| paper | d4-conf-ijcai-2011-0466 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
Proposition 2 states a structural optimum, but the paper’s quadratic-time computation claim and its CLOSEST STRING hardness discussion are unnumbered; neither supplies the required named computational result. The support-based continuous agenda is recognizable and straightforward to solve, but that cannot repair bit (a); a mass-weighted violation objective would be a separate, plausible extension.
fails bit a — no named computational result to mirror
The proposed mirror covers Proposition 2's canonical-agenda optimality under zero dependency violations; it leaves the quota-based and constraint-based procedures, axiomatic results, and experiment aside.
There is a natural population mirror for the agenda-selection subproblem. In a large multi-issue election, let each type be a voter’s dependency graph over the issues, and let \(\mu_t\) be the fraction of voters with graph \(t\). Given the finite support and these rational masses, choose a meta-agenda—a partition of the issues into local elections and an acyclic order of those elections—that respects every dependency edge appearing in a positive-mass type, while minimizing the size of the largest local election. This is a plausible high-multiplicity regime when many participants share a small number \(\tau\) of dependency graphs. The solution is to take the union of the supported graphs, condense its strongly connected components, and order the resulting components topologically; the paper says the canonical agenda can be computed in quadratic time.
The nearest named result is Proposition 2, proved in the paper: *the canonical MACF minimizes the size of the largest local election among all MACFs without dependency violations.* That is a strong structural match for the candidate mirror. But it does not assert a complexity classification, and the quadratic-time claim is not numbered. Likewise, the reduction from CLOSEST STRING for constraint-based procedures appears in the prose of §3.4, not in a numbered theorem, lemma, corollary, or proposition.
So the paper has a credible continuous-population angle, but it supplies no named computational result that qualifies as an anchor under your rule. I would not pass off Proposition 2 or the unnumbered hardness statement as one. The mirror above is the strongest plausible case; it cannot meet the requested anchor requirement.
Proposition 2 is the proponent’s only named anchor, and it does not establish a computational result. It characterizes the canonical MACF: take the union of all dependency graphs and condense it. The paper’s quadratic-time computation claim is in the prose, while its closest explicit hardness discussion—the reduction from CLOSEST STRING for constraint-based procedures—is also unnumbered. So the proposed mirror does not meet the requested anchor standard.
The continuous version of Proposition 2 is well-defined, but its zero-violation condition makes every type with \(\mu_t>0\) count equally, however small its mass. The resulting agenda depends only on the support union, so the computation is the same graph operation as in the paper. That may be a valid continuous restatement, but it does not turn Proposition 2 into a complexity result about a population distribution.
A stronger candidate would allow a small mass of dependency violations and minimize their total mass subject to a bound on the largest local election. That makes the proportions matter and connects to the paper’s balancing objective. But it is a new weighted optimization problem, not the continuous form of Proposition 2; the paper leaves the violation measure open and gives no named result for this objective. This defeats the proponent’s actual anchor, though it does not prove that such a new problem would be unworthy of study.
I would therefore reject the case *as anchored*, but I cannot honestly claim that no worthwhile mirror exists in any scenario. A mass-weighted agenda problem is plausible, and the paper’s framework gives it a natural home. The negative case is strongest on the absence of a named computational result to mirror, and weak on ruling out a better, newly formulated agenda problem.
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.