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arxiv: 2604.08482 · v1 · submitted 2026-04-09 · 🧮 math.OC · math.PR

Collective deterrence as a classification problem: Voting rules, deterrence credibility, and escalation risk

Torgeir Aamb{\o} This is my paper

Pith reviewed 2026-05-10 17:02 UTC · model grok-4.3

classification 🧮 math.OC math.PR
keywords collective deterrencevoting rulesROC curvesbinary classificationescalation risksignalling modelsocial choice functionsretaliation decisions
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The pith

Deterrence coalitions can treat retaliation choices as binary classifiers and compare voting rules by their empirical ROC performance.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Deterrence coalitions that collectively control retaliation technology must choose an institutional rule for deciding when to respond to an attack or incident. This rule creates a direct tradeoff between making deterrence credible and limiting the risk of escalation from mistaken responses. The paper recasts the decision as a binary classification task in a simple signalling model, where the coalition's voting rule acts as a classifier that distinguishes warranted retaliation from false positives. It then computes and examines the statistics of the resulting ROC curves for several choice functions and probability distributions, with explicit calculations for a four-member coalition.

Core claim

The choice of institutional design for collective deterrence, expressed as a social choice function, maps onto a binary classifier that separates true attacks warranting retaliation from false incidents. For a coalition of four members, the empirical ROC curves generated by different choice functions and different distributions over retaliation probabilities and false-positive rates can be computed and compared statistically, revealing which designs achieve better tradeoffs across varied environments.

What carries the argument

Social choice function (voting rule) recast as binary classifier in a signalling model of attacks, evaluated by its empirical ROC curve statistics.

Load-bearing premise

The simple signalling model together with the selected probability distributions for true and false positives adequately represent the information and payoff structures that matter for real deterrence coalitions.

What would settle it

Historical records of deterrence incidents in which the relative success of different voting rules at avoiding escalation or sustaining credibility fails to match the ordering predicted by their ROC curves under realistic attack and false-positive distributions.

Figures

Figures reproduced from arXiv: 2604.08482 by Torgeir Aamb{\o}.

Figure 1
Figure 1. Figure 1: ROC curves for high accuracy and resolve. [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: ROC curves for low accuracy and resolve. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: ROC curves for increasing p. varied. The best performer is again the unbiased scheme. The worst performer is still the dictator scheme, which here has an AUC of under 0.5, meaning it is essentially worse than random guessing when trying to distinguish attacks from false alarms. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: ROC curves for the unbiased scheme on the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: ROC curves for the technology scheme on the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

Deterrence coalitions that collectively own their deterrence technology, need an institutional design to decide when to retaliate against an attack or incident. This choice of institutional design, formalized through a social choice function, introduces a tradeoff between credible deterrence and escalation risk. We study this tradeoff via a simple signalling model, and use it to construct an associated binary classification problem to determine institutional designs that perform well in a variety of environments. For a small coalition of four members, we compute and study the statistics of the empirical ROC curves associated to a variety of choice functions and probability distributions for retaliation and false positives.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper frames the institutional design of deterrence coalitions as a binary classification problem, where social choice functions (voting rules) act as classifiers in a simple signaling model. It computes and analyzes the empirical ROC curves and associated statistics for a variety of choice functions under different probability distributions for true retaliation signals and false positives, with the analysis focused on a small coalition of four members to quantify the tradeoff between deterrence credibility and escalation risk.

Significance. If the modeling assumptions hold, the work supplies a quantitative, computational lens for comparing voting rules in collective deterrence settings by mapping them to classification performance. The explicit focus on small-n coalitions permits detailed statistical examination of ROC behavior across environments, which is a constructive step toward falsifiable evaluation of institutional designs. The approach is exploratory rather than axiomatic and its policy relevance hinges on the realism of the chosen distributions and signaling structure.

minor comments (3)
  1. The manuscript should include explicit pseudocode or a clear algorithmic description of how the empirical ROC curves and their statistics are generated from the signaling model and the chosen distributions.
  2. Provide a brief sensitivity analysis or justification for the specific families of probability distributions used for true and false positives, as the performance rankings may depend on these modeling choices.
  3. Clarify the precise definitions and parameterizations of the social choice functions (voting rules) employed in the n=4 computations, including any tie-breaking conventions.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our work, including its framing as a binary classification problem and the focus on empirical ROC curves for small coalitions. The significance assessment correctly notes the exploratory, computational approach and its potential for quantitative institutional comparison. We have no specific major comments to address point-by-point, as none were raised beyond the overall evaluation.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper constructs a stylized signalling model, maps it to a binary classification task, and computes ROC statistics for social choice functions under explicitly chosen probability distributions for retaliation and false positives. All reported results are direct numerical outputs of this forward simulation for n=4; no equation or statistic is obtained by fitting a parameter to a data subset and then relabeling the fit as a prediction, no quantity is defined in terms of itself, and no load-bearing premise rests on a self-citation chain. The modeling choices are stated as the scope of the exercise rather than derived from the results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the signaling probabilities and choice functions are treated as modeling primitives whose justification is not detailed.

pith-pipeline@v0.9.0 · 5390 in / 1101 out tokens · 67009 ms · 2026-05-10T17:02:17.565152+00:00 · methodology

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