administrators

I’ve been considering generalizations of SSVV designed to improve robustness against strategic voting, and landed on the following design outline for a voting system, which can be called “MARE,” standing for “Majoritarian vs. Alternative with Rescue Election.”

I tested this framework using limited simulations of strategic voter behavior, and found significantly improved outcomes against benchmarks. For example, successful burial rates dropped from ~15% to ~7%, with >50% of buried Condorcet winners being rescued. This needs further investigation and more rigorous analysis.

The idea is as follows: in the first round, voters submit rank-score ballots, which determine two sets of candidates: a Majoritarian set M, and an Alternative set A.

For example, M could be the Smith set or Bipartisan set. A could be the Approval winner set or the IRV winner set.

Next, voters are given information about M and A. For example, M may be made public. A may also be made public, or some relevant statistics about A may be made public. For example, maybe instead of revealing the score winner, only the score is shown.

The key is, voters can use the information about M and A to do two things at once: (1) vote for whether to proceed by electing a candidate from A, or a candidate from M. And (2) possibly submit a “Rescue” signal, designed to counter burial tactics that may have manipulated M.

For example, the Rescue signal may be implicit, as the M-outsider with the highest top-rank support among outsiders. The design goal for the Rescue signal is to re-introduce a buried candidate into M with high efficiency, without ruining a sincere election. The cost is strict Smith compliance (although, if the Smith set is already manipulated and insincere, that may not be a bad thing).

If the electorate chooses M, then the pre-specified completion rule is run on M with the Rescue set R. For example, Benham could be run on M, and the winner could go head-to-head against a winner in R.

Otherwise, if they choose A, then the pre-specified completion rule is run on A.

The goal of MARE is to enable information/incentive engineering by selecting the rules for M, A, and R. In some experiments, I had M be Smith, A be IRV, and R be top outsider. There are various other considerations to explore within this framework. I just wanted to share it to see if others wanted to experiment with simulations.

@toby-pereira makes sense, it seems Condorcet/Smith methods consistently rise to the top in multiple ways.

I think Smith//STAR (implicit) as mentioned above has some problems, but I think Smith//Approval (explicit) as denoted in the electorama vote is a very good method despite taking two rounds. I’m half surprised Smith//Approval (implicit) didn’t do better.

I understand the general aversion to two-stage methods, but in the USA, we often effectively do that with primaries anyway, and it seems commonly used elsewhere. I think introducing alternative methods into party primaries could be pretty significant change in itself.

@cfrank There was a vote on electorama not that long ago Ranked Pairs with winning votes (as opposed to margins, which wasn't on the ballot) won the poll. It was the Condorcet and approval winner. In that poll I put approval as my top method.

@masiarek I think this is a useful way of looking at it: sincere, consistent voting should lead to Smith//Approval, as long as the Approval (or score) round is conducted after the Smith set is already known. So I would push back somewhat on “same winner, no second election,” because in SSVV, the Smith set (as well as the Score winner set) is known before the scoring of candidates in step (2.2). That sequencing can matter, even if sincere voting ultimately produces the same outcome as Smith//Approval, unless voters have genuine independent approvals per candidate.

In fact, it may be that most strategic benefits of SSVV are caused by the score/approval in the Smith set being informed by the Smith set itself, which would mean Smith//Smith-informed-Approval is a reasonable comparator, and it may be superior.

I also agree that in the singleton case with sincere voters, the validation step is redundant. If the Score set is ({A}) and the Smith set is ({B}), then a majority vote consistently with sincere preferences should choose the Smith set, since that same majority sincerely prefers (B) to (A). Probably, often the Score winner and Condorcet winner will coincide anyway.

Where I think SSVV differs most substantially from Smith//Approval is in strategic behavior rather than sincere outcomes, particularly when strategic voting changes the composition of the reported Smith set. Smith methods like Smith//Approval automatically commit the electorate to choosing from the reported Smith set, whereas SSVV does not—since voters first see the Score and Smith sets, the majority can decide whether they actually want to validate a Smith set that may have been distorted by tactical voting.

That may matter specifically for burial. Suppose burial changes the Smith set from something relatively compelling into a larger or stranger set. The burial strategy has succeeded in manipulating the pairwise structure, but has also changed the object voters are being asked to validate. Voters who prefer the Score winner to every member of the Smith set obviously choose Score, but even some voters who prefer one Smith candidate to the Score winner might choose Score rather than risk one of the other Smith candidates winning.

