| paper | d4-conf-aldt-2024-0005 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorems 1 and 2 give explicit rules with quantitative coalition-manipulation guarantees, and Theorem 3 constructs an extension with such a guarantee, so the paper has algorithmic anchors. But the input is an arbitrary tournament whose teams have identity-specific pairwise outcomes, leaving no high-multiplicity type representation that preserves it; fixed-size coalitions also lose mass in a continuum. A model with positive-mass coalitions and type-level match interactions would change the input and strategic question, so none of these anchors yields a recognized continuous-population problem.
fails bit b-none — no population with multiplicity to relax
For Theorems 1 and 2, the strongest point is that a team's complete description must preserve its outcomes against the other named teams, so aggregating teams into types loses the arbitrary tournament input; the proponent notes near-unique types but supplies no preserving alternative.
fatal: True
No continuous-population question is anchored by the paper. Theorems 1 and 2 establish strategic guarantees for explicit tournament rules, while Theorem 3 extends a rule as the number of teams grows; these remain discrete tournament results.
I can’t make a case with a qualifying anchor: the paper has no numbered result classifying a problem as polynomial-time solvable, NP-hard, FPT, or similar.
The closest results are all proved in this paper, and they concern strategic guarantees for tournament rules:
These are results about rule design and manipulability. The paper’s discussion of an LP for optimal rules cites prior work; it gives no numbered complexity result that could serve as an anchor here.
A continuous team-population model is conceivable, but it would be a weak fit for these theorems. A type would need to capture a team’s match behavior across the other teams. In arbitrary tournaments, that behavior can require nearly as many distinct types as teams. Also, a coalition of at most \(k\) teams has vanishing mass as \(n\) grows. Giving coalitions positive mass would change the strategic guarantee the theorems establish. Theorem 3 scales the number of discrete teams, but does not give a high-multiplicity model.
So there is no per-anchor prover question to state under the requested standard. A mass-based tournament-rule design problem could be proposed as new research, but the paper’s results do not anchor it as a continuous mirror.
There is no qualifying computational anchor in this paper. Theorem 1 bounds how much a coalition can improve its chance of winning under RdSEB; Theorem 2 gives strategic guarantees for SIGNIFICANTONLY; Theorem 3 extends a rule from \(n\) teams to more teams. These are results about rule properties and design, not complexity or algorithms for a computational problem. The LP for optimal rule design is discussed as prior work, and the tournament-fixing problems appear only in related work. Neither supplies a result of this paper to mirror.
The best population-based reinterpretation still has a basic mismatch. In these theorems, teams are the vertices of an arbitrary tournament: their identities and pairwise match outcomes define the input. A team type that preserves all information relevant to manipulation would have to preserve its relationships to the other teams. In general those relationships distinguish teams, so grouping many teams into a small set of types loses the tournament the rule acts on. Giving type pairs match probabilities or outcomes introduces a different, stochastic or graphon-style input model.
That mismatch is especially clear in each candidate theorem. For Theorem 1, a fixed coalition of at most \(k\) teams has zero mass in an atomless limit, so its manipulation guarantee disappears. Scaling the coalition with the population would pose a different question. For Theorem 2, the rule’s “significant” objects are particular MW pairs and triples; they have zero mass in such a limit. Giving positive mass to coalitions requires replacing the theorem’s finite structural classification with a new one. Theorem 3 scales the number of teams—the alternatives in the tournament—rather than a high-multiplicity society. Its most direct limit therefore continuizes the wrong axis; a fixed coalition again vanishes if teams are treated as a population.
One could formulate a new model of continuum teams, positive-mass coalitions, and winner distributions over team identities. That may be mathematically interesting, but it would need its own input representation, strategic notion, and computational questions. It would not be a continuous mirror of a named computational result in this paper. The negative case is strongest on that narrower point; it cannot rule out the value of inventing such a new tournament model.
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.