I think there are many of us here who prefer some voting system or another over approval voting. I also think there is room for improvement. However, approval voting has a huge advantage in its simplicity and potential for integration into existing infrastructure. This is totally besides the comparisons to make in terms of game theoretical stability with Condorcet methods and expressivity with Score or others.

My thought is that, if we are really going to make progress by consolidating our support behind a single voting system, then realistically, Approval voting fits the bill. That isn’t to say that it should be the final destination for voting reform, but it would absolutely be a major step forward. While IRV is something of a tokenism, Approval would be an actual game changer.

Any thoughts about this are welcome.

This is a minor attempt to modify Condorcet methods in a simple way to become more responsive to broader consensus and supermajority power. It’s sort of like the reverse of STAR and may already be a system that I don’t know the name of. In my opinion, the majority criterion is not necessarily a good thing in itself, since it enables tyrannical majorities to force highly divisive candidates to win elections, which is why I’ve been trying pretty actively to find some way to escape it.

For the moment I will assume that a Condorcet winner exists in every relevant case, and otherwise defer the replacement to another system.

First, find the Condorcet winner, which will be called the “primary” Condorcet winner. Next, find the “secondary” Condorcet winner, which is the Condorcet winner from the same ballots where the primary Condorcet winner is removed everywhere.

Define the Borda difference from B to A on a ballot as the signed difference in their ranks. For example, the Borda difference from B to A on the ballot A>B>C>D is +1, and on C>B>D>A is -2.

If A and B are the primary and secondary Condorcet winners, respectively, then we tally all of the Borda differences from B to A. If the difference is positive (or above some threshold), then A wins, and if it is negative or zero (or not above the threshold), then B wins.

For example, consider the following election:

A>B>C>D [30%]
A>B>D>C [21%]
C>B>D>A [40%]
D>B>C>A [9%]

In this case, A is a highly divisive majoritarian candidate and is the primary Condorcet winner. B is easily seen to be the secondary Condorcet winner. The net Borda difference from B to A is

(0.3+0.21)-2(0.4+0.09)<0

Therefore B would be chosen as the winner in this case.

Some notes about this method:
It certainly does not satisfy the Condorcet criterion, nor does it satisfy the majority criterion. These are both necessarily sacrificed in an attempt to prevent highly divisive candidates from winning the election. It does reduce to majority rule in the case of two candidates, and it does satisfy the Condorcet loser criterion, as well as monotonicity and is clearly polynomial time. It can also be modified to use some other metric in the runoff based on the ballot-wise Borda differences.

Continuing with the above example, suppose that the divisive majority attempts to bury B, which is the top competitor to A.
This will change the ballots to something like

A>C>D>B [30%]
A>D>C>B [21%]
C>B>D>A [40%]
D>B>C>A [9%]

And if the described mechanism is used in this case, we will find instead that C is elected. So burial has backfired if B is "honestly" preferred over C by the divisive majority, and they would have been better off indicating their honest preference and electing B.

And again, suppose that the divisive majority decides to bury the top two competitors to A, namely B and C, below D, keeping the order of honest preference between them. We will find

A>D>B>C [30%]
A>D>B>C [21%]
C>B>D>A [40%]
D>B>C>A [9%]

In this case, the secondary Condorcet winner is D, and the mechanism will in fact elect D, again a worse outcome for the tactical voters.

Finally, suppose that they swap the order of honest preference and vote as

A>D>C>B [30%]
A>D>C>B [21%]
C>B>D>A [40%]
D>B>C>A [9%]

Still this elects D.

As a general description, this method will elect the Condorcet winner unless they are too divisive, in which case it will elect the secondary Condorcet winner, which will necessarily be less divisive. I believe that choosing the runoff to be between the primary and secondary Condorcet winners should maintain much of the stability of Condorcet methods, while the Borda runoff punishes burial and simultaneously addresses highly divisive candidates.