So I think your observation points toward an interesting strategic question about the method. Manufacturing a cycle can indeed get a candidate into the Smith set or remove another candidate from it, but unlike under Smith//Approval, that does not automatically get the preferred candidate into the decisive election, nor does it necessarily eliminate the buried candidate from consideration altogether, since the manipulated Smith set has to survive validation by majority vote.

I don’t know yet whether that additional hurdle is strong enough to make enough of a difference to warrant it, but I think that’s the main distinction from Smith//Approval.

My simulations so far have been exploratory and conducted interactively through ChatGPT 5.6-Sol, using spatial and nonspatial electorates with coordinated factions iteratively trying various score-compression, compromise, and burial strategies, so I would not treat them as an equilibrium analysis. They do suggest that the validation stage can sometimes neutralize successful manipulation of the Smith set (primarily accomplished through burial), but that result needs more systematic investigation.

I also just experimented with public B and hidden A, or revealing only the mean score of A rather than candidate identity. This mostly improved behavior even more, because manipulating the Smith set becomes more risky in validation if the Score winner set is kept hidden. But it opens a can of worms in terms of “information engineering” to improve incentives. Even if the Score “escape hatch” isn’t used, its mere existence changes strategic incentives.

This is a single-winner system with two voting stages. I did some cursory simulations against related alternatives, and this looked like the most promising of them.

Definition

(1.1) Voters submit a rank-score ballot: candidates are scored, with the induced score ordering determining the ranking; candidates receiving equal scores may be explicitly ranked to break the ordinal tie.

From (1.1), compute:

• A, the Score winner set; and
• B, the Smith set induced by the rankings.

Both sets are then made public.

In the second voting stage, knowing A and B, voters answer two independent questions:

(2.1) Vote either to elect from the Score winner set A, or to elect from the Smith set B.

This is deliberately an ex ante judgment. The voter knows both candidate sets, but—when either contains multiple candidates—does not necessarily know which particular candidate will ultimately be selected from the chosen set.

(2.2) Cast a fresh ballot over the candidates needed to resolve the chosen branch. In the version I tested, this was a fresh Approval ballot over the Smith set; if the Score winner set contains multiple candidates, the ballot can analogously include the members of A needed to break that tie.

Finally:

• if a majority in (2.1) chooses the Score branch, elect the fresh-ballot score winner from A (ordinarily A will contain only one original Score winner);
• otherwise, elect the fresh-ballot score winner from B.

Thus the first ballot produces two competing claims about the appropriate winner: an unrestricted cardinal winner and a winner drawn from the reported majority-dominant set. The second stage asks the electorate, after seeing those sets, which claim it wishes to validate.

The structure can be generalized, for instance, using the IRV winner rather than Score/Approval, or using a different completion method in the Smith set.

I wanted to bring up something from the past that never came to fruition, which was the idea to vote on voting systems. The idea was to have users include a ranked score-carrying ballot in their forum signature (you can see mine below as an example), and to intermittently compare them to see what users thought. All that was ~discussed here:

https://www.votingtheory.org/forum/topic/237/proposed-options-for-voting-on-voting-methods/25?_=1785984453512

Anyway, after digging through the old forum threads, I tried to reconstruct a “metaelection” from the score ballots that various users have put in their signatures or explicitly posted.

So far I’ve recovered commensurate ballots from only a small collection of users:

• cfrank (myself)
• Jack Waugh
• multi_system_fan
• Marylander
• Andy Dienes (former user)
• Keith Edmonds

(I also found evidence that rob had a ballot in his signature, but I haven’t yet recovered the actual scores.)

While this is not necessarily representative of all users or even voting theory enthusiasts in general, and does not include all voting methods one might in principle prefer, I wanted to see what the results were from the limited scope and “turnout.”

To make the ballots comparable, I grouped together the various rated/cardinal Condorcet methods (e.g. Score Sorted Margins, generic cardinal Condorcet, rated Condorcet), rescaled Marylander’s 0–100 ballot to 0–10, and then compared the common methods.

