| paper | d4-journals-geb-2024-0024 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 4, Corollary 3, and the other discussed results characterize strategic properties; none asserts that an object can be computed or gives a complexity result, so the paper fails bit (a). Theorem 5 makes the alternative space continuous while keeping the electorate finite. The opponent’s possible population-based repair, bloc manipulation, changes the unilateral question into a coalition question, leaving no qualifying anchor for a continuous-population mirror.
fails bit a — no named computational result to mirror
No results are covered by a computational mirror; the paper's named results give strategic characterizations, and Theorem 5 concerns a continuous alternative space with a finite electorate.
I can’t make a rubric-compliant case for a continuous mirror: the paper contains no named computational result asserting a complexity classification or algorithmic bound.
The strongest nearby result is Theorem 4, proved in this paper: for a non-dictatorial voting-by-committees rule \(f^W\), the rule is not obviously manipulable exactly when, for every object \(k\), the intersection of all coalitions in \(W_k\) is empty and every coalition in \(W_k\) has size at least two. Corollary 3 similarly characterizes quota rules: they are not obviously manipulable exactly when \(2\le q_k\le n-1\) for every \(k\). These are characterizations of strategic properties, not computational results. A continuum version involving a positive mass of voters changing reports would turn individual obvious manipulation into a coalition question, so it would not be a faithful mirror of either result.
Theorem 5 does introduce a continuous alternative space, but the population remains finite; the paper itself therefore does not provide the continuous-population anchor this programme requires. There is no qualifying anchor here, and thus no per-anchor continuous problem I can honestly propose.
The “for” case has no qualifying anchor. Its strongest candidates, Theorem 4 and Corollary 3, characterize when voting-by-committees and quota rules are NOM. Theorem 1 gives the general structural criterion, and Theorems 2 and 3 specialize it to median schemes. None states an algorithm, a complexity bound, or the complexity of a computational problem. In particular, the quota condition \(2\le q_k\le n-1\) is a characterization, not a complexity result. Theorem 5 does not fill the gap: it makes the alternative space continuous while keeping the electorate finite.
There is a substantive obstacle to turning those results into population mirrors. NOM asks whether a *single agent’s* report changes the outcomes available under different reports. In an atomless population model based on a distribution of voter types, changing one person’s report changes the distribution by zero. The option sets are therefore unchanged, and the individual-manipulation test loses its bite. This applies to median rules as well as committees and quotas. Scaling quotas to population shares or scaling phantom ballots can preserve the rules’ aggregate form, but it does not restore an individual’s influence.
The better possible proposal is to let a positive-mass bloc change reports and ask whether that is an obvious manipulation, perhaps also asking for the least mass needed. That keeps population mass central, but it changes the strategic unit and the question: the paper studies unilateral deviations under an individual’s uncertainty about others, whereas this version studies coordinated deviations by a bloc. Its answer would depend on choices absent from the paper, including what counts as a bloc, how its members coordinate, and what information they share. It could be a worthwhile new project, but the paper’s theorems do not supply a computational problem for it to mirror.
So the strongest negative case is narrow but firm: there is no named computational result here for ChoCo to continuize, and the natural individual-level continuation degenerates in an atomless society. I would not claim to have ruled out every worthwhile population-based extension; the bloc-manipulation direction is the honest weak point in a universal “no scenario” claim.
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.