| paper | d4-journals-geb-2026-0095 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Results 1–3 are empirical findings about participants’ choices, while Appendix A summarizes prior equilibrium theory without a computational claim by this paper. Continuous Community Targeting is a statable adjacent allocation problem, but it does not supply the missing computational result of this paper.
fails bit a — no named computational result to mirror
No computational result is covered; Result 1 concerns observed best-response choices, and Results 2–3 concern behavioral biases.
This paper has no qualifying computational anchor. It reports three numbered empirical results, but no numbered Theorem, Lemma, Corollary, or Proposition asserting that a problem is tractable or hard. The nearest anchor in spirit is Result 1, reported from the experiment: a majority of participants chose a best response, and this was more common among participants with higher mathematical and cognitive abilities. Results 2 and 3 report behavioral biases in targeting. These are findings about observed choices, not complexity results. Appendix A summarizes equilibrium results from Grabisch et al. (2018), but it presents no named computational result. So I cannot honestly supply a continuous problem per qualifying anchor.
The strongest positive case I can make is an adjacent high-multiplicity version of the targeting problem. Call it *Continuous Community Targeting*. An instance has a finite support of local-community types \(T\). A type \(t\) specifies a small network and its interaction matrix \(W_t\), the opponent’s target \(q_t\), and the opponent’s influence \(\lambda_t\); it may also specify the initial opinions. The input gives rational masses \(\mu_t\), summing to one. Think of many similar local networks—such as branches of an organization or local campaign groups—with many more communities than distinct configurations.
For each type \(t\) and node \(v\) in its network, let \(g_t(v)\) be the resulting average steady-state opinion when the player targets \(v\) and the opponent targets \(q_t\). The decision is \(x_{t,v}\geq 0\), the mass of type-\(t\) communities assigned target \(v\), with \(\sum_v x_{t,v}=\mu_t\). The task is to choose \(x\) maximizing \(\sum_{t,v}x_{t,v}g_t(v)\); a solution is an optimal rational allocation. Each community still receives one integral target. The continuous object is the distribution of community types and their aggregate targeting decisions.
This mirrors the best-response targeting rule underlying Result 1, but it is not an anchor and it changes the paper’s single five-node network into a portfolio of local networks. Its expected classification is tractable: compute the steady-state payoff for each candidate target and choose the best target within each type. With fixed-size networks this is just enumeration over the support and its nodes; even with larger rational input networks, computing the steady state for each candidate target requires solving linear systems. The result is an easy aggregate optimization problem, not a continuation of a hardness question. Natural follow-ups include adding a shared campaign budget across communities, allowing interactions between communities, or studying what changes when targeting capacity must be integral across a finite number of groups.
The case for plausibility is that campaigns really can operate across many repeated local groups, with a small number of network configurations and a target chosen in each group. The weak point is that the paper’s strategic object is a single target in one interconnected network. Its network structure and node roles matter, so a simple distribution over individual node attributes would lose essential information; the type here must carry the local network itself. Moreover, the paper is chiefly an experimental study of behavior, and the proposed model does not explain its findings about cognitive ability or opinion biases. I would offer this as a plausible research extension, but not claim that the paper supplies the computational result needed for a strong, anchored continuous mirror.
The paper has no computational result to continuize. Results 1–3 are empirical findings about participants’ choices. Appendix A summarizes equilibrium results from Grabisch et al.; it does not analyze the complexity of computing a best response. In the experiment, that response is a choice among five nodes under a fixed network and opponent move. The paper reports how often people made that choice, not an algorithmic problem or a complexity claim.
The behavioral results do not supply a computational anchor either. A distribution over participants’ cognitive or behavioral types could describe the share who best respond, target central nodes, or show affinity bias. That would aggregate experimental behavior; it would not turn the paper’s findings into computational targeting questions. Results 2 and 3 are especially tied to observed human choices, while the model says initial opinions do not affect the payoff-maximizing target.
The proposed *Continuous Community Targeting* is a plausible neighboring model, but it changes the object. Each “type” contains an entire local network and its opponent configuration, so the population is a collection of separate games rather than a continuum of nodes in the paper’s interconnected network. With no shared constraint, each type’s targeting decision can be optimized independently. A campaign budget could couple those decisions, but that introduces a pooled resource-allocation problem absent from the paper. It may be worth studying on its own; it does not provide a continuous mirror of a computational result this paper established.
The more direct population mirror also faces a structural problem. Each strategic player chooses one node. In a diffuse continuum network, a single targeted node has zero population mass and generally no effect on aggregate opinion. Keeping a pivotal target as a special atom preserves an individually identifiable node, while targeting a positive-mass cohort changes the action from forming one link to influencing a group. Either may motivate a new model, but neither is the high-multiplicity version of the paper’s single-target game without substantial additional choices about the network and intervention.
So the negative case is strongest as a case against treating this paper as a ChoCo anchor: it supplies neither a computational result nor a population model whose central decision survives a straightforward continuum limit. It is weaker as the universal claim that no useful campaign-level model could be built from these ideas. The community portfolio is a credible extension; the case against it is that it is a new allocation problem, not a continuous mirror of this paper.
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.