The aggregate score totals are:

• Cardinal Condorcet: 55.0
• STAR: 48.0
• Approval: 42.9
• Score: 39.1
• IRV: 12.8
• Choose-one/FPTP: 4.0

Pairwise, cardinal Condorcet defeated STAR, Approval, and Score by 4–2, making it the Condorcet winner of the metaelection as well.

It also won under Score, STAR, Borda, Plurality, and IRV. Under Approval, the outcome depended on the approval threshold: using the suggested threshold of 5 gave a three-way tie between cardinal Condorcet, Approval, and STAR, while a stricter threshold (>5) elected cardinal Condorcet outright.

At least from the ballots I could recover, the collective ordering was:

1. Cardinal/rated Condorcet
2. STAR
3. Approval
4. Score
5. IRV
6. Choose-one/FPTP

If anyone knows of additional signature ballots (or can recover rob’s old ballot), it would be interesting to incorporate them.

We can compare with an external poll on Reddit (this poll is not a vote, but asks which single-winner system among alternatives is most preferred):

https://www.reddit.com/r/EndFPTP/comments/1cukxrz/what_singlewinner_method_do_you_support_the_most/

Interestingly (or perhaps uninterestingly?), if we pool together all Condorcet methods, our small toy election matches quite well with the top preferences in the Reddit poll.

I would also like to hold that kind of election not in terms of the most preferred voting method outright, but in terms of what the most feasible reform target to implement would be. That’s a bit vague—for example, would that mean implement state-based/federal approval voting? Or to push for proportional representation in districts?

Based on this preliminary outcome, a cardinal-Smith method with a STAR-style fallback or completion rule might be worth considering, although that specific composite was not itself included uniformly on the ballots. I was also surprised to find that, unless I overlooked something, this specific hybrid had not been proposed before now on this forum. It has been proposed elsewhere, including within various Reddit threads.

Finally, on the subject of voting for voting methods, I wonder if it would make sense to have the electorate vote on their preferred method along with their ballots, or to vote for their preferred method in advance. That’s probably a different topic.

@clay I have watched that video, so thanks for that. But the bottom line is that I am making an argument about semantics, not ethics. And you insist that it's an argument about ethics. There's nowhere to go from there.

@clay, this appears to undermine itself at several important points. You claim to have completely debunked Kant, but then concede that your definitional move yields only a stalemate, that the genealogical critique cuts equally against your own foundation, that “free and fully informed” may smuggle in normativity, and that Kantian constitutivism remains a live dispute. Those concessions are incompatible with the claimed total refutation. I recommend writing the argument as explicit premises and implications; the problems should become apparent.

Even if we admit preference sovereignty, its own formulation is severely self-limiting. It applies only where all affected parties would freely and unanimously choose an outcome while fully informed, which is already immediately divorced from any dilemma that involves conflicting interests. Consequently, that principle in itself does not imply aggregate utility maximization in cases of conflicting interests.

To derive aggregate utility maximization, Harsanyi introduces additional assumptions through an identity-lottery construction. That construction can make aggregate utility numerically equivalent to the expected utility of a hypothetical identity-uncertain chooser, but it does not make that quantity identical to each actual person’s utility, nor does it establish why taking Harsanyi’s hypothetical standpoint is normatively authoritative.

What you have, in effect, is a selected collection of normative operations—idealized preference under conditions of rationality, freedom, and full information; identity uncertainty; expected-utility reasoning; and interpersonal aggregation—that define your ethical framework. Choosing different operations can and does yield competing ethical theories that you have not eliminated.

To be clear, some of those operations are at least superficially appealing. The preference-sovereignty principle is almost a tautological no-brainer within its stated scope, and the arguments that follow once we accept the normative premises built into Harsanyi’s construction may be perfectly valid. But those premises are exactly where justification is lacking, where competing alternatives are abundant, and where legitimate disagreement obviously exists.

We are clearly not getting anywhere, so I’ll offer my ultimate relevant point on this subject and stop. I think the election-by-jury concept is an interesting and reasonable proposal with compelling arguments in its support, and that while there are also completely valid concerns, it’s also plausible that those concerns could be effectively addressed with more collaborative examination and careful approaches to implementation. It has controversial aspects, but it isn’t a wholly radical idea. I think there are also legitimate generalizations that are equally interesting and reasonable topics of discussion.

@clay you can plug your ears and say La La La all you like. Kantian ethics is a perfectly legitimate alternative to utilitarian ethics.