# What are the best ways to do allocated cardinal PR in public elections?

The Wolf Committee, the currently leading committee for choosing great cardinal PR methods, has not yet seriously considered an allocated cardinal PR method. As allocated PR methods are, essentially, almost all of the PR methods that have ever been implemented, I think they must be included and given a fair chance to make their case before they can be ruled on. So, with the constraint in mind that the committee is not too interested in allocated PR, and so might only want to examine the few best that there are, what are the best allocated cardinal PR methods practical enough to be passed and implemented for public elections?

I think Apportioned Cardinal Voting with any of the approaches discussed at https://www.reddit.com/r/RanktheVote/comments/cw7ep6/what_would_you_guys_think_of_sequential_monroe/ would be best, but the Monroe version of Utilitarian Sum vs Monroe Selection might be good enough too.

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In what ways do you think apportioned cardinal voting is superior to something like sequential Monroe or even just normal score selection + normal allocation?

Does ACVâ€™s lack of clone-proofness or possible lack of monotonicity bother you at all?

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Itâ€™s not superior, but sequential Monroe seems too complex to be viable. If Iâ€™m wrong on that though, then itâ€™d be great to have that simulated as well.

How would this differ from ACV? Is this simply using the â€śScore for Candidateâ€ť metric rather than â€śScore - Mean of Scoresâ€ť?

I donâ€™t know enough about either of those. If not using the â€śScore - Mean of Scores on Ballotâ€ť metric means ACV has monotonicity and clone-proofness restored, then Iâ€™d be fine with just using Score for Candidate as the metric. Iâ€™m guessing the benefit of Score - Mean of Scores on Ballot outweighs the harm caused by those monotonicity and clone-proofness failures, but thatâ€™s not my main concern; Iâ€™m more interested in getting any kind of viable allocated PR proposal vetted by the committee so that it can give a strongly reasoned rationale for or against allocated PR methods (cardinal or otherwise) when it makes its final choice.

Itâ€™s definitly a big part of it but itâ€™s not the only thing.

Thereâ€™s also that step in the purple box about selecting the winner who wins a score voting election among the quota of ballots that most support the candidate who would of won if you didnâ€™t have this rule (and repeat if this new candidate doesnâ€™t win their own quota). This rule is another bad way of fixing a problem because now if a winner doesnâ€™t win their own quota (and if they donâ€™t, it will likely be because of candidate cloning), what ballots count towards choosing the winner for that round is now going to be determined by a completely arbitrary variable: what score voters give to some candidate who may not win a seat. Ciaran may be good at noticing flaws but heâ€™s also terrible at fixing them. If youâ€™re not going to pick a winner like in sequential Monroe, a better solution would be to just see if the candidate with the 2nd highest score wins their quota (and if not, the 3rd highest, etc.)

While the loss of clone-proofness is just caused by the â€śScore - Mean of Scores on Ballotâ€ť, that along with the winner selection are both likely violate monotonicty so you would need probably need to git rid of both of them to get both clone-proofness and monotonicty. Though if strip all that away, what you have left is just allocated score voting (normal score selection + allocation), which is one of the two methods I asked you why you prefer ACV over.

I think, but would need simulations to prove, that prioritizing unsatisfied voters via the â€śScore - Mean of Scoresâ€ť metric would yield a lot more voter utility under honest voting. I suppose Iâ€™d also need simulations (maybe each candidate has a clone automatically) to see how much less utility ACV yields under strategic voting compared to allocated score voting. For now, simply simulating allocated score voting should give us an approximate enough result to decide whether the allocated category of PR methods are worth further consideration or not.

You would not only need to simulate normal strategic voting by just voters, but also their use of write in candidates to lower a voterâ€™s mean score (if thatâ€™s allowed), as well as candidates (both regular candidates and candidates that are practically clones of another candidate that are just there to help their original) that strategically entered or left the race in order to affect voter mean score averages, which are things that I donâ€™t think ever been simulated in VSE sims before.

I just donâ€™t know what Ciaran was thinking with this method.

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So, assuming we can come to a consensus here on allocated score voting as the â€śviableâ€ť allocated cardinal PR method, what are the particular implementation details to be simulated? Take the score winner and allocate a Hare Quota of ballots based on highest scores first, and fractional surplus handling? Is there anything else anyone would like to add to that, like how to deal with identical ballots in choosing for the quota?

Explain what you mean. I think thatâ€™s solved by fractional surplus handling.

Fractional surplus handling makes the system no longer really allocative. Jameson had an idea for this where you choose people based on how they scored others

Well technically, but itâ€™s the same basic idea. Also fractional surplus handling is the only way to preserve properties like the independence of irrelevant alternatives (and maybe even some very rare violations of monotonicity) unless you use a nondeterministic allocation procedure like Ireland does where they allow the votes passing the surplus to be chosen at random. The only benefit I see to using a tie-breaking metric like the one Jameson came up with rather then fractional allocation is practicality.

Do you think there would be enough viability benefits from the more practical metrics that they ought to take precedence in simulation over fractional allocation? Or would the quality difference be minimal?

Fractional surpluses should be used whenever possible, but in most situations they might be much more impracticable so yes.

Wait, how can a fractional surplus be impossible?

OK maybe impossible is too strong a word. But whenever computers arenâ€™t involved, it might be pretty difficult since you would have to keep track of how much weight each ballot has: you canâ€™t just determine that by looking at the ballot like in RRV; or at-least so I thought. Now that I think about it, it is more do-able if you keep track of what the cut-off-score was for each previous winner, and then keep track of what weight a ballot would have based on whether it gave the cut-off score or a score below the cut-off score for each winner (below or equal to cut-off for 1st winner? below or equal to cut-off for 2st winner? etc). Though this would still make tabulation much harder but maybe not as hard as STV.

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We need to be technically and practically accurate for a system to be viable. This is why I have avoided allocation methods. They get very complicated if you try to do it properly.

STV is a viable method, and thatâ€™s allocated and more complex than whatâ€™s being discussed here. Certainly, it might be possible to get an allocated cardinal method passed in places that have chosen to adopt Score or STAR Voting for their single-winner elections. And the Equal Vote Coalition has some incentive to consider allocation, as it fits with STARâ€™s overall bias towards group preference rather than utility, though it wonâ€™t matter much if a sufficiently proportional consensus PR method is chosen, or at least, one where voters can vote strategically with enough ease to get more proportional results.

OK lets put surplus handling aside for now. If we aretruely going to be allocative in the STV sense then we can do random like Ireland.

I guess its either sequential Monroe or Utilitarian then.

It might be a good idea to simulate Approval Voting used as the baseline method for PR. That would probably lower utility under honest voting but might decrease the likelihood of minorities winning majorities or otherwise make things more proportional under more strategic voting, because it makes it less likely for all voters to spend voting power on a candidate they only somewhat like.