| paper | d4-conf-ijcai-2018-0122 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The named theorems classify when axioms permit a lifted order; they do not assert an algorithm, complexity bound, or hardness result. The polynomial recognition and construction discussion appears in Remark 17, while the cited NP-completeness result is prior work on a different problem, so neither supplies a qualifying anchor in this paper.
fails bit a — no named computational result to mirror
The proposed mirror would cover none of the paper’s structural classification results; Remark 17 discusses polynomial recognition, and the cited NP-completeness result is from prior work.
I can’t make a defensible anchor-based case for a continuous mirror. The paper’s numbered results are structural classifications: for example, Theorem 13 proves that strongly DIS-, DISE-, and DISES-orderable graphs are exactly the forests; Theorem 16 proves that the corresponding weakly orderable graphs are exactly the bipartite graphs. They characterize when a lifted order exists, rather than state a computational complexity result about a population problem.
There are nearby results, but they do not supply the required anchor. Remark 17 notes that the strict-independence classifications yield polynomial-time recognition. Section 6 cites NP-completeness for a different lifting problem from Maly and Woltran (2017); it is prior work, not a numbered result proved in this paper.
A possible wrapper would treat residents’ rankings of rooms as types, \(\mu_t\) as their population shares, and ask what fraction can receive a ranking over connected bundles that satisfies the axioms. But the paper’s results concern whether an order can be lifted for some or every ground order. They do not analyze this population-coverage question, and the mass values would add little to the universal-order result. More fundamentally, the paper studies axiomatic preference extension, not computation over a continuous society—an angle the programme places out of scope. So I have no qualifying anchor and no per-anchor continuous problem to offer honestly.
Theorem 13 and Theorem 16 are the paper’s strongest-looking anchors, but both classify graph structure: forests guarantee a lift for every ground order, while bipartite graphs guarantee one for at least one. Remark 17 notes that these classes can be recognized in polynomial time. That is graph recognition, not a complexity result about computation over a society. The cited NP-completeness result from Maly and Woltran (2017) concerns a different lifting problem and is not established for this paper’s graph model.
The best population-based reformulation is to imagine many users choosing connected bundles of rooms, with a shared room graph and a distribution \(\mu\) over users’ rankings of the rooms. One could ask what fraction of users’ rankings admit a lift satisfying dominance and independence. But each user’s lifting question remains independent of how many other users share that ranking. The paper’s strong and weak orderability results concern all ground orders or the existence of some ground order; they do not use \(\mu\). Asking for the mass of supported rankings that succeed would be a new distributional measure of axiomatic representability. The paper neither studies that measure nor gives its complexity.
One could make the population matter by requiring a common lifted order, or by choosing which users to exclude. That would add a social aggregation or intervention problem, respectively. Neither follows from the paper’s results, and either would need its own justification as the authors’ problem.
This is a strong reason to reject the paper as an anchor-led ChoCo candidate: none of the results the other analyst named supplies the required computational anchor. It is not proof that no useful population question could ever be built around preference lifting. My negative case is weaker at that universal claim; the distributional representability question is coherent, but its connection to this paper’s results and to a collective decision problem is thin.
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.