A Design-Theoretic Taxonomy for Participatory Systems: Orthogonality, Minimal Completeness, and the Dual-Layