In cardinal PR, the only way to guarantee your favorite party gets its proportion of seats is to give all its candidates maximum scores. But this reduces your ability to evaluate any individual candidate. In STV, ranking allows voters to evaluate individual candidates while guaranteeing proportionality for each party. The only way cardinal PR can avoid this issue is if voters are okay with slightly or somewhat consensus-biased results, or with potentially losing some seats they deserve; if they are insistent on getting their favorite in proportion, it may devolve into party-line voting and not looking at individual candidates.

To be clear, 80% of STV voters use above-the-line voting (party line), so thatâ€™s not a huge improvement. Also, if 20%+ of cardinal PR voters are okay with slightly consensus-biased results or losing a couple of seats, then the problem resolves itself. But what can be done to rectify this?

# Could cardinal PR result in less candidate-centric voting than STV?

This is all that the standard party PR criterion guarantees, yes. But stronger criteria can be made to accommodate partial disagreement within a party. For example, one I came up with says that the winner set should pass party PR even if some losersâ€™ scores were lowered on some ballots and some winnersâ€™ scores were raised. For example, if two Hare quotas of voters approved ABCD and two approved ABCDE, under this modified criterion, 4 of ABCDE would need to be elected. Thereâ€™s also extensions of ULC-PR to party factions.

Hereâ€™s another extension of party-PR: no candidate can be counted as a representative of multiple parties. In other words, it should be possible to repeatedly take a Hare quota of ballots that all vote identically (and in a binary, approval style) and have not previously been assigned to a candidate, and assign it to a member of the winner set who has not already been assigned a group of ballots, until it is no longer possible to form such a quota from the ballots that remain. (Like Monroe, but all the votes have to be from a single party.)

So if 2 quotas voted ABCD and 2 voted ABEF, then standard party PR would consider both groups of voters satisfied after AB are elected, but this criterion would require 4 of ABCDEF to be elected to satisfy both groups.

These sound brilliant, but do any current or proposed methods pass these? Also, do they fully solve the problem here?

Also, Iâ€™m just wondering, if a Nazi voter decided to vote for the mainstream parties alongside Hitler, is there any way they can free-ride off these criteria?

The first one I mentioned, which I have termed â€śIndependent Proportionalityâ€ť, is passed by all methods with approval cases of PAV, including RRV and SPAV. Iâ€™m pretty sure that Keith Edmondsâ€™ method also passes. ULC-PR is mostly only passed by quota based methods. It is tough to reconcile with IIB, to say the least. The last one is failed by PAV in the following 6 winner election:

2 ABCD

2 ABCE

2 FGH

The winners are ABFCGH, in that order.

No, because the standard PR criterion only recognizes extreme support. I also created an aggregated PR criterion that attempts to address this by counting ballots that gave a minimum score of X to a party slate and a maximum score of Y to the remaining candidates (where X>Y) as (X-Y)/MAX party votes. This can be combined with Independent Proportionality, by requiring the winner set to pass aggregated PR rather than party PR under the conditions required by the independent PR criterion. I havenâ€™t thought of a way to incorporate the criterion I described in post 3.

Voting for the regular parties under these criteria wonâ€™t help you increase your proportional allotment, only to possibly preserve it. Free riding is really the exact opposite of the behavior you described: it would be **not** voting for mainstream parties that you consider decent in order to ensure that your ballotâ€™s proportionality guarantee is applied to your fringe party and not a mainstream one.

@Keith_Edmonds, what do you think? If your method passes this, it might be like a gold standard for PR, and a proof for Vote Equity as a standard criterion, since it would be unfair for a voter to lose out on good representation because they didnâ€™t min/max.

I think my system passed but I am not 100% clear on the definition. Could you maybe rephrase?

This seems completely at odds with consensus PR, and thus Sequentially Subtracted Score. If there is a Consensus Party candidate, and Party A, B, C, and D voters give that candidate a 1/5, it could prevent one of their own parties from winning a seat. So it seems if we want totally safe party PR, we must entirely prevent later no harm violations in PR, which can be done via ranking, and probably to a near-total extent with certain cardinal PR methods.

Thus, consensus PR is an experiment. It could either decimate votersâ€™ ability to evaluate individual candidates, because they must min/max to get accurate party-line representation (though STV hardly fares better with above-the-line voting), or usher in a new era of consensus with good representation of dissatisfied minorities. I think thatâ€™s a small downside, but it still is a downside.

This sounds incredibly computationally expensive. Itâ€™s essentially running a ranking algorithm step in the middle of the cardinal algorithm.

It is a good thing. It is compramise. Only FairVote will say otherwise

Iâ€™m not questioning later no harmâ€™s many benefits, but what do you think of the potential downside it has in PR? (that a voter who wants party-line representation canâ€™t make distinctions between their partyâ€™s candidates unless they had, say a scale of 0 to 100 or 1000, because to do so jeopardizes their partyâ€™s chance of winning seats.)

