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Here are the results from 6-day-long research sprint on some mathematical formalisms for power:
Mathematical Foundations for Power Analysis: Dahlian Power, Power-Preference Connection, Absolute-vs-Relative Power
https://drive.google.com/drive/folders/1a4C5NI_xy9q1ISqomQ0ZPraGT26yPE1r?usp=drive_link
Disclaimer: This is an exploratory, partially abandoned line of work. Some characterizations (e.g., Dahl, Lukes), derivations, proofs, or statements may be incomplete, incorrect, or incoherent. I’m sharing this work because it may be useful or inspiring despite underdevelopment.
Briefly: I formalize and extend Dahl’s 1957 concept of power for complex, pseudo-multi-agent systems. The framework (i) generalizes from binary to multi-valued means, (ii) models pseudo-multi-controller settings and environmental outcomes, and (iii) introduces comparative measures (marginal, adversarial pairwise, and coalition power) with accompanying diagrams. I then make explicit three structural limitations of Dahlian power: the inability to represent means–response chains without information loss, the lack of principled cross-domain scope comparisons, and ambiguity in action-space and controller selection. On the broader topic of power, I argue that modeling power as relational instead absolute is necessary. I describe why utility-based formulations of power (relevant state spaces, alignment/aggregation) are prerequisites for complete power analysis.