| paper | d4-conf-wine-2018-0027 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The paper’s numbered results establish asymptotic probability bounds for tournament solutions, not algorithms, complexity classifications, or computational formulations used to compute. Computing a choice set from ranking masses is a plausible related problem, but it does not mirror the paper’s random-edge threshold result.
fails bit a — no named computational result to mirror
The proposed problem would cover computing the top cycle of a weighted-majority tournament; it does not mirror the paper’s probability thresholds for the top cycle, uncovered set, or other tournament solutions.
The strongest honest positive foothold is that the paper studies a social-choice object that can be built from a large electorate. Let the voter types be complete rankings \(T\), with rational masses \(\mu_t\) summing to \(1\). Orient \(a\) toward \(b\) when more than half the mass ranks \(a\) above \(b\). A concrete continuous problem is then: compute the top cycle or uncovered set of this weighted-majority tournament, or decide whether it contains every candidate. In a regime with many voters but relatively few ranking types, that is a sensible high-multiplicity problem; the output is a choice set, and computing it is tractable.
The paper’s nearest result is Theorem 1, proved here: in its independent-edge random-tournament model, if every edge probability satisfies \(p_{i,j}\in[f(n),1-f(n)]\), where \(f(n)\leq 1/2\) and \(f(n)\in\omega(1/n)\), then the top cycle contains all alternatives with high probability. This gives the positive case a recognizable target—complete inclusion in the top cycle—and a natural population interpretation through majority tournaments. [The paper’s full text](https://pmc.ncbi.nlm.nih.gov/articles/PMC6989623/)
But this is only a weak bridge, not a valid ChoCo anchor under your criteria. Theorem 1 is a probabilistic threshold result, not a named complexity result about an algorithmic problem. Its parameter \(n\) counts alternatives; its edge orientations are independent random variables. A continuous electorate with fixed masses over rankings instead induces a deterministic majority relation, with correlations constrained by those rankings. The theorem’s probability threshold therefore does not carry over. The voter-preference results in Section 5 do not fix the mismatch: they take an odd constant number of voters while the number of alternatives grows.
So I cannot honestly provide a prover-ready continuous question *per qualifying anchor*: the paper has no named theorem, lemma, corollary, or proposition asserting a problem is in \(P\), NP-hard, FPT, or similarly classifying its computational complexity. The weighted-majority choice problem above is a plausible continuous problem in the paper’s neighborhood, but presenting it as the continuous mirror of the paper’s results would overstate the case.
The strongest negative point is a category mismatch: this paper contains no named computational result to mirror. Its theorems classify when events occur with high probability in random tournaments; they do not classify the complexity of an algorithmic problem. The paper’s experiments assume tournament solutions can be computed, but computation is not what its results study.
The proponent’s weighted-majority construction is a sensible high-multiplicity regime. Given ranking masses \(\mu\), pairwise margins determine a tournament, and one can compute its top cycle or uncovered set. But this does not mirror the top-cycle threshold theorem: with fixed \(\mu\), the tournament is deterministic, while that theorem assumes independently randomized edges and lets the number of alternatives grow. For a sampled electorate, pairwise outcomes are correlated because each voter supplies a whole ranking; as the electorate grows, non-tied margins settle into a deterministic tournament. Random behavior remains mainly at tied margins.
A stronger bridge would sample \(N\) rankings from \(\mu\), then ask for the probability that the resulting tournament is strongly connected or that every alternative is a king. That is a coherent computational question, but it adds a sampling process and a joint regime for \(N\), the number of alternatives, and the margins of \(\mu\). It is a new hybrid question, not the computational mirror of the paper’s edge-probability theorem. Likewise, minimizing the voter mass that must be changed to make an alternative leave the choice set would be a plausible control problem, but it replaces the paper’s random threshold question with an intervention objective.
So the top-cycle anchor does not survive as a mirror, and the same mismatch applies to the uncovered-set threshold. I would argue against treating this paper as a ChoCo anchor. The broader claim that no scenario could yield worthwhile related work is harder to defend: large electorates with repeated rankings are sensible, and the sampling or control extensions might be valuable in their own right. The case against is strongest when limited to what this paper actually establishes.
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.