Itâ€™s not at odds with consensus PR if you maintain Pareto. In the example I gave:

2 Hare quotas ABCD

2 H.Q. ABCE

2 H.Q. FGHI

By Pareto, all of A, B, and C have to be elected before either D or E. However, unlike party PR, with this criterion, if you elect A and B, then you canâ€™t say that A and B satisfy the both the top two Hare quotas and the middle two Hare quotas. You can use it to satisfy the top two H.Q.s or the middle two, or one of each, but you canâ€™t satisfy 4 H.Q.s of voters with 2 candidates. When you add C, one quota on the top or middle is still unsatisfied, so one of D or E must win.

So the consensus candidates can still win, they just canâ€™t then be used to fulfill multiple proportionality guarantees.

What consensus PR methods pass Pareto?

They actually do that?!

So this means the consensus candidates get less representation, right? How would Pareto interact with Sequentially Subtracted Score in an example? If you have a consensus candidate with a Hare Quota of points, and 5 other parties with Hare Quotas of points, but every quota of voters prefers one of the 5 over the consensus candidate, does the consensus candidate get squeezed out? Is there a possibility to maybe add overhang seats for consensus candidates?

Edit: forgot to say that only 5 seats should be up for election in this example.

I do not want pepple to vote for a party. Here in Canada we have the westminster system which is a representative government. You do not and should not vote for parties. Parties are part of the system but you delegate your democratic power to a person not an institutuon which is largely unelected. Read â€śConsiderations on a representative governmentâ€ť by Mill for details.

Anyway, this is why I will never care about partisan PR over other systems.

But to get the system implemented, you will have to work with and address the concerns of the majority that do tolerate or prefer parties, not only when passing the system but in getting advocates and donors for it.

I am not sure exactly how you define consensus PR candidates, but the answer is probably all of them. Pareto says that if all ballots score X at least as high as Y, but not vice versa, then Y should not be elected unless X is as well.

The standard party PR criterion does.

The criterion neither requires nor forbids it.

Iâ€™d say any candidate that may not be any Hare Quotaâ€™s highest-preferred candidate (a much more precise way may be to focus on only the Hare Quotas identified by Sequential Monroe), but nevertheless has a Hare Quota of points/can be elected by the cardinal PR method in question.

But not party list methods themselves, as I take it?

Well, with party list methods, no candidates are on multiple party lists, so this sort of situation never occurs.

Actually, it turns out that this criterion can only be passed by allowing for bias in the reweighting order. By a biased reweighting order, I mean that not all ballots that approved an elected candidate pay an equal portion of their weight. Keithâ€™s method has an unbiased reweighting order- each ballotâ€™s cost is proportional to its weight. So it will not always pass. As an example,

While it passes in this case, if the FGH voters split into 3 groups each with 2/3 of a quota, then the result is the same as in PAV.

Optimal Monroe may still pass, and would in this case. For Sequential Monroe, it would probably depend on how ties are broken.

Would Sequentially Shrinking Quota pass?

Also, are there any cardinal PR methods likely to be viable that can accommodate partial disagreement within a party without defaulting to an STV-like ordinal algorithm? I think it might be possible if the ordinal algorithm (i.e. look at which set of candidates ~~the most voters~~ a Hare Quota of voters, or whateverâ€™s closest to that, prefer, elect the highest-utility of them) is only run on the last seat, though that somewhat defeats the purpose of cardinal PR.

Iâ€™m trying to find a way to avoid the following scenarios (https://www.reddit.com/r/RanktheVote/comments/d09lyi/an_interesting_take_on_pr/ez8nu2e/):

Number Ballots 50 a1:5 a2:5 b1:3 b2:3 c1:0 c2:0 50 a1:0 a2:0 b1:3 b2:3 c1:5 c2:5

After reweighting b2 only scores 50 whereas all other candidates score 125; so the final set is going to be b1 and any candidate except b2 with equal probability.

I fundamentally disagree with this result. For a PR method, the proper return here is something like {a1, c1}.

and

Number Ballots 49 a1:5 a2:5 a3:5 b1:0 b2:0 b3:0 17 a1:0 a2:0 a3:0 b1:5 b2:4 b3:4 17 a1:0 a2:0 a3:0 b1:4 b2:5 b3:4 17 a1:0 a2:0 a3:0 b1:4 b2:4 b3:5

Number Ballots 49 a2:1.454 a3:1.454 b2:0 b3:0 17 a2:0 a3:0 b2:0.393 b3:0.393 17 a2:0 a3:0 b2:2.114 b3:1.114 17 a2:0 a3:0 b2:1.114 b3:2.114 So either a2 or a3 wins the last seat. I think most people would (myself included) argue that this is an incorrect result.

No, SSQ would not pass. For a sequential method to pass, it would have to use information about votes for candidates who havenâ€™t been elected yet to decide which ballots to spend. (Or have a way of changing which ballots get spent.) While SSQ has a way of changing how many votes are spent per candidate, it doesnâ€™t have a way of biasing the order in which ballots are used. It might be possible to modify SSQ to do this, but it might make calculation more challenging.