Different reweighting for RRV and the concept of Vote Unitarity


The Droop Proportionality Criterion is indeed a multi winner analogue to the ‘Mutual Majority Criterion’. However, the single winner case of a ‘Hare Proportionality Criterion’ would require that if a set of candidates were unanimously preferred to all others, that a candidate in that set is elected. The modified version I described in the previous post would require in the single winner case that if a candidate A is unanimously preferred to B, then B can’t win. (The modified version with Droop Quotas would be impossible; in the single winner case it’s “if a candidate A is majority preferred to B, then B can’t win.”)
It’s worth noting that Droop-STV fails the modified HPC:
With 3 winners and the ballots 5 a>d; 6 d; 8 f>a; 20 b>c, STV elects b,c, and d, but 13 of the 39 voters preferred a to every winner.
However, I am thinking that the modified HPC is more restrictive than my original concern that caused me to bring it up, specifically, cases like this: 2 winners, half the voters vote A9,B5,C5,D0 and the other half vote A0,B5,C5,D9, which results in the election of B and C. It’s not an indefensible decision, but it’s also not really PR.
I think the best Score-PR method would probably be one of the optimization based ones. Unfortunately they may be too complicated to be attainable.
That said, I can understand the value of having Vote Unitarity, and it would be interesting to see whether this change leads to an improvement over RRV in BR simulations.


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.


Can a legislature of one picked by Score be more satisfying than the bill-passing majority of a Ideally Representative legislature? This is a conundrum which makes PR look like only the first step, with us then requiring the use of Score or any utilitarian voting system in the legislature as well.


I am not sure I follow. I made another post about my thoughts on what I think you are talking about Asset Voting and Government Formation


Essentially, one person maximizing everyone’s utilities can make bills that maximize everyone’s utility, while a PR legislature passes bills that favor the majority. The only way to make PR, utilitarian is to have Asset or Score used in the legislature to pass laws.


Ahh I think I get it. A single benevolent “monarch” could be better than a parliament if they were chosen optimally and had knowledge of all citizens desires and expertise on all topics. I would agree with that but I believe that the “if” would never be satisfied. There is a lot on this in John S. Mill’s “Considerations on a representative government” and I don’t think I can summarise. T. Sowell also covers it in “Intellectuals and society”. The hardest if to satisfy is the knowledge part.

About a binary approval vote on bills vs a score vote. I think that does not take into account the nature of the development of bills. They go through many revisions in an effort to satifsy every bodies concerns and get a majority vote. I would argue the iterative approach here takes many steps towards optimizing national.


True, but at the end of the day, there’s actually punishment for legislators who don’t pass bills the way they said they would from voters. With a better voting system for passing laws, you could have amendments evaluated at the same time, and a legislator could legitimately say he had to give up X to get Y - the whole point of democracy. The current legislative process is just symbolic representation for the minority.