Score–Smith Validation Voting (SSVV)

[cfrank]

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.

[masiarek]

@cfrank Interesting construction, but I think stage 2 is close to null in the common case,
and it's worth checking before the simulation numbers carry any weight.

Take the ordinary situation: A = {a} (one score winner), B = {c} (a Condorcet
winner exists), a ≠ c. Both sets are published, so every voter in (2.1) knows
branch A elects a and branch B elects c. But c is by definition the candidate a
majority prefers to a — that's what being a Condorcet winner means. So sincere,
consistent voters hand branch B a majority every time, and SSVV elects the
Condorcet winner. The ex ante veil you're relying on only exists to the extent
that |A| or |B| exceeds 1.

That leaves the cycle case, where the veil is genuine — and there (2.2) is an
approval ballot over the Smith set, which is Smith//Approval. Same winner, no
second election.

Which makes me want to ask about the simulations: under sincere voting SSVV
should score identically to Smith//Approval. Was that in the comparison set, and
how were stage-2 voters modeled? If they're sincere and the electorate is stable
between rounds, I don't see where a difference could come from.

One other thing that might be worth modeling: stage 1 is now a qualification
contest with two doors, and burial has a payoff it doesn't have in a one-shot
Condorcet method — manufacturing a cycle moves you from "loses deterministically"
to "is in B and can win the fresh approval round."

None of which kills the idea, if the goal is legitimacy rather than optimality.
"Publish both answers and let the electorate ratify one" is a genuinely different
thing from "compute a better winner," and it's a reasonable thing to want. I'd
just pitch it on those grounds — the simulation framing invites the reduction
above.

[cfrank]

@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.