| paper | d4-conf-atal-2014-0243 |
| 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 is a structural implication about \(Vbf\), not a result about computing it or its complexity. The other named theorems establish axiomatic properties or structural relationships, so the paper has no computational result to anchor a continuous population question.
fails bit a — no named computational result to mirror
No result supports a continuous computational mirror; the named results concern axiomatic properties of dependence and power functions or their structural links to equilibria.
I can’t make an anchor-compliant positive case from this paper: it contains no named computational result of the kind your brief requires. Theorems 1–16 analyze dependence and power functions against axioms, establish structural properties, and combine those properties. None gives a complexity classification or an algorithmic result; the paper also does not compute with a formal encoding that could qualify under your exception.
The closest near-miss is Theorem 4, proved here: for a two-player Boolean game, if the game has more than one strict Nash equilibrium, then the veto-based dependence relation is complete, \(Vbf(B)=A\times A\). That is a structural fact about dependence, not a complexity result about a computational problem. Its two-player premise also gives little support for a many-agent mirror: scaling the population changes the premise, while taking a distribution over two-player games would make instances—not the society—the continuous object.
The most plausible setting suggested by the paper is a large web-service or recommender-system deployment with many agents sharing the same Boolean goal and control role. One could imagine types as goal-and-control schemas and \(\mu\) as their population shares, then ask for type-level power rankings. But the paper defines neither Boolean games over type masses nor a mass-based ranking problem, and no named result supports its computational analysis. So I would treat that as a possible future direction, not a mirror of one of this paper’s results. The missing computational anchor is the decisive weakness.
There is no computational result here to mirror. Theorem 1 compares a dependence function with axioms; Theorem 2 shows another function satisfies them; Theorems 3–5 relate veto dependence to Nash equilibria; and Theorems 6–16 analyze power functions and their axiomatic combinations. None classifies the complexity of a computational problem or gives an algorithmic result. That rules out a direct mirror under the programme’s stated criteria.
Theorem 4 is the closest candidate the positive case identifies, but it says that a two-player game with multiple strict Nash equilibria has a complete veto-dependence relation. Its subject is the structure of a relation between strategic agents, not the computation of that relation. Duplicating players to make a large society does not supply the missing computational result. The stronger possible rescue is a symmetric family of games with many replicated agent schemas, asking how veto dependence or power rankings behave in a population limit. But veto dependence asks whether a *particular* agent is indispensable across all choices of the others. In an atomless population, a particular agent has zero mass. Replacing individual vetoes with positive-mass or threshold coalitions might be sensible, but it changes the dependence notion and the question. Theorem 4 does not tell us which change to make or provide a result for that new model.
The web-service or recommender-system scenario has a related problem. A type would need to capture an agent’s goal, controlled propositions, and relevant position in the dependence structure. Repeated services might be grouped when their games are symmetric, but a type distribution alone does not preserve who depends on whom. A graphon model of dependence, followed by a continuum version of PageRank or another power function, is the strongest version of this idea. It could motivate a separate project; it would require new semantics and new results, rather than continue a computational question addressed in this paper.
The continuum issue is therefore more fundamental than the paper’s literal finite-agent definitions: its named results concern logical and structural properties of agent-level relations and rankings. Turning mass into the object of study would require inventing a population model and a computational objective first. That may be worthwhile research, but it is not a continuous mirror of this paper’s results. The negative case is strong for the paper as written; it cannot rule out every future population model one might build around Boolean games.
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.