More excellent feedback @marylander. It is important to note that I define Hare Quotas in terms of score and that it gets used up. So one person could put out a total of 9 score and another could put out 90. It is hard for me to reconcile that with ‘Hare Proportionality Criterion’ in a way that my system does not pass optimally. The candidates are chosen in that exact order.
For the example: A9,B5,C5,D0 and the other half vote A0,B5,C5,D9, which results in the election of B and C. This is not really a question of Proportional Representation but a question of polarization. Polarizing systems like STV would get the two polarizing candidates mine does not. I know Score is unbiased in the single winner case but I am not sure how my reweighing changes this in multi-winner elections. I would like to be unbiased to polarization.
This debate has been covered before in the old forum. Have a look at the first picture. For me Proportional Representation is only a measure of something more important which I call Ideal Representation. Ideal Representation is that the parliament is statistically distributed in “opinion space” in the same way as the population for things that the government would decide. This is not equivalent to Proportional Representation since that has to do with parties. If there are no partisan votes in a system then the level of Proportional Representation can be a good metric for judging level Ideal Representation. I say “if” because partisan voting ruins Proportional Representation as a metric since it makes the candidates of each party more monolithic in opinions. So we want good Ideal Representation in the sense that the whole of the ideological space is covered. In this blog post it shows some plots to give an example in the common left-right political spectrum. Please see the plots. I postulate an unbiased system is better at producing a parliament with the same distribution as the public. Polarizing systems tend to have no members in the parliament who are in the center.
My reweighing could easily be applied to a harmonic voting model. They normally maximize sum(score) but my new method would maximize min(sum(score), 9). Different but totally possible. The question for all these is what reproduces the distribution of voter ideology the best with distribution of the parliament ideology. I could do simulations but I do not have time for such things unless somebody wants to pay me enough to quit my job.
Bayesian regret is another interesting question. For honest voters in the single winner case, their score is the utility of the candidate to them so score gives optimal Bayesian regret by definition. I have never seen a good definition of Bayesian regret for multi-winner cases. Warren said he has not seen one either, and if he has not I doubt it exists. The concept of maximizing min(sum(score), 9) is sort of an extension of Bayesian regret since if they get a score of 9 satisfied then they have no regret.