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LIT-1170: Measuring Autonomy and Emergence via Granger Causality

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Properties6
StatusActive — read in full 2026-10-16 (NOTE-935); worth reading as the source of G-emergence, the Granger-based measure the causal-emergence readings name as a rival (NOTE-726, NOTE-791, NOTE-010). Read it knowing that its measures are predictive and relative to a regression model and a variable set, as Seth himself says (§5.2), so that "downward causation" here means Granger causation from a macro variable to micro variables, and that the validation is two agent-based models with hand-chosen conditions. Filed as THEORY-703.
Tagscomplex-systems, causality
ExtendsLIT-1173 — Investigating Causal Relations by Econometric Models and Cross-spectral Methods
Cited as “grounds” byCLAIM-334 — Granger causation from a macro variable to the micro variables it supervenes on, Seth's downward Granger causation, is not evidence of a macro-to-micro intervention effect, even with every micro variable measured: supervenience leaves no intervention on the macro variable that holds its micro base fixed at the same time
Cited as “paper” byNOTE-935 — Seth — Measuring autonomy and emergence via Granger causality
Cited as “source” byTHEORY-703 — Weak emergence of a macro variable from micro variables can be measured as its Granger autonomy from them times their mean Granger causation of it, which is zero if it is independent of them or fully predicted by them; in a boids model this measure, and Granger causation from the flock's centre of mass to each boid, are higher for flocking than for random or rigid motion; the measure is relative to the regression model and the variables included

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Anil K. Seth (2010), “Measuring Autonomy and Emergence via Granger Causality”, Artificial Life 16(2): 179–196 — doi:10.1162/artl.2010.16.2.16204

Key takeaways

From the reading, NOTE-935.

  • G-autonomy (Eq. 3). ga_{X1|X2} = log(var(ε₁ without X1’s own lags)/var(ε₁ full)): how much a variable’s own past improves its prediction once external variables are in the model. A white-noise variable and a variable driven only by white noise both score zero.
  • G-emergence (Eq. 4). ge_{M|m} = ga_{M|m} · (1/N)Σ gc_{mᵢ→M}: a macro variable is emergent from micro variables to the extent that it is both G-autonomous from them and G-caused by them. Nonlinear versions use Taylor-expanded regressors (Eqs. 5–6).
  • Validations. An evolved predator controller has higher G-autonomy than a rule that also uses internal state, which beats a pure pursuit rule (§3.2). In boids, the hand-chosen flocking condition has higher G-emergence of the centre of mass than random or rigid motion, and higher Granger causality from the centre of mass to each boid (§4).
  • What it is relative to. G-emergence can be positive because micro causal factors are missing from the model, or because the macro variable is easier for the prediction algorithm; with the system itself as predictor it would be zero (§5.2). Downward causation is called “ontologically innocent”: Granger causation from macro to micro (§4.2).

Standing in the record

Filed on 2026-10-16 as the Granger rival that three causal-emergence readings name, and read the same day. Filed as THEORY-703 (Proposed). Seth’s §5.2 concedes most of what the record would object to: the measure is epistemic and model-relative. CLAIM-334 says why its “downward causation” is not an interventional claim even with every boid measured. complex-systems is primary for its question; causality is for downward causation and the Granger measures.

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