This is a concept I had in mind which may already have been described, although not all of the logistics are necessarily hashed out and there may be issues with it. The idea is described below, but first I want to make a connection to “cake-cutting.” The standard cake-cutting problem is when two greedy agents are going to try to share a cake fairly without an external arbiter. An elegant solution is a simple procedure where one agent is allowed to cut the cake into two pieces, and the other agent is allowed to choose which piece to take for themselves. The first agent will have incentive to cut the cake as evenly as discernible, since the second agent will try to take whichever piece is larger. In the end, neither agent should have any misgivings about their piece of cake.

So this is my attempt to apply that kind of procedure to political parties and representatives. Forgive my lack of education regarding how political parties work:

• There should be a government body that registers political parties and demands the compliance of all political parties to its procedures in order for them to acquire seats for representation;
• (Eyebrow raising, but you might see why...) Every voter must register as a member of exactly one political party in order to cast a ballot (?);
• Each political party A is initially reserved a number of seats in proportion to the number of voters with membership in A; the fraction of seats reserved for A is P(A). however
• For each pair of political parties A and B (where possibly B=A), a fraction of seats totaling P(A~B):=P(A)P(B) will be reserved for candidates nominated by A, and elected by B; these seats will be called ambassador seats from A to B when B is different from A, and otherwise will be called the main platform seats for A;
• Let there be a support quota Q(A~B) for the number of votes needed to elect ambassadors from A to B, and call P(A~B) the ambassador quota of party A for B. If E(A~B) is the fraction of filled A-to-B ambassador seats (as a fraction of all seats), I.e. nominees from A who are actually elected by members of B, then A will only be allowed to elect P(A~A)*min{min{E(A~B)/P(A~B), E(B~A)/P(B~A)}: B not equal to A} of its own nominees. That is, the proportion of reserved main-platform seats that A will be allowed to fill is the least fraction of reserved ambassador seats it fills in relation to every other party, including both the ambassadors from A to other parties, and the ambassadors from other parties to A.

This procedure forces parties to also nominate candidates that compromise between different party platforms in order to obtain seats for any main-platform representatives. If a party fails to meet its quota for interparty compromises, it will lose representation. On the flip side, this set up will also establish high incentives for other parties to compromise with them in order to secure their own main-platform representation. In total, this system would give parties high incentives to compromise with each other and find candidates in the middle ground, which will serve as intermediaries between their main platforms.

Basically, here the outlines indicate seats open to be filled by candidates who are nominated by the corresponding party, and the fill color indicates seats open for election by the corresponding party:

Seats with outlines and fills of non-matching color are ambassador seats, and seats with matching outline and color are main platform seats. In terms of party A, by failing to nominate sufficiently-many candidates who would meet the support quota Q(A~B) to become elected as ambassadors from A to B, or by failing to elect enough ambassadors from B to A, party A restricts its own main platform representation and that of B simultaneously. By symmetry the reciprocal relationship holds from B to A. Therefore all parties are entangled in a dilemma: to secure main-platform representation, parties must nominate a proportional number of candidates who are acceptable enough to other parties to be elected as ambassadors.

To see that all needed seats are filled in the case of a stalemate, where parties refuse to nominate acceptable candidates to other parties and/or refuse to elect ambassadors, the election can be redone with the proportions being recalculated according to the party seats that were actually filled.

The support quotas collectively serve as a non-compensatory threshold to indicate sufficient levels of inter-party compromise. Ordinary PR is identical to PR with ambassador quotas but with all support quotas set to zero, whereby there is no incentive to nominate compromise candidates.

The purpose of this kind of procedure is twofold: firstly, it should significantly enhance the cognitive diversity of representatives, and secondly, it should significantly strengthen more moderate platforms (namely those of the ambassadors) that can serve as intermediaries for compromises between the main platforms of parties. Every party A has a natural “smooth route” from its main platform to the main platform of every other party: The main platform of A should naturally be in communication with ambassadors from A to B, who should naturally communicate with ambassadors from B to A, who should naturally communicate with the main platform of B.

