| paper | d4-journals-geb-2014-0005 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
Theorem 1 and Theorem 2 are axiomatic characterizations, and Proposition 1 relates axioms; none states an algorithm, complexity bound, or hardness result. Computing the winner from weighted rankings is a plausible nearby task, but it is not a computational result established by this paper.
fails bit a — no named computational result to mirror
Theorem 1 and Theorem 2 characterize the two procedures through axioms; Proposition 1 establishes an equivalence between axioms. The proposed winner-computation task is not a result of the paper.
The paper has no named computational result in the sense required for an anchor: none of its numbered results asserts a complexity classification or an algorithm. Theorem 1 says that a decision rule satisfies Condorcet Consistency, Condorcet Priority, and Division Consistency if and only if it is the undominated Nash equilibrium outcome of a Euro-Latin procedure for some agenda. Theorem 2 gives the corresponding characterization for the Anglo-American procedure using Condorcet Loser Consistency, Condorcet Antipriority, and Elimination Consistency. Both are proved in this paper, but they are axiomatic characterizations, not computational results.
The nearest honest lead for a continuous mirror would be: given a finite-support distribution over complete rankings, with rational masses summing to \(1\), an agenda, and one of the two procedures, compute its undominated-equilibrium winner. A plausible regime is a large assembly with many members but relatively few shared preference types—for example, large caucuses whose members share rankings over a fixed, modest set of alternatives. Each type is a ranking, its mass is the fraction of the assembly with that ranking, and the answer is the selected alternative. To preserve the paper’s assumption of an odd electorate, the continuous instance could require that no pair of alternatives is tied at exactly half the mass.
That is a recognizable population-continuous version of the procedures’ outcome problem, but it is only a proposed computational question. It is not an anchor supplied by this paper, and the paper does not analyze its complexity. The central weakness is that the authors’ contribution is explicitly about axiomatic characterization; a computational mirror would extend their subject rather than continue a computational result they established.
The strongest case against is that this paper has no computational result to mirror. Theorem 1 and Theorem 2 characterize decision rules over every preference profile and every menu of alternatives. They do not give an algorithm or classify the complexity of a computational problem. That distinction matters: a continuous version of those theorems would still be an axiomatic characterization, outside ChoCo’s stated scope.
The proponent’s proposed winner-computation problem is the best alternative, and its population regime is sensible: a large assembly can have many members sharing a modest number of rankings. But it is a new problem, not a computational reading of either theorem. Given rational type masses and an agenda, one can compute pairwise majority comparisons by summing over the \(\tau\) types, then evaluate the procedure’s equilibrium outcome. The paper’s own proofs provide the relevant recursions; the computation takes polynomial time in \(m,\tau,L\). This does not make the question unworthy because its answer is easy. It shows that the proposed question is simply to run a specified voting institution on a weighted profile, whereas the paper’s contribution is a characterization of which rules coincide with that institution across all profiles and menus.
A more ambitious version—finding an agenda that implements a target outcome, for example—would add an agenda-design objective the paper does not study as a computational problem. Likewise, asking whether axioms characterize a rule on a continuum of societies remains an axiomatic question; making rule verification computational would require a new representation of the rule and a new task. Those might be worthwhile projects, but they are not mirrors of this paper’s results. The negative case is strongest on that boundary: it cannot rule out interesting computational work nearby, but the paper itself supplies no computational anchor for a continuous mirror.
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.