| paper | d4-journals-mss-2012-0063 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The paper reports software-calculated power indices for a fixed 27-country game, but no numbered result asserting an algorithmic guarantee or complexity claim. The closest continuous-population alternatives either keep the countries as finite players and vary population inputs, or define a new federation with many member states; neither gives a continuous mirror of a computational result in this paper.
fails bit a — no named computational result to mirror
The paper compares Council voting rules and reports power-index calculations, including demographic projections in Tables 3–5 and A.6–A.7. Its varying population figures are real-valued inputs to a finite game, not a continuous population model.
The paper contains no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational complexity result. Its results are numerical power-index calculations for the Council’s 27 member states, including the projected decisiveness and country power shares in Table 4 and Tables A.6–A.7. Those findings are not eligible anchors under the requested standard.
A possible population-continuous angle would assign mass to citizens by member state and study how population shares affect representation. But the paper’s power indices measure the pivotality of states, and its rules also depend on the number of states and a safeguard involving three states. That makes a citizen-mass model a questionable analogue of the paper’s central problem. Without a qualifying anchor, I can’t state a per-anchor continuous problem honestly.
The negative case is unusually strong because the paper supplies no qualifying anchor. Its findings are numerical calculations of Banzhaf and Shapley–Shubik indices for the 27 Council members under specified rules and demographic forecasts. It states no complexity result for a computational problem. That rules out a direct mirror under ChoCo’s standard.
The most promising replacement would vary the countries’ population shares continuously and trace the power indices. That keeps the Council’s finite game intact: each country remains one indivisible player, while population is an input to the voting rule and to the per-capita representation calculation. Citizens do not cast votes in the model, and the paper sets aside their policy preferences. A distribution over citizens therefore cannot stand in for the coalitions of countries whose pivotality the indices measure.
A citizen-mass model would also need to reconstruct rules based on the number of countries, including the majority-of-countries threshold and the Lisbon safeguard involving at most three countries opposing. In a continuum of countries, an individual country has zero mass, so its pivotality disappears; retaining 27 country atoms preserves the finite game. Grouping countries by type would preserve power only by keeping each named country distinct, leaving finite support.
One could study asymptotic power indices for a newly defined federation with many similar member states. That may be a worthwhile project, but it changes the institutional regime and has no computational result in this paper to mirror. I see no plausible scenario that passes ChoCo’s gate for this paper itself.
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.