining candidates with equal probability.

The probabilities would be the weight in parliament.

As for score voting, I would always advocate using the KP transformation.

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Nope. The candidate D in my example will always have 0 votes. Every round will put D against some other candidate and thus lose (unless D goes against A and wins, but then B gets the majority).