| paper | d4-conf-ijcai-2018-0890 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
Theorem 4 is a structural characterization of which counting rules satisfy an axiom, not a computational result about finding manipulations or their complexity. The positive-mass-bloc problem is a plausible future extension aligned with the paper’s closing agenda, but it has no qualifying computational result from this paper to anchor a mirror.
fails bit a — no named computational result to mirror
The proposed bloc-manipulation question does not cover Theorem 4’s characterization or the other axiom characterizations; the tables and figures report experiments without computational guarantees.
I can’t give a compliant computational anchor: the paper has no numbered result establishing that a problem is in \(P\), NP-hard, FPT, or otherwise computationally classified. The closest is Theorem 4, proved in this paper: among non-trivial ABC counting rules, Multiwinner Approval Voting is the only one that is SD-strategyproof. Theorems 1–3 likewise characterize axiomatic properties, and Table 1 reports experiments rather than a named complexity result. Theorem 4 is a meaningful strategic-voting result, but it is not a computational anchor; treating it as one would stretch your criteria.
The strongest adjacent lead is a new problem suggested by the paper’s conclusion, which calls out finding successful SD manipulations as an algorithmic challenge and proposes studying coalitional SD manipulations. Call it Minimum-Mass SD Manipulation. A large electorate has approval types \(T\subseteq C\), with rational masses \(\mu_T\) and support size \(\tau\); this fits, for example, a large membership organization where many people use the same ballot. For a counting function \(f\), committee scores are
\[
\mathrm{sc}_{\mu,f}(W)=\sum_{T\subseteq C}\mu_T f(|T\cap W|,|T|).
\]
Given a sincere type \(S\) and a rational budget \(\beta\), ask whether some mass \(0<\delta\leq\min(\beta,\mu_S)\) can report according to a distribution \(q\) over approval sets, so that \(\mu'=\mu-\delta e_S+\delta q\) makes the uniform lottery over winning committees strictly SD-dominate the truthful winner lottery, evaluated by type \(S\)’s approved-candidate counts. A solution is such a pair \((\delta,q)\), or a correct “no.” I would tentatively expect the committee search over \(m\) and \(k\) to preserve hardness, but the paper supplies no result that establishes this; the complexity remains open. Natural follow-ups include whether one report suffices instead of a split across reports, and how the problem behaves when parameterized by \(\tau\).
The weakness is substantial: this is an extension of the paper’s proposed coalitional direction, not a mirror of Theorem 4. In an atomless society, one voter has zero mass and cannot change the outcome. Giving a coordinated positive-mass group influence restores strategic relevance, but changes the actor from an individual voter to a bloc. So the paper motivates a plausible continuous follow-up, but it offers no named computational result to anchor a ChoCo mirror.
The strongest case against a ChoCo mirror is that the paper has no named computational result to mirror. Theorems 1–4 characterize axiomatic properties; the tables report experiments. Theorem 4’s claim that AV is the only non-trivial ABC counting rule satisfying SD-strategyproofness is not a complexity classification. Turning manipulation into an algorithmic search problem would be a new contribution, not a continuization of that theorem.
The proposed mass-manipulation problem does not preserve the theorem’s strategic actor. In an atomless society, one voter’s report changes the distribution by zero, so the original individual-deviation axiom becomes vacuous for every rule. The proposal restores influence by moving positive mass: \(\mu'=\mu-\delta e_S+\delta q\). That is a coordinated bloc, potentially splitting its reports across approval sets, rather than one voter. The paper itself presents coalitional SD manipulation as future work. That makes the proposal recognizable and plausible, but also confirms it is a new problem rather than a continuous version of a result established here.
The best repair would define a type-homogeneous bloc and study the infimum mass needed for it to obtain a strict SD improvement. That is cleaner than calling the proposed budget decision problem “minimum mass”—strict improvement can make the infimum zero without attaining a minimum. But the repair still asks about coalitional manipulation. It does not supply a computational anchor from this paper. Large-electorate strategic-voting work nearby studies best responses and equilibria, not this complexity question; that is useful context, not an existing computational answer ([Laslier and Van der Straeten, 2016](https://ideas.repec.org/a/spr/sochwe/v47y2016i3d10.1007_s00355-016-0983-y.html)).
So I would reject this paper as a mirror of a named computational result. The universal claim that no worthwhile continuous project could follow from it is weaker: the coordinated-bloc problem may be worth pursuing, but it is a future research direction, not a mirror of the paper’s theorems.
The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.