@SaraWolk I agree with you. When I say majoritarian, I only mean in the sense of Lijphart’s ontology, because you’re right that ultimately it isn’t even actually majoritarian but largely an illusion of it.

I’m curious about examples of this: “the center-squeeze effect ensures that over time the two opposing factions become more and more polarized.” I feel you know more than I do in this area, but it seems possible to me that there could be a stable polarization that doesn’t necessarily explode. In principle, as long as there is a large enough population of centrists, if one party leans too far in one direction, naively I would imagine the other could gain more power by appealing to those centrists than by appealing to the fringes.

Naivety aside, I think you’re probably right. The problem is that even if there is a population of centrists, if the representatives aren’t held accountable to them, then the parties themselves seem to have no good reason not to polarize once they’ve duopolized the political market. I’m really just curious about what causes that—is polarization actually steadily preferred? Or is it just a matter of time and drift before one party tips over the edge? It seems like the opposite of Hotelling’s law.

I also don’t think multiparty systems or PR for instance alone would solve the problem, there are examples of both systems falling to authoritarianism, and resistance depends on many contingent factors that ultimately bring about your main point, which is preventing extremists from gaining leverage or control.

Hopefully we can get some technical voting reform and see whether things change. Approval would be great.

This looks quite nice. Presumably for PR elections? I came up with something similarish when doing a mixed member system that used score/approval ballots, and you could vote for candidates and their parties together / separately.

@toby-pereira I agree with this. Something in that spirit I am considering is that the power allocations can still be traced back to ballots. For example, if the seated representatives and powers were {A:45, B:35, C:20}, in principle, those single seats could be subdivided into multiple seats of roughly equal power, depending on the candidate pool (i.e. how many candidates are available).

Possibly, a sub-election could be run to determine the representatives within the A:45 group, etc. Maybe they could be given 4 seats, the B:35 group 3 seats, and C:20 2 seats. That could refine representation, some candidates might pick up multiple seats. It’s probably getting messy and complicated, it essentially becomes a hierarchical partitioning of ballots. I’m not sure what to make of that prospect, it starts looking like a network/phylogenetic tree or forest architecture, and that can become arbitrary fast.

I do see what you mean. An individual voter may actually prefer a particular coalition of candidates, rather than just want to get their top guy in. I wonder if non-strict rankings and distributed power would mitigate this issue, or for instance, if the A:45 group's sub-election guaranteed a seat for A, and ran the election on the remaining candidates, that might align with the spirit of preference for whole coalitions.

You definitely are more familiar with this space than I am, so I wager some of my objections may be non-issues when one considers alternative PR methods. But it seems to me that in this case, pushing for coalitions that respect single individual preferences for whole coalitions can lean toward reduced diversity and reduced minority representation. Is that inaccurate? Or is that a common tradeoff issue in PR systems?

“Would the weighting purely count towards their voting power in the elected body, or does it have other effects such as more time to speak?”

Yeah, it does beg some questions.

EDIT: After multiple adjustments made to guard against clone dependence and tactical voting, there is a non-monotonicity issue in my latest version (/branch, it is not my original concept so I don’t claim ownership in any way), where a minority faction can gain strictly preferred representation in the form of a seated candidate by merely withholding approval for that candidate. I have a concrete example of this, and may try to see how to address it. It may be due to something unnecessary.

@tec referenda are interesting as an example, I would say they are more efficient in a sense, but the cost of that can be coherency. For example, referenda in California have led to incoherent policies, because the public often wants to have its cake and eat it too: the public wants service X, but simultaneously doesn’t want to pay for it, so they vote for X but also vote against tax increases that would pay for X. This effectively forces the government to borrow to reconcile public demands, which leads to debt that the public also doesn’t want.

The government then gets criticized for borrowing, but in a sense, that is misplaced responsibility—the direct translation of an incoherent set of policies is the source of the issue, and borrowing is a symptom. This shows that representatives also serve the role of taking on coherent responsibility for coherent policy decisions, but citizens’ policy referenda can undermine that role in the kind of situation I described. Probably, the effects of this kind are less severe or even negligible in smaller, more internally cohesive populations like in Switzerland.

Feedback is absolutely necessary, and structural issues as you indicate are major obstacles. If SAVE is a policy proposal generator, it seems to serve the role of a structured public forum. Is that accurate in your view? It seems like a more democratized form of a special interest group. How would the interests become translated into policy?

I made a bit of conceptual progress with a potential proof (or route to a counterexample?) of participation for approval vs. B2R.

