Counting Dependencies: Aggregation Rules and What Official Dependency Indices Identify¶

Stefane Fermigier (Abilian) · sf@abilian.com

Draft working paper v0.1, 2026-07-18. Three propositions, each with a proof and a numeric cross-check against brute force, plus a Monte-Carlo report on rank stability. The application reconstructs a published index from its own published cells; nothing new is measured.

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Abstract¶

European economic-security policy now rests on official dependency indices. The instrument in current use scores technology areas against a fixed list of dependency dimensions on a two-level ordinal scale, counts the dimensions rated high, and reports the difference between that count and the corresponding count of reverse dependencies. We ask what such an index identifies.

Threshold counting and weakest-link exposure are different functionals and rank the same latent profiles differently, so an index that counts cannot represent a system its own authors describe as failing when one essential component fails. On a two-level scale the weakest-link reading is worse than approximate. Where every unit scores high on some shared dimension, the maximum is constant across units, all ranking content comes from the additive rule, and the choice of rule is doing the work the data are assumed to do. Netting counts of high dependencies against counts of high reverse dependencies is a third distinct object, and because a two-level scale discards intensity, the net count can invert the ordering of bargaining positions it is read as describing.

We reconstruct the index published for the European Commission from its own cells. The reconstruction reproduces twelve of thirteen printed totals; the thirteenth row carries seven high cells and prints six. Applying the index's own stated rule to its own tables contradicts its published prose: the area described as showing net dependency of more than three types scores minus one, a net reverse dependency. Under the strict reading of the accompanying claim, three of the remaining eight areas also fail it. Every one of the thirteen areas scores high on digital infrastructures and software, so the weakest-link reading is degenerate on this data. And under random positive reweighting of the eight dimensions the most-dependent area changes on 49.8% of draws, alternating between two areas. We then state what a path-aware instrument has to supply instead, and connect the requirements to the measured-graph approach developed in the companion papers.

Keywords: composite indicators, economic security, strategic dependency, aggregation, interdependence, measurement.

JEL: C43, F52, L86, O38.

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Fermigier, S. (2026). Counting Dependencies: Aggregation Rules and What Official Dependency Indices Identify.
Draft working paper v0.1, Abilian Econ Lab.
https://econ.lab.abilian.com/papers/counting-dependencies/