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LIT-1839: Causal Emergence: When Distortions in a Map Obscure the Territory

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Properties7
StatusActive — read 2026-10-29 (NOTE-1413) in full, from the publisher's PDF as deposited in Caltech's CaltechAUTHORS repository; worth reading as the published case that effective-information maximization, with a uniform intervention over macro states realized as a uniform average over their micro states, merges states with different effects (ambiguous manipulations) and picks levels that change with the time step (abstraction and marginalization do not commute). Read it knowing that its target is Hoel 2017, not Hoel, Albantakis and Tononi 2013; that its examples are numerical, found by a 0.1 grid search on 3×3 matrices; that it argues the uniform distribution is extraneous but never computes what happens when one micro distribution is used at both levels; that its commutativity example is a partition that is strongly lumpable, so the coarse-graining commutes and only the EI-optimal choice does not; and that its 8-state ambiguity example is unambiguous with respect to the macro effect it is scored on.
Version2
Tagscausality, information-theory, complex-systems
RivalsLIT-1843 — Causal emergence is widespread across measures of causation
Cited as “grounds” byARG-041 — From the effective-information bound and its ties to proportionality: a gain that depends on the intervention distribution is not a property of the system, the coarse-grainings that lose nothing are, and the coarsest of them is where the causes are
Cited as “paper” byNOTE-1413 — Eberhardt and Lee — Causal emergence: when distortions in a map obscure the territory
Cited as “source” byTHEORY-1167 — When one intervention distribution over micro states is used at both levels, the effective information of a coarse-graining of a discrete mechanism, with each macro intervention realized by that distribution within its block, cannot exceed the micro effective information; so a positive causal emergence of effective information, scored with a uniform distribution at each level, equals the micro gain from changing the distribution minus a non-negative loss, and is a gain from the change of distribution, THEORY-1169 — For a discrete mechanism scored with one full-support intervention distribution over micro causes at both levels, a coarse-graining of cause and effect keeps all of the micro effective information if and only if it merges only causes with identical rows P(Y | do(x)) and only effects with proportional columns, whatever the distribution; so the coarsest coarse-graining that ties the micro is the causal partition of causal feature learning, with effects grouped by normalized likelihood, and any merge of causes with different effects loses information under every such distribution

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Eberhardt, F. & Lee, L.-L. (2022). Causal emergence: when distortions in a map obscure the territory. Philosophies 7(2), 30. doi:10.3390/philosophies7020030

Read in full on 2026-10-29 (NOTE-1413).

Why this is here

The triage of 2026-10-29 (curation entry of 20:59) filed it for QUESTION-204, for THEORY-787’s “in trouble if” clause and for QUESTION-115’s admissible macro-interventions (A21). The record held the causal-emergence defenders’ replies to this paper (CE 2.0, NOTE-1387; Zhang et al., NOTE-1399) and not the paper. Read with Comolatti and Hoel 2022 (LIT-1843), it bears on whether THEORY-787 can be promoted.

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