| paper | d4-conf-ijcai-2011-0118 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The paper’s numbered results are axiomatic or structural, and none asserts a computational result. The mass-weighted DBGD medoid is a well-posed population question, but its polynomial-time winner-determination observation is unnumbered and cannot supply the required anchor.
fails bit a — no named computational result to mirror
The candidate mirror concerns DBGD from Definition 4 and Proposition 10; it does not computationally mirror the paper’s other named results.
I can’t make a qualifying positive case under the anchor rule: the paper has no named result asserting a computational complexity classification. Its numbered results are axiomatic or structural—for example, Proposition 4 proves an impossibility result about social welfare functions, Proposition 8 characterizes when majority aggregation preserves an integrity constraint, and Proposition 10 establishes axioms satisfied by the distance-based generalised dictatorship. None says that a computational problem is in P, NP-hard, or has another complexity classification.
The closest foothold is an unnumbered observation in Section 5 that winner determination for the distance-based generalised dictatorship is polynomial. An informal continuous mirror would take types to be complete binary ballots \(B\in\{0,1\}^m\), with mass \(\mu_B\) on each supported ballot, and choose a supported ballot minimizing \(\sum_{B'}\mu_{B'}H(B,B')\). That is a plausible high-multiplicity version of the paper’s rule: many agents share a small number \(\tau\) of ballot types, and the collective choice is a mass-weighted medoid. It is tractable by evaluating the \(\tau\) supported ballots.
But that mirror is anchored only by Definition 4, Proposition 10’s axiomatic claim, and the unnumbered complexity observation—not by a named computational result of the kind requested. So it is a possible research direction, not a compliant lead anchor for this paper.
The decisive problem is that there is no named computational result here to mirror. Propositions 4, 5, 8, 9, and 10 are impossibility, axiomatic, or structural characterizations. They say which procedures satisfy properties or which constraints they preserve; none classifies the complexity of a computational problem. The paper’s brief note that DBGD winner determination is polynomial is unnumbered and incidental to its axiomatic contribution. That leaves no qualifying anchor for a continuous complexity question.
The strongest alternative is the mass-weighted DBGD medoid. Let \(\mu\) be a distribution over complete ballots, with support \(S\); choose a ballot in \(S\) minimizing \(\sum_{B'\in S}\mu_{B'}H(B,B')\). This is a sensible high-multiplicity model: a referendum population could contain many people with each ballot type, and DBGD’s output depends on their ballots rather than their identities. So I would not argue that mass is meaningless or that the continuous object degenerates. But this is a new formulation of DBGD, not a continuous mirror of a named computational result in the paper. A question about its axioms would still be axiomatic; a complexity question would be a follow-on project the paper does not pose.
The case against a mirror is therefore strongest on programme fit, not on modelling possibility. A continuous population version of DBGD is plausible, and it is the honest weak point in the negative case. But the paper supplies no computational anchor for it, and the other named results do not provide one either.
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.