| paper | d4-journals-mss-2007-0032 |
| 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 has no numbered theorem, lemma, corollary, or proposition of its own asserting a computational result, so the required computational anchor is absent. Its IAC probability calculations are substantive computational work, but they are unnumbered; the proposed minimum-cost manipulation problem would also change the paper’s probability question into an optimization problem.
fails bit a — no named computational result to mirror
The paper computes limiting IAC probabilities for coalition manipulability, Condorcet phenomena, rule agreement, participation paradoxes, and referendum paradoxes; none is a qualifying numbered result.
The strongest positive evidence is that this paper already uses the right population regime: for three candidates, the six rankings are the types, and their masses \(x_i=n_i/n\) form a point in the simplex. As \(n\) grows, IAC probabilities become volume ratios over that simplex. For coalition manipulability, the paper describes regions of mass profiles where a coalition can change the winner, then computes their limiting probabilities. The regime is \(n\to\infty\) with at most six types, and the authors plainly treat normalized population shares as the natural variables.
But the paper contains no numbered Theorem, Lemma, Corollary, or Proposition of its own asserting a computational complexity result. Its computations and complexity observations are unnumbered; the reference to “[18, Theorem 2]” is a citation to another paper. So there is no qualifying anchor for the required per-anchor mirror question or for predicting whether an anchored hardness result dissolves.
That is also the case’s weakest point: the population-continuous model is already central to the paper. Its finite IAC profiles become lattice points in dilated polytopes, and their limiting probabilities become volumes. This is strong evidence that the continuous population regime is sensible, and the discrete-to-continuous limit is itself a result. It does not, however, furnish a fresh, named complexity result to mirror under the stated rules.
The strongest case against using this paper as a mirror is that its central probability calculations already use a continuous population. In the three-candidate examples, the six ranking counts become type shares \(x_i=n_i/n\). Manipulability defines a region in the type-share simplex, and the limiting IAC probability is computed as that region’s volume. The paper gives, for example, the exact Borda manipulability probability \(132953/264600\). Asking for that same probability over continuous societies would restate a computational result the paper already obtains.
The other analyst is also right that the paper has no numbered theorem or lemma asserting a complexity result. Its computational contribution is a method and a set of probability calculations. A tempting extension would ask for the minimum mass or cost needed to manipulate a *given* society. That is a sensible high-multiplicity problem, but it changes the task from measuring how often random societies are manipulable to optimizing an intervention on one society. It could be worthwhile ChoCo work; it does not supply a mirror of a result in this paper.
This makes the negative case strong for choosing this paper as a mirror candidate, but weak as a universal claim. The paper’s use of type shares is evidence that continuous societies are sensible, and the minimum-cost manipulation question is a plausible adjacent problem. I cannot honestly rule out every worthwhile mirror scenario.
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.