I am breaking this off from another thread and taking a step back. @Essenzia recently proposed a system called distributed voting. It is a multi member cardinal system. Unlike the standard systems like RRV, SMV, SSS, ect which select a winner then reweights to find the next, distributed voting eliminates a candidate then reweights. This would be done down to the desired number of winners. This was not the exact formulation it was given in so I will redefine it.
- Voters score candidates like in other score systems
- Each ballot is normalized by the total score given to all remaining candidates by that voter [divide by sum(score)]
- The candidate with the lowest sum over the normalized scores is eliminated
- Return to step 2 until the number of candidates is reached.
The difference to what was originally proposed is that @Essenzia wanted voters to give the normalized ballot at voting time. There are two reasons why I think doing it this way is better. The first is that this does not require the voters to do any math. The math may not be hard but it does complicate things. It would make it harder than ranking and that is one things that cardinal systems have over ordinal systems. The second reason is that the normalized scores can be any real number. The original proposition was for the normalization to be done to 100 and the scores given would be integers only. It would have some edging and binning effects which are undesirable. In the end these are the same system so it should not make a mathematical difference.
The big advantage I see in this system is that it is closer to STV in design. STV is a sequential elimination method since you can’t really select with ranking. The institutional power is behind STV so a better system which is similar might be better for advocacy.
There is also no explicit quotas so it might be better for free riding.
A potential complication is that it might be non-monotonic. This is just my intuition based on the similarity to STV
This method is philosophically from the Vote Unitarity school of Proportional Representation. I always thought of that as a subclass of the Monroe school but this does not seem very Monroe. There are likely “sequential elimination systems” based on the Phragmen or Theile schools. For the optimal metric you could eliminate the candidate which contributes least.