Complementarity in Social Measurement: A Partition-Logic Approach

TL;DR

This paper introduces a partition-logic framework to model social systems with incompatible observation modes, illustrating its application through six diverse social science examples and exploring implications for quantum cognition models.

Contribution

It develops a novel partition-logic approach to social measurement, demonstrating its applicability across various social science contexts and clarifying the nature of social complementarity.

Findings

Six explicit social science examples modeled with partition logics

Distinction between social complementarity and contextuality or indeterminacy

Comparison of classical and quantum-like probabilistic models in social contexts

Abstract

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually incompatible coarse-grained modes of observation. We show that this structure arises in a range of social-science settings by constructing six explicit examples from personnel assessment, survey framing, clinical diagnosis, espionage coordination, legal pluralism, and organizational auditing. For each case we identify the latent state space, the observational contexts as partitions, and the shared atoms that intertwine contexts, yielding instances of the $L_{12}$ bowtie, triangle, pentagon, and automaton partition logics. These examples make precise a notion of social complementarity: different modes of inquiry can be incompatible even though the underlying system remains fully value-definite. Complementarity in this sense does not entail contextuality or ontic indeterminacy. We further compare the classical probabilities generated by convex mixtures of dispersion-free states with the quantum-like Born probabilities available when the same exclusivity graph admits a faithful orthogonal representation. The framework thus separates logical structure from probabilistic realization and suggests empirically testable benchmarks for quantum-cognition models.