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THEORY-804: Ince's common change in surprisal is a correct measure of the redundancy among any number of sources, and the negative partial-information atoms it gives are local misinformation and mechanistic redundancy, not defects of the measure

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Properties5
StatusProposed
Tagsinformation-theory, complex-systems
SourceLIT-1201 — Measuring multivariate redundant information with pointwise common change in surprisal
ExtendsTHEORY-714 — Ince's I_ccs, the expected local co-information over only those events where every source, the joint source and the overlap change the target's surprisal in the same direction, under the maximum-entropy joint that preserves the source–target and joint-source marginals, is symmetric and self-redundant and satisfies the independent identity property; it fails Harder et al.'s identity and monotonicity, so its atoms can be negative, and, though its paper says otherwise, it fails subset equality
AnswersQUESTION-223 — Is Ince's common change in surprisal a correct redundancy measure: is it continuous, does it agree with a redundancy fixed by mechanism where rivals with non-negative atoms do not, may unique information depend on the source-source marginal, and can a modified sign rule restore subset equality?

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Source

Ince (2017), “Measuring multivariate redundant information with pointwise common change in surprisal”, LIT-1201, read in NOTE-968. The paper offers I_ccs as a measure of redundancy that keeps symmetry, self-redundancy, subset equality and identity for independent sources, and gives up Harder et al.’s identity, monotonicity and non-negative atoms. It reads the resulting negative atoms as “misinformation” and “mechanistic redundancy” rather than as defects.

What is asserted, and by whom

That I_ccs is the right redundancy function for the partial-information lattice, and that the axioms it drops ought to be dropped. Ince argues it from examples judged by intuition and from the claim that unique information may depend on the source–source marginal, which Bertschinger et al. (LIT-1162) deny.

What the record holds toward it

  • THEORY-714 (Active): the definition, the three properties that hold, the failures of identity and monotonicity, and every discrete example, all re-derived.
  • Against it: subset equality fails (THEORY-714’s note of 2026-10-20, a two-source counterexample giving 0.0272 bit against 0.0073). Ince’s proof cancels the co-information but not the sign rule. Since subset equality is what licenses restricting the measure to the lattice’s antichains, the measure’s rationale needs repair.
  • For it, weakly: on XORCOPY I_ccs takes the negative atom exactly at the −1-bit bound THEORY-713 proves, rather than violating independent identity as I_min does.
  • Continuity is conjectured and checked only locally.

What would confirm or reject it

As the promote_when says: continuity plus agreement with a mechanism-fixed redundancy where non-negative rivals disagree, or a settled answer on the source–source marginal. QUESTION-223 asks the same thing as a question.

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