Different reweighting for RRV and the concept of Vote Unitarity


One thing that always bothered me about RRV is that somebody who gave a full score of 9 to the winning candidate in the first round still gets to influence subsequent rounds. In the next round their scores are reduced by half following the formula w = 1/(1+sum/9) where “sum” is the score given to elected candidates. To me this seems wrong since a voter who gets a candidate elected should influence further rounds by an amount proportional to the amount they are left unsatisfied. A voter who has elected a candidate they scored with 9 would then be fully satisfied and out of further rounds.

If a voter got a candidate elected in the first round who they scored 5 then they have 9-5=4 score remaining to be satisfied. This, 9 - sum, formula should keep track of the amount they voter has yet to be satisfied. Additional, This is the current maximum amount that they should be allowed to influence the election. So instead of reweigting by a factor after each round the scores are adjusted to min(S,9-sum) where S is the original score. The property I am trying to maintain is the “one person, one vote” concept. I call this “Vote Unitarity” and to the best of my knowledge I have invented it. It is also a multi winner generalization of Bayesian Regret. Minimizing the amount of score points left to be satisfied would minimize this sort of regret.

Aside from this reweigting change to RRV I have to make one more change to keep Proportional Representation. The only time this method would break down is when a candidate wins in surplus as define by a Hare Quota

sum(score/9)> (# voters)/(# seats)

In this case the voter need not “spend” as much of their score to meet the quota so each voter has their scores reduced by just the amount needed to produce an exact Hare Quota. ie it gets divided by W= sum(score/9) x (# seats)/(# Voters)

in summary the method would work like this

  1. All voters start with 9 score points, P
  2. When a candidate they scored, S, is elected their points are reduced
    • For a non surplus win it is reduce by the score itself ie P_new = P_old - S
    • For a surplus it is reduce less so that the Hare Quota is just met ie P_new = P_old - S/W
      where W= sum(score/9) x (# seats)/(# Voters)
  3. After each round, all remaining scores on the ballot are adjusted to the minimum of the ballot score and the current points P remaining

I realize that this is more complicated than RRV but I really think that the concept of “Vote Unitarity” is worth preserving. The surplus handling feels awkward but it works. STV does a similar thing with its surplus handling. In fact it is even less elegant since you can’t scale a rank.

Would approval voting create strong voting blocs?

Suppose 99% vote A=9. Then do you want ALL of their votes to be shredded, letting The 1% (uh, sure, that 1%) have the only say in the remaining 4 seats?

What should happen is that what is equal to 20% of the electorate should be removed, and if B and C have good ratings among the lower 99%, they will also win, and the rich people cannot force any seats without a good portion of the lower 99%.


If 99% vote for A=9 then that candidate was elected with a surplus. This means they will not have to spend all their score since the Hare Quota would be exceeded. This means they do not lose all their score points but a fraction,W, of them. This is the part of the system that ensures proportional representation. It sort of follows how STV allocates winners. It is similar to Market Based Voting except that I enforce this vote unitarity property which is like a multi-winner Bayesian Regret.


One idea would be to let voters circle or specifically mark one candidate who would have the right to score additional candidates on your behalf. That way, a voter could walk into the booth, and just vote Plurality-style. That candidate would then be responsible for filling out your RRV ballot. If a voter chooses, they could score some candidates while leaving others to their proxy.

One implementation would have candidates lock in their scores for other candidates before the election, while another would leave them free to score as they please. Another would be to let voters check a second box “freeing” their candidate from their locked in preferences.


The method I proposed here is intended to remove the necessity and utility of something like asset voting. If the candidate fills out the ballot then the assets are passed around optimally. As an advocate of Asset Voting are you convinced that this method is an improvement over standard RRV? The algorithm should behave as the asset redistributor but better.

To your modification, it is never a good idea to underestimate the laziness or stupidity of people. In the current system there are many who cannot even remember the name of the person they intend to vote for since they are only voting for a party. So we need to make the voting process less cumbersome. What you propose is a good idea except that it might allow people to behave strategically. If one new that a large fraction of the voting population would score according to a specific set then there may be a way to game that. I would have to think more about this to come up with a specific example. Also, this need not be part of the process for the ballot explicitly. As far as I know there is nothing in election rules preventing people from bringing in a sheet of paper with their scores on it and then transcribing. Parties, candidates and friends could distribute recommendations and people could follow as they see fit. I know people in Australia who do this for their STV system. That said I am not sure this addition is really adding anything which would not evolve naturally.


It is likely that in the beginning, the ability to delegate will save a lot of effort for voters, which is a concern many people have about multiple-evaluation voting systems. It’s practically guaranteed that more info would be gathered from voters choosing whether or not to delegate in the ballot box and all the info the candidate provides rather than the voter having to copy a sheet of paper - the former seems like a more “democratic” choice, whereas the latter might bring up current concerns of voters being coerced or fooled into voting a certain way, with no easy way to hold the distributors of the strategy guide accountable in any way.

The ability to delegate is not just a practice of getting more representativeness, but a fundamental change to how our politics works. Instead of making politics zero sum, we instead encourage politicians to work for different voters, but also work together. Other systems don’t do this at all. What this means for an area that adopts voter delegation is that its political class will naturally be cleansed, so that only the who are the most honest and capable of cooperating are making it to the top.

The great thing about delegating is that you also get an idea of who’s most trusted by the voters - this is a very useful thing when it comes to forming a healthy political class. You can’t get that kind of thing with just top preferences; no, it’s when voters expose themselves and candidates either deliver or betray that you really start seeing who should be gaining power and who shouldn’t. Without that kind of real-world “evaluation”, there’s no way to help good candidates rise from election to election other than just by word of mouth without a record.

I have to also say that Australian STV is incredibly complex, mainly because voters (usually) have to fill out every spot on the ballot with a rank to have their ballot even counted! This makes those voter cards so ubiquitous, but in the absence of such a strong incentive, I think the beginnings of the system will not see enough help given to voters. This also strongly affects implementation, as many will not believe that RRV is simple enough for every voter to fairly fill out. Adding delegability makes it simple once again, though we have to find answers for the new questions that brings :slight_smile:

The key here should be letting voters have greater choice, and using the power of the candidates to boost our political process. If we can get both with other added benefits, that’s just extra, though in this case, I believe those extras amount to a lot over time, maybe half as much as the whole voting reform in general.


I am still not convinced it is better. I am also not sure which of us is being more idealistic. I am asserting that taking down all the information and allocating it optimally would be best but you retort that voters will not give enough information since many will not show up or just bullet vote. On the other hand, you are asserting that this will change the type of candidate to “honest” so more will vote and the candidates will distribute the votes. But I retort that this distribution would necessarily be less optimal.

It would be good to have empirical evidence on how this would play out but that is never going to happen. In the end I would rather less voters with a better representation than vice versa. In the end, those who cannot sort out how to vote likely would not have expressed their will in a well informed manner in any system. If they choose to stay home that leaves the better informed more say.

But enough of this tangent, what about my allocation algorithm vs RRV. Mine is much closer to an asset voting system.


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.