Also, this procedure gives small parties significant bargaining power in securing representation. Large parties will have much more representation to lose than the small parties that are able to secure seats if the small parties refuse to elect any ambassadors, so rationally speaking, large parties should naturally concede to nominating sufficiently many potential ambassadors whose platforms are closer to the main platforms of those small parties. The same rationale holds for the potential ambassadors nominated by small parties, who also should tend to have platforms closer to the main platform of the small party.

Finally, this system creates significant incentives for voters to learn about the platforms of candidates from other parties who stand to reserve seats for representatives.

@rob especially if the state is a swing state, making it more difficult for the large parties to secure voters for their platform I think would be a significant influence forcing large parties and their candidates to more scrutinizingly determine the real interests of voters in those states. It may dilute the interests of less competitive states, but since the competitive states are crucial to obtaining the presidency, the large parties will still have to invest strongly in the interests of voters in those states in order to compete with alternatives (and obviously each other) for the crucial swing points. This may lead to something like an arms race of concessions, which happened in New Zealand in 1996 and led to the national adoption of a PR system, according to Arend Lijphart. Obviously that's quite a leap for the U.S., but maybe a less extreme analogue is not so far-fetched.

Maine is one of the thirteen most competitive states for elections according to a 2016 analysis (Wikipedia: Swing state), so I’m not sure their recent establishment is actually strategically foolish, although it’s possible that it wasn’t fully thought through. I agree it isn't clear.

I think it will definitely be interesting to observe how the current political apparatus responds to Maine--and apparently, more recently, and strangely, Alaska:

https://news.yahoo.com/alaska-is-about-to-try-something-completely-new-in-the-fall-election-193615285.html

Since Alaska is far from competitive, I do think this transition was in fact foolish for the reasoning you stated, but it remains to be seen. If we saw a state like Florida transition to a system like Maine's, it would be very interesting to study the relative differences between federal treatments of Florida, Maine, and Alaska as a case study for how "swingy-ness" might influence the effect of such voting system transitions. If Maine experiences an increase in federal power, it would be a good case for the remaining swing states to make a similar transition. If that occurred, the swing states would become a platform foothold for alternative parties to grow.

@k98kurz I don’t think there should be any uncertainty in the default for a voter’s ballot.

@lime the point of this post isn’t to argue that approval voting is superior to other methods or that modifications wouldn’t improve approval voting, it’s to point out that despite other methods being potentially superior, standard approval voting is probably the most realistic target for near future steps toward substantially reformed voting.

Unfortunately, more choices does mean the system is more complicated. You can observe that the addition of even a very simple, marginal modification as you suggest already raises questions. Every question about a method is an opportunity for distrust to be exploited, even if the method is ultimately better. Plurality is terrible, but almost nobody had questions about it, and that’s why it’s stuck around for so long. Do you see what I mean? I may be a bit jaded, but I’m hoping to be realistic.

I don’t mean to be a downer, but my point is a bit sad: in terms of what people would prefer, such as more choices or buttons, what we have to deal with is exactly the fact that people are having a hard time getting what they prefer. The political status quo is strongly opposed to voting reform, it will have to relinquish substantial power and accountability to the people under an effective voting system. There’s a reason only flawed tokenisms like IRV have passed through legislature in recent times. In fact, there is a history of voting reforms being enacted and then reversed.

@democrates I meant a Condorcet winner only among the front runners (for example, the candidates with the top K scores, here we are taking K=2). If there is no Condorcet winner among them, then we can choose the top scoring candidate.

In your case, if two candidates have the same second-greatest score, and the three front runners form a Condorcet cycle, then you can use the scores to break the tie. If this was used, then Jill Stein would have won the election.

That isn’t “the correct” solution (there is no such thing), but it is somewhat less arbitrary than flipping a coin or operating by alphabetical order, neither of which has anything to do with relevant information that is readily available on the ballots.

