Different reweighting for RRV and the concept of Vote Unitarity


I still do think you ought to retain some delegation. I don’t know enough to evaluate the Hare or Droop Quota when implemented as steps in a much larger voting system, so I’ll not suggest changes to that, though I do think it’s a little scary when you have to explain the basis of how the voting system will pick winners.

In my opinion, just go with some basic amount of delegation, or transfers if you prefer that. A voter’s unitary vote should not be subject to any kind of reweighting, it should flow somehow from candidate to candidate, which I think you’d best like with the vote going from first preference to second preference to etc. as measured by the scores on the ballot. Ties are randomly broken, or perhaps we could have minimal delegation there to let a higher preference candidate decide to whom the tie should be broken.

Essentially, I like your system, but keep it simple. Going with a fluid vote that oozes down from higher preferences to lower until every voter is satisfied feels a lot nicer than the overall scheme you proposed. You shouldn’t go with any of the remains of RRV when the whole point is to transition the scores to being cumulative and finite.

For what it’s worth, similar ruminations to yours are what led me to Asset.


FPTP: Vote for me because my main rival is a no-good, corrupt, lying politician.
IRV: Vote for me because my main rival is a no-good, corrupt, lying politician and if you rank me second I could lose.
Approval: Vote in favor of me because I am an honest, hard-working individual, I support Causes X, Y, and Z, and I am better than THOSE GUYS.
Score: Give me a high rating because I am an honest, hard-working individual and I support Causes X, Y, and Z.
Asset: Vote for me because I support causes X, Y, and Z and will only give my votes to people who support those three causes if I can help it.


I love your description of IRV. But there is a need to get stuff done, even if that means working with FairVote, right?


There is something that bothers me about the fact that if, say, a voter scores A9, B5, C4, after B is elected, that this voter will be treated as having scored A and C the same.


This seems like either a way of shoehorning delegation into score-based methods or shoehorning score into a delegation-based method. That said, delegation does has the advantage of allowing for more winners than anything that expects voters to score all the candidates, and thus finer proportionality. (Well, there’s also party lists, but in some ways that is delegation, but arguably with less choice than Asset.)


Thank you for putting this thread back on topic.

I suspect that this might be a common criticism but this is an intentional design feature. Let me run you through the logic. So lets say you voted A=9, B=5, C=4, D=0 and E=2. We sum everybodies score and B comes out on top in the first round. They are elected as being the person who maximally satisfies the most people and thus minimizes Bayesian regret. You have now been satisfied 5 out of the maximum 9. 9 being totally satisfied. This means that we can only let you influence all future candidate selections by the amount left to be satisfied, ie 9-5=4. So you ballot will now be altered to A=4, B=N/A, C=4, D=0 and E=2. Directly tying the amount of influence to the amount of satisfaction is the key.

Lets say it is a 3 seat district and the next two are C and D. This means your end satisfaction is 5 + 4 + 0 = 9 and you are exactly satisfied. It may “seem” unfair to this one individual that you could only push for A as hard as C but the point is that at each round we are minimizing the remaining Bayesian regret for those still unsatisfied by the amount they are currently unstatified. You can end up getting more than optimal satisfaction of 9 if say A, B and C were the winners, 9+5+4=18. But you would not have influences with more than 9. This will minimize the under-satisfied people. You would have been under-satisfied if C,D and E were elected. 4+0+2=6. The point is that RRV does not try to do it in this way at all. It just reduces scores to get PR but there is no care to “vote unitarity”.

Asset voting is an attempt to do this exact process but through delegation. It cannot satisfy as many people due to the complexity needed to do so. This means my system will always be proportional at a finer level than asset.

Make sense?


Your example has obvious strategic potential. If that voter knew B was a consensus pick, they probably wouldn’t give any points to B. Theoretically, if everyone gave a consensus candidate a 9, they’d all run out of points, right? I don’t fully understand the Hare and Droop quotas, so I’m probably wrong.

What part of Asset’s complexity makes it less proportional?

Your system is a good one, and I’m not going to compare it to Asset, but adding delegation here means that voters who want a second opinion can get it without having to see that second opinion themselves. It’s faster, and it also gives the frontrunners more time to negotiate, and potentially give one of the better lesser known candidates a points boost, which adds to the deliberations happening in politics.


The strategy of not voting for a popular favourite in the hope that they will be elected anyway is something which is present in all proportional systems. There is the risk that many people do this and they do not get elected. I would think that most people would vote more honestly under this than other PR systems in general since the risk of wasted vote is low.

Yes, you did miss the point of the Hare quota for the case when everybody give a consensus candidate a 9. Please see my previous reply on this thread which starts with “If 99% vote for A=9…”

Under Asset the complexity of a candidate delegating optimally is intractable in general. Maybe it is common that they can delegate in the manner that everybody would have chosen but it is at least less common to be optimal. My system is optimal under a specific metric and asset can never be better than that. If you want to choose a different metric than I have used that is fine but doing it algorithmically will always yield the maximum value. Asset voting will only get to this point some proportion of the time.

