If you have an allocation game dividing a budget, a pizza, etc... this game is zero-sum in the sense that a you getting a slice of pizza is a slice that isn't going to me.

If you are negotiating with an agent who you are unsure is altruistic, rational, or spiteful there is a strategic incentive to misrepresent as a spiteful agent. An altruistic agent gets less than their fair share and a spiteful agent gets more than the rational agent if they can credibly convince other agents they are spiteful. It is worth it to pay off a spiteful agent rather than provoke it.

So if you are trying to optimize for the social choice there's a big problem with spiteful agents. With limited information all agents are incentivized to misrepresent as spiteful and over-represent how much they care about minor concerns. And for making social choice with limited resources there is a genuine zero-sum nature to the problem. Rational agents operating in a zero-sum environment will behave spitefully (you having it is negatively correlated with me having it.)

So with that irrationality baked in, if we could magically find what the social choice was, with spiteful agents the social choice isn't very sociable. And spiteful agents should be common under resource constraints. This correlation between individual's utility functions will also heavily restrain the types of group choice sets which exist.

@toby-pereira Thanks for the feedback!

National elections generally take place several years apart and a lot can change in between, and so voters wouldn't be able to apply game theory in the same way as they would with multiple elections close together under the same conditions. And also I imagine people in the study are more likely to be "clued up" than the average member of the public.

One of my goals is looking towards what the long-run equalibria might be after people have figured out the system. So in this way I see that as a plus.

So that raises a question - with multiple elections, will it just be the same conditions each time just to see how the methods behave in these ideal conditions, or will certain variables change to make it more "realistic", or possibly you'd model both? Both would be interesting in their own ways.

In trying to set up the models one of my conclusions is that a "correct" set of parameters doesn't exist. I think instead of trying to make a study "correct" or "accurate" it would be more useful to search for robustness. A common result of repeated games is multiple Nash Equalibria. Another common result is sensitive Nash Equalibria. So if one number changes slightly a whole new set of equalibria might be optimal now. So I think it is important to vary conditions to see if an equilibrium is stable.

Reading on different strategies and failure conditions of voting systems you come across some really weird ones where it is technically optimal to do make some really weird decision. But that often requires very specific information. An important concept I came across while brushing up on my game theory is imperfect and incomplete information. When you change the information available it can sometimes change what the Nash Equilibrium strategy is. There's also an idea that a strategy might not be optimal over any specific set of game parameters but is optimal when you are unsure of the exact parameters. The more limited the information the simpler a game sometimes becomes.

Yes, for PR elections. Candidates from the voter's district could be optionally identified by name in bold font.

@cfrank If others have examples, simulations, or citations for my claim that "over time the two opposing factions become more and more polarized” I'd love to have those on hand too. I'm not sure I'm referencing any one thing I've read or heard in particular, but more putting multiple things together to get the big picture.

On the math alone I think you're right that the center is an important block for the two parties to court as well, but in practice I think that that incentive is outweighed by the other perverse social incentives to demonize the other side, to punish "traitors" considering switching, and so on.

Cancelling people who question the party line costs center voters, but it also discourages others from following. I think this was the subliminal Democratic Party tactic over the last decade that paid dividends for a while but then ultimately lost them the "big-tent" advantage and the presidency. I'm not saying it was an intentional strategy. There are big cultural forces at play here. That's obviously my own personal opinion.

Back on topic: As the narrative gets dominated by two polarized factions and the middle is silenced, the real middle (the center of public opinion) almost ceases to be a part of the political spectrum because it's doesn't actually map on to the left, right, and swing voter boxes.

Identifying and presenting consensus win-win policy and then getting it passed is the goal. We need to incentivise and empower that one way or another.

@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.