If we were being engineers about choosing a high quality candidate to win the election, we could even compute the distribution of scores, take the candidates whose scores exceed some elbow point, and find the Condorcet winner among those candidates with the top scoring candidate as the backup if no Condorcet winner exists. That’s basically a generalization of STAR with a dynamic front-runner selection method.

There are other ways to proceed. For example, we could remove Condorcet losers, then try to find the Condorcet winner of all remaining candidates, iteratively eliminating the lowest scoring candidate until a Condorcet winner emerges.

@toby-pereira yes you’re right, it was just a thought that occurred to me when I was thinking about how to discourage bullet approvals, but it has irreconcilable flaws that are now apparent.

@k98kurz mirroring @Lime, I think any advantage conferred to one candidate over any other in an election should be granted on an opt in basis. A voter shouldn’t have to opt out from conferring an advantage to a candidate.

@wolftune this is a well-known Condorcet method due in spirit to Tideman and called “Bottom N Runoff” where N=2 (hence “Bottom Two Runoff,” I.e. BTR or B2R). Generally speaking, these methods use some kind of absolute criterion (like least number of first place votes, lowest score, lowest approval, etc.) to decide which “bottom” candidates to subject to an elimination round, eliminates a Condorcet loser among them, and iterates until the desired number of winners remain. You are right, they’re pretty good methods. I like them.

The notion of consent is of foundational concern in political philosophy and has come up many times in this forum over the years. I wanted to share this lecture from a bioethics perspective, as food for thought:

Youtube Video

@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.

@tec I agree, most informed, pro-democracy people demand structural change to improve faithfulness of policy as well as more civic engagement. Direct policy-focused voting is ideal in principle, but on a large scale, it could be very inefficient. In my conception, the purpose of representatives is essentially to specialize in the aggregation and fusion of policy information and then interface with policy decisions. Unfortunately, removing that layer of abstraction might lead to chaos in various ways.

I think your question/title of this post gets to the practical heart of what voting theory is about. Since we're concerned with consent here, what do you think the "ingredients" of consent might be? For example, I roughly imagine that to give consent, an individual needs adequate information about a proposal, sufficient resources to process that information about it, and mitigated or minimized "unnecessary" conflicts of interest. Those are all normative constructs, but the idea is that maybe we can decompose a complex construct like consent into simpler pieces, and then examine how those pieces might or might not hang together in the right way.

More thought can make the construct of consent more complicated and multidimensional, It’s definitely something I want to read more about. I think core “defeaters” of consent would be sufficient severity of avoidable conflict between interests, plus epistemic aspects, and maybe others not considered.

To me, some of the main issues with our current system is that we lack various aspects of that triangle. Individually, we don't have enough information, we hardly have sufficient resources to process what information we do have, and conflicts of interest are baked right into our institutions. Including the vote-for-one system, where the conflicts of interest are obvious, it's essentially extortion. In my view, representatives should function to address the first two points about information processing. What are your thoughts?

Also no worries about prior engagements with conference and delay, I'll be frank in that I also haven't been able to give your proposal more than cursory consideration because of my own business, but as we and possibly others discuss, I'm sure we'll be able to prepare more food for thought. On the surface, it seems like your proposal does address the ingredients of consent I outlined, but efficiency and practical adoption may be significant issues. Not insurmountable though, and you may have already considered as much.

@tec I think it sounds like it would yield good results. I think we might need to have a more step-by-step dialogue about this to get a real understanding of what you’re proposing.

One thought that comes to mind is that while multiple rounds of voting is simple on its face, it’s also a radical adjustment to the approach we are currently entrenched in. For that to fly, it would require significant efforts to educate and familiarize the public with the concept. Generally speaking, the simpler a system is, the more likely it is to be adopted.

So my point is that I do like the principle, but personally I see it as something that could only realistically exist after a more foundational adjustment is made for it to develop on top of. Does that make sense?

For example, it seems to require adoption a priori of an approval voting paradigm. That in itself is a significant hurdle.

