| paper | d4-journals-mss-2025-0003 |
| 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 results establish analytical relationships between voting rules and election outcomes, not computational claims. The paper also already models voters as a continuum with masses over rankings, so translating its group shares into a distribution over types would restate its model rather than create a continuous mirror.
fails bit a — no named computational result to mirror
No result yields a computational mirror; Lemma 1 and Theorems 1–2 are analytical claims about winners and polarization.
The strongest honest point in favor is that the paper’s population description has exactly the right shape for a continuous society: types are strict rankings, and \(\gamma_i\) are population shares. That is a sensible model for a large electorate with repeated preference types.
But it is already the continuous-population model. Section 2.1 explicitly places voters on \([0,1]\), restricts profiles to Borel sets, and represents the polarized electorate by group masses over preference rankings. Recasting those masses as a distribution over types would restate the paper’s model, not give its results a new continuous mirror.
There are no eligible computational anchors. Lemma 1 says that, on the paper’s polarized profiles, a consensus candidate is a Condorcet winner and cannot be defeated under Borda. Theorem 1 says that whenever Borda elects a polarizing candidate, plurality does too, and—if a Condorcet winner exists—the Condorcet method does too; the converses need not hold. Theorem 2 says that if a scoring rule with parameter \(\lambda\) elects a non-polarizing candidate, increasing \(\lambda\) preserves a non-polarizing winner. These are analytical results about election outcomes, not named results about computational complexity.
One could formulate a separate algorithmic question about computing winners from rational type masses, but it would be a new question built around a model the paper already makes continuous. Under the requested anchor rule, there is no honest per-anchor problem to hand to a prover.
The central obstruction is a genuine model collision: this paper already takes the population to a continuum. Its voters are indexed on \([0,1]\), and the electorate is described by masses on preference types. The polarized profiles are distributions over strict rankings, with group shares \(\gamma_1,\gamma_2,\gamma_3\). Recasting those shares as a distribution \(\mu\) over types would restate the paper’s model; it would not continuize a discrete population.
None of the three results the proponent identifies supplies a computational anchor. Lemma 1 relates consensus candidates, Condorcet winners, and Borda winners on the paper’s existing continuum of profiles. Theorem 1 compares which candidates win under Borda, plurality, and Condorcet. Theorem 2 compares winners as the scoring parameter \(\lambda\) increases. They are analytical claims about outcomes, not complexity results about an algorithmic problem.
The strongest attempted repair would turn each claim into an input-output task: given rational type masses, compute the winner or check whether the relevant polarization property holds. But that task uses the same continuous input and outcome the paper already studies. It changes a comparative theorem into a per-instance computational question without producing a continuous mirror of that theorem. Enlarging the type space or candidate set could motivate new computational work, but it would be an extension of the paper, not a mirror of its named results. A different proposal based on uncertain profiles or evolving voter opinions would continuize noise or time rather than the population, so it would miss the programme’s target.
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.