A Simple Hierarchical Causality Primer

Abstract

We provide a brief primer for the idea behind formalising hierarchical causality in the context of complex systems. Here actors are not simply agents. Actors instantiate causation classes. Agents implement local dynamics in given levels or organisation in a given system. Hierarchical causality then describes how actor-level roles constrain, select, and organise agent-level behaviour across levels. The system then necessarily requires three additional structures. First, causation classes to abstract a given form of causal influence that an actor instantiates. Second, aggregation operators to move across the levels. Third, discrete event-time maps are required because the system comprises events, and the relation between local event counts and any global clock must be specified. Our formulation here is purposefully simple and discrete.

15 pages, 1 figure; short technical primer with a toy example in an appendix, corrected minor typos, refined the admissible kernel notation, added a rough Appendix B with the start of an outline of an experimental design requirements specification based on feedback from colleagues and readers (thank you for the feedback and comments)