I was discussing voting systems with a friend, and he was curious about how alternative voting systems would integrate into existing infrastructure such as districting and the electoral college.

This seems like it could be a ground-up, potentially idiosyncratic thing, but we have seen adoptions in certain states of alternative systems and they have obviously integrated into a national level system. My curiosity is about the logistics of this on a larger scale, and if there is a clear roadmap that offers generality of scope for other states to follow suit.

I’m wondering if people have more knowledge on this subject, and if they would be willing to share or collect resources here for others to investigate. I’ll probably look into this myself. I’m also opening a subject about historical examples of alternative systems, please chime in with any thoughts or considerations!

@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.

@Isocratia I mean, maybe. But if you bail from a conversation just because people are discussing ideas that don’t neatly align with your views, I think that kind of runs counter to productive discussion. Engagement is the whole point of a forum. Why not take the opportunity to make your case? On that point, I don’t think I was being dogmatic, I was just putting a moderate, measured perspective out here. In particular, that if a candidate has comparable support to what Nader did, he should also be on the debate stage.

As for Kennedy, I’m not sure if you followed his campaign directly, but from what I saw, his platform had some surprisingly rational moments. Whatever mistaken views he holds about healthcare, his core message was about dismantling corporate capture of government—which, let’s be honest, is exactly the route that’s brought us to the brink of fascism today. Frankly, he seemed more committed to stopping Trump than the Democrats did.

Like him or not, he was a third-party candidate who genuinely threatened to shake up the duopoly—something we haven’t really seen since Nader. And given how deeply dysfunctional the two-party system has become, that’s not nothing. The political landscape is a real-time disaster, and reform doesn’t just happen on its own. While it wasn’t his main agenda, one thing I appreciated about his run is that he was literally the only candidate to talk about ranked-choice voting and other technical fixes.

That said, I completely checked out when he aligned himself with Trump. At that point, his platform basically collapsed. His current sellout stance disillusioned a lot of his supporters—and honestly, he should’ve just bowed out once it was clear he couldn’t win.

If you see it differently, I’d be interested to hear why. That’s why I brought this topic up in the first place.

@toby-pereira yes definitely. I started trying to actually prove participation last evening, and it got much hairier than I would have liked... lots of branching edge-case conditions. I think an actual proof (or counterexample) of participation for this system would require some nice insights, and/or a larger scale planning and brute-force organized accounting of every relevant case.

For example, I’m quite certain the new participant V can never change the top sorted candidate to somebody they prefer less. So it would have to be an upset via the B2R survivor, who would have to become the new winner, and be preferred less than the old winner by V. But that situation gets complicated in terms of the sorting and the rank tie-breaking authority… Maybe some day!

@toby-pereira yes it’s a bit particular, that’s the part that’s designed to preserve participation. The +1 advantage plus tie break conferred to the adversary is essentially to prevent any single vote from changing the outcome of the participation criterion-satisfying method. It still needs proof or more auditing and adjustment. But it was motivated empirically by finding examples of participation failure without introducing the advantage and some other aspects.

I think voters could have an anonymous ID given to them upon voting, it would have to be done with encryption. You’re right that in this case we would have to preclude latecomers, which I think would be fine. I think it could be done securely without an extra trip. This whole situation really makes “recounts” potential difficult though.

Having the “sincere” rank be attached to the original ballot might also be an option, but voters would somehow need to know that the second ballot would not be used in the first election, for instance. The only way they can know for sure is if they don’t provide it until after the first election winners are revealed. That could also be done with encryption.

In terms of preserving participation, the final runoff may not even be necessary. I’m trying to combine two things that can be looked at separately.

Also thanks for reading and your thoughts! I’m starting to wonder about how to guarantee the Condorcet loser criterion while still preserving participation. As of now though I think the method is essentially approval but with significantly stronger Condorcet-like guarantees.

EDIT: I just learned that there is an impossibility theorem about participation, independence of clones, and Condorcet loser. My guess is that the context and proof are similar to Arrow’s theorem, but the details I don’t know.