Quantifying causal emergence shows that macro can beat micro.

Area of Science:

• Complex Systems Analysis
• Causal Inference
• Information Theory

Background:

• Causal interactions in complex systems are studied across multiple spatial and temporal scales.
• Supervenience assumes fixed macro levels from fixed micro levels, with micro-level causation considered complete.
• The causal completeness of micro-levels is often assumed, limiting the recognition of macro-level causation.

Purpose of the Study:

• To evaluate the assumption of micro-level causal completeness using a quantitative measure of causation.
• To investigate whether macro levels can exhibit genuine causal power beyond micro-level descriptions.
• To introduce and apply effective information (EI) as a measure of causation.

Main Methods:

• Utilized effective information (EI), a measure combining mechanism effectiveness and state space size.
• Analyzed EI at both micro and macro levels in simple systems with fixed micro-mechanisms.
• Quantified causal power by measuring how effectively mechanisms constrain system states.

Main Results:

• Demonstrated that EI can peak at macro levels in space and/or time for specific causal architectures.
• Showed that more effective (deterministic, less degenerate) macro-level mechanisms can overcome smaller state spaces.
• Identified conditions for genuine causal emergence, where macro levels causally supersede micro levels.

Conclusions:

• Macro levels, despite supervening on micro levels, can possess greater causal effectiveness.
• Genuine causal emergence is possible, characterized by a gain in EI at higher levels of analysis.
• Challenges traditional views of micro-causal completeness in complex systems.