| paper | d4-conf-ecai-2014-0315 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The distribution over ranking types is a plausible extension of the paper’s preference-diversity framework. But Propositions 2 and 3 are axiomatic results, and the experiments state no computational guarantee; the paper therefore supplies no named computational result to anchor a continuous computational question.
fails bit a — no named computational result to mirror
No named result is covered: Propositions 2 and 3 are axiomatic, while the experiments are empirical.
There is a natural continuous population model for the paper’s subject. Let each type be a complete ranking \(t\in L(X)\), and let \(\mu_t\) be the fraction of a large electorate with that ranking. A plausible regime is a large election with millions of voters but only a moderate number \(\tau\) of distinct rankings. The paper’s indices have sensible mass-based extensions: support diversity can count the rankings with positive mass; distance diversity can average pairwise Kendall distances over \(\mu\); compromise diversity can average each type’s distance to a compromise computed from the population. That is a genuine continuization of the population, and the authors would likely recognize it as a natural extension of their framework.
But there are no qualifying computational anchors in this paper. Proposition 2 says that, for \(m>2\) and \(n>m!\), no preference diversity ordering can be both support-invariant and strongly discernible. Proposition 3 characterizes the simple support-based ordering by support-invariance, independence, and weak discernibility. Both are axiomatic results, not results about computational complexity or algorithms; the experiments report empirical correlations but do not supply named computational results either.
So the continuous object is plausible, but I cannot honestly give the requested prover question *per anchor*: doing so would require inventing a computational result that this paper does not establish. The mirror would cover the paper’s preference-diversity framework, but its weakest point is decisive for this assignment: the paper offers no named computational result to anchor the case.
The strongest negative case starts by conceding that the proponent’s population model is natural. A large electorate with a small set of ranking types is a sensible high-multiplicity regime, and these authors would likely recognize a distribution \(\mu\) over rankings as an extension of their framework. That establishes a plausible continuous object, but it does not supply the kind of computational question ChoCo is meant to study.
The three proposed extensions make that gap clear. Support diversity becomes \(|\operatorname{supp}(\mu)|-1\). A normalized pairwise-distance index becomes a weighted sum such as \(\sum_{t<t'}\mu_t\mu_{t'}\delta(t,t')\). For the paper’s Borda and majority-graph compromises, the compromise and the weighted distances to it are likewise computed directly from the supported rankings and their masses. Given \(\tau\) supported rankings, these are finite counting and summation tasks, with straightforward polynomial-time evaluation. The paper gives no algorithmic result about them, and there is no exponential-variable optimization or pricing problem waiting to be unlocked.
The named results do not provide a computational anchor either. Proposition 2 is an impossibility theorem about axioms for preference-diversity orderings; Proposition 3 characterizes one such ordering. Extending those questions to distributions would still be an axiomatic study, which is outside the programme’s computational scope. The experiments compare distributions of finite profiles; turning them into exact probability or optimization problems would require adding a new task. For example, asking how to alter a population to eliminate Condorcet cycles would be a control problem built around the paper’s subject, not a mirror of a computational result in the paper.
So the proponent’s candidate mirrors survive as meaningful definitions, but not as worthwhile computational mirrors of this paper. The honest limit of the negative case is that one could invent a useful algorithmic project around preference diversity. The point is narrower: doing so would add the computational problem the paper never posed, rather than continuize one it actually studied.
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.