The setup is as follows: E is an electorate, C is a candidate set, and v is some single new voter that when combined with E forms E'=EU{v}.
The electoral processes of interest are then E(C) and E'(C), where we hope that participation is satisfied in the sense that if the winner of E(C) is W, and the winner of E'(C) is W', then v does not strictly prefer W to W'.

We can consider the sequence of B2R losers L1, L2, ... Lk, and the corresponding L1', L2', ... Lk'.
Then since under B2R the first k losers can never include the top-sorted candidate who is the adversary of the B2R survivor, it follows that the participation property will propagate by an inductive hypothesis if at any point (as in for some k), the sets {L1, L2, .. Lk} and {L1', L2', ... Lk'} coincide.
It could also be possibly useful to know that B2R is equivalent to BNR. Furthermore, the methodology is only really of interest when there are more than two candidates.

In any case, I think this method makes sure that the winner is either a highly approved candidate, or a candidate that a majority prefers over a highly approved candidate, which to me is an interesting guarantee. I still have not been able to find an example of participation failure... I have found instances though where the Condorcet loser is elected. Still, the Condorcet loser criterion seems only possible to fail by small chance when small electorates vote over very few candidates.

@wolftune Oh I see, the link is just from someone's website not something you wrote up. Got it, sorry.

I guess where I had seen the description of a "simplified variant" was on the ElectoWiki site, at the bottom of the page. https://electowiki.org/wiki/Bottom-Two-Runoff_IRV

Simplified Variant
If you remove the redistribution step, leaving the candidates in the initial 1st choice sort order for the entire process, BTR-IRV becomes precinct summable. Vote counting only requires the 1st choice vote counts and the pairwise preference matrix from each precinct, not the complete ranking counts.

I think it's an interesting difference. Using your paper ballot example, this would mean putting the ballots into piles based on first choices only, and never redistributing them for the purposes of selecting the bottom two candidates in any round. This is what I understood from that write-up that is linked, as it does not mention any redistribution. It's "simpler" in the sense that you can skip the redistribution process at each step. It is also "simpler" in the compilation complexity sense, that it is precinct summable.

It raises an interesting question- if someone were to go to an IRV advocate and pitch them on a tweak, which variant to propose? BTR-IRV with distribution is closer to traditional IRV, so perhaps that is a reason to propose it, as it is more similar to traditional IRV. But on the other hand, BTR-IRV without distribution is simpler in some ways, which can be viewed as a virtue as well.

It's also worth thinking about how much the distinction matters in practice. Curious if anyone has thoughts on that.

@toby-pereira apparently so, because they left. But honestly in terms of the purpose of a forum, that doesn’t really subtract from anything.

Anyway, this original post was made well before RFK Jr.’s (imo reluctant) alignment with Trump. At least one of RFK Jr.’s predictions was correct, namely that Biden and/or Harris would not beat Trump. His “no spoiler” pledge would have given beating Trump the greatest possible chance, but Democrats refused to cooperate because they are power hungry, greedy, and benefit too much from the duopoly to concede to a third party candidate, even at the cost of Trump winning.

IMO, that’s primarily why RFK Jr. angled against them, in game theory terms it was as a punishment. It was a textbook failed prisoner’s dilemma, and they got a taste of their own medicine in a way that hurt everybody and could have been avoided. But I digress.

There is an online obituary if you want to read it here.

@kodos I've changed it so new users have to register with an e-mail address. I don't think that's too onerous, and it should make the problem go away.

@jack-waugh but that’s always the tradeoff with score systems, which is why people bullet vote and/or min-max (translate to approval). I totally understand what you’re saying though.

I’m not saying the “Condorcet adversary” should be the score winner, just that they should be a strong alternative. Your approval-seeded Llull ballot could accommodate an approval winner as the Condorcet/Smith-method’s adversary, for example.

I think a “rank with approval cutoff” ballot makes sense. Then there could be the approval winner, and, say, the B2R (Smith compliant) winner, followed by an independent head-to-head.

https://forby.io/

@toby-pereira said in General stuff about approval/cardinal PR:

This project hasn't purely been altruistic - it's been helpful to me by laying everything out for reworking my COWPEA paper!

And the new version can be seen here (as I mentioned in the separate COWPEA thread anyway).

The paper has been updated and some errors corrected.

Thank you both for keeping an eye on this and deleting the spam. If you have suggestions for the settings I'm open to whatever seems like the best option. I don't have strong opinions either way as long as people like you both are taking care of it if it does occur.

If that wasn't the case I'd say we should look into other options.

I understand. Will do.