| paper | d4-journals-geb-2019-0006 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
Every numbered result is an axiomatic characterization or a structural rule-property theorem, so none meets the required computational-result gate. Section 3.3 states a polynomial-time evaluation algorithm, but it is unnumbered and cannot anchor the mirror under this rubric.
fails bit a — no named computational result to mirror
A support-based evaluation mirror would cover only the lexicographic fixed order status-quo rule’s unnumbered polynomial-time algorithm; it would not cover the numbered characterizations, solidarity results, or rule-property results.
I can’t make a standards-compliant positive case from this paper: none of its numbered Theorems, Lemmas, Corollaries, or Propositions asserts a computational complexity result. Theorem 2 characterizes fixed order status-quo rules axiomatically; Proposition 4 establishes their incentive, solidarity, and efficiency properties. Neither classifies an underlying computational problem.
The closest candidate is the unnumbered algorithm in Section 3.3, which says lexicographic status-quo rules can be evaluated in polynomial time. Its continuous analogue would take a rational distribution \(\mu\) over ranking types and return the lexicographically first ordering extending every ranking pair shared by all types in \(\operatorname{supp}(\mu)\). But the result is stated only in prose, so it cannot serve as the required numbered anchor. Also, the masses themselves do not affect the answer: only the support matters, making this essentially a compressed evaluation of the discrete rule.
So there is a plausible population-continuous formulation nearby, but no qualifying named computational result to mirror under the requested standard. The main weakness is decisive: presenting that formulation as anchored would misstate what the paper’s numbered results establish.
The proponent’s strongest point is also the limit of the paper’s computational content: none of its numbered results states a computational complexity result. Theorem 2 is an axiomatic characterization; Proposition 4 establishes rule properties. The only computational foothold is the unnumbered claim in Section 3.3 that lexicographic status-quo rules can be implemented in polynomial time. Under the requested standard, that leaves no numbered computational result to mirror.
The best rescue is still a plausible high-multiplicity scenario: a large professional association aggregates members’ rankings of candidates, represented by ranking types and their population shares. The continuous rule is well-defined. But its output depends on the intersection of rankings in the positive-mass support: an arbitrarily small positive share has the same effect on unanimous comparisons as a large one. Thus the continuous input collapses to a support question, rather than making the shares themselves part of a computational problem.
That support dependence also makes a natural intervention mirror degenerate. With reference ordering \(abc\), start with unit mass on \(cba\), so the rule selects \(cba\). Move mass \(x>0\) to type \(abc\). The support now contains both rankings, their only common comparisons are reflexive, and the rule selects \(abc\). If the transfer cost is proportional to mass moved, the cost is positive for every feasible \(x\), yet can be made arbitrarily close to zero. The minimum cost is not attained. Requiring a minimum cohort size would regularize this, but adds a threshold absent from the paper’s rule.
This is a negative case, not a proof that no scenario could yield a worthwhile mirror. A large association is a sensible high-multiplicity setting, and the evaluation problem remains well-posed. The case is weaker precisely there: its force is that the paper offers no numbered computational result, while its best computational candidate uses only positive support and its natural mass-intervention version has a continuum-specific degeneracy.
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.