| paper | d4-conf-ijcai-2017-0370 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The Chamberlin–Courant mass-weighted objective is a plausible, direct continuous question, and the opponent does not defeat it. But the paper mentions its NP-hardness only as prior work in prose and contains no numbered computational result, so bit (a) fails.
fails bit a — no named computational result to mirror
The candidate mirror covers Chamberlin–Courant winner determination; it leaves the paper’s axiomatic challenges, rule classifications, and other computational challenges outside the mirror.
The paper has no qualifying anchor: it contains no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational result. Its numbered formal statement is Definition 1. Section 4 does report computational results in prose, including that computing Chamberlin–Courant winning committees is NP-hard, citing Procaccia et al. (2008) and Lu and Boutilier (2011). That claim was proved elsewhere, and it is the strongest candidate for a mirror, but it does not meet your anchor rule. There is therefore no continuous problem I can honestly present as anchored to a named result of this paper.
If the prose-cited claim is admitted as a lead, the strongest mirror is continuous Chamberlin–Courant winner determination. An instance has \(m\) candidates, committee size \(k\), and a finite support \(T\) of complete ranking types with rational masses \(\mu_t\ge 0\) summing to \(1\). Choose a size-\(k\) committee \(S\) maximizing
\[ \sum_{t\in T}\mu_t\bigl(m-\min_{c\in S}\operatorname{pos}_t(c)\bigr). \]
Here, mass is the fraction of society holding each ranking, the decision is the committee \(S\), and the objective is its average Borda score for each type’s best-represented member. A plausible regime is a large electorate voting from a bounded set of recurring ranking templates: millions of voters and a support of hundreds or thousands of types.
The authors would likely recognize this as the same Chamberlin–Courant winner problem with a high-multiplicity society. The expected classification is hardness transfers: a discrete electorate with type counts \(n_t\) maps to masses \(\mu_t=n_t/n\), preserving the winning committees, so discrete NP-hardness carries over. This mirror covers winner computation for Chamberlin–Courant; it does not cover the paper’s other computational challenges. It raises follow-up questions about approximation and parameterization by \(k\), \(\tau\), or \(m\).
The weakest point is decisive under your rules: this is a precise and plausible mirror of a complexity claim the paper discusses, but it is not anchored to a numbered result of the paper.
The strongest case against is the paper’s lack of a qualifying anchor. Its numbered statements are definitions and research challenges, not results establishing the complexity of a computational problem. The NP-hardness of Chamberlin–Courant winner determination appears only in prose, attributed to earlier work. Under the instruction to anchor the case in a named result of this paper, that claim does not qualify.
But if the Chamberlin–Courant claim is admitted anyway, I cannot honestly defeat its mirror. With ranking types \(t\) and rational masses \(\mu_t\), maximizing
\[
\sum_t \mu_t\bigl(m-\min_{c\in S}\operatorname{pos}_t(c)\bigr)
\]
is a well-posed computational question about a continuous society. Large electorates with recurring preference patterns are a plausible regime; committee selection does not depend on voter identities; and the paper’s discrete model already aggregates voters by their scores. The discrete-to-continuous correspondence is not an objection under the programme’s rules, and the cited NP-hardness is neither a novelty collision nor evidence that the question is uninteresting.
So the negative case succeeds only at the paper-level anchoring requirement: this paper supplies no named computational result to mirror. It does not establish the stronger claim that no worthwhile mirror exists. The Chamberlin–Courant candidate survives that broader test, and the honest negative case is weak if prose-cited results are allowed.
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.