There are other metrics like the one used in Harmoic Voting. I do not like this because there is greater “satisfaction inequality” in the sense that centerist people can be very over satisfied. It is maximized on sum(score) across all voters. Mine maximizes on sum(max(score,9)) across voters. The key being that once somebody gets to 9 we stop worrying about them and focus on those who have less. Harmonic is a strict Utilitarianism view where increasing the satisfaction of somebody over satisfied is equivalent to that of somebody under satified. If anybody knows the philosophical name for the maximizing the amount of people who are satisfied I would be in your debt.


Is there a reason that capping the scores at 4 is any better than scaling them all by 4/9? (The latter is not traditional RRV. In traditional RRV, a 9-9-0-0 vote still has weight when a 9 wins; in my idea that vote would become 0-0-0-0.)


Asset isn’t as good as your system, but I think it’s rather close. Perhaps you assume that people will often have a common favorite but very different ideas on where the votes should go after that favorite, which is the kind of situation where your system comes out most ahead of Asset. I assume most people are somewhat “linear” in their opinion, meaning that a liberal generally prefers a moderate to a conservative, etc. There’s some IRV data that contradicts this slightly, but I think that politics itself would realign on many axes under any voting reform to give voters more personally relevant first and second choices, in which case the linearity is near-maximal and the difference between Asset and your system minimal. A huge conjecture though.

I don’t like the amount of math behind RRV, and I can’t account for all the slight strategies in PR methods such as the ones we’ve discussed, so I’ll simply recommend you try a few examples out where you compare the additional utility your system gives voters against the likelihood of them using certain strategies. The trouble with trying to go for a “Vote Unitarity” system is that voters may feel pressured to put all their points behind their frontrunner (the candidate who they strategically need to support to make it over the points threshold), and not their honest favorites, because they both want to maximize their influence and are scared their points won’t do as much as they want. Probably wrong since you did point out the highest points candidate in a round would win, meaning the system itself ensures you’re grouped with all other voters… But that incentive for not voting for a popular candidate is the biggest problem. Adding some level of delegation might let the popular candidates redistribute some unnecessary points, which probably makes voters want to give them points instead.

I think you’ve come up with one of the best PR methods yet, though.


RRV has a couple other issues besides Vote Unitarity, though, that this revision doesn’t address. They are somewhat related.
While insisting on Droop Proportionality (that if at least k Droop quotas put n candidates ahead of all other candidates, at least k of those n candidates should be elected), described here would require Majority in the single-winner case, which would rule out any extension of range, both regular RRV and RRV with this reweighting scheme fail this with Hare quotas. Also consider this slightly modified version of the criterion: if at least k Hare quotas put n candidates ahead of all elected candidates who aren’t among the n candidates, at least k of the n candidates should be elected. (Though for score based methods, if some of the n candidates aren’t scored 9 this might be less important.)
The other issue is that choosing winners sequentially without regard to the number of winners to be elected doesn’t always work well. See: https://www.rangevoting.org/AssetBC.html. Adding vote unitarity here helps with taking into account the number of winners a little, but only during the reweighting phase. Starting by electing the best single winner isn’t always compatible with PR.

As for fineness of proportionality: how many seats could you elect in each district? A legislature with 50 seats could not be elected all at once.


That is some great feedback @Marylander . I do not however find the “Droop proportionality criterion” compelling. It does seem to be something like the multi-candidate version of the Majoritarian criterion which I also do not think is compelling. You can either have majoritarian or low Bayesian Regret. It is a classical philosophical debate topic, majority rule vs Utilitarianism. I am 100% in the Utilitarian camp with my update that past a threshold an increase in individual utility is not an increase in global utility. Another related criteria is the “later-no-harm criterion” which is again another restatement of not wanting to take a compromise for the majority to increase overall utility.

Starting by electing the best single winner isn’t always compatible with PR but it is randomly disproportional and only slightly. When combined across many multi-member districts this effect will tend to cancel. Furthermore, exact proportionality is a little suspect. Many systems have a threshold of 5% popular vote for a party to get a seat. In the end, this system is proportional in the broad sense which puts it ahead of Score and Approval in the eyes of many.

Unless there is something I am missing this system is:

  • Better than STV because it has Monotonicity
  • Better than RRV because it has Vote Unitarity
  • Better than MMP since there are no partisan votes
  • Better than DMP because there is no vote splitting and it is non-partisan

Are there other big name contenders?

My pet system would also add the concept of local district clusters which solves a bunch other issues. Please have a look at this thread for that Local district clusters vs Multi-member districts


I’m trying to understand how the voters would be satisfied under your system versus RRV, but I need numbers and I don’t understand either system well enough to do the math. Could you make an example showing how your system, by capping each voter’s gained utility, helps the electorate more than focusing on overall utility? Also, please address how various realistic strategies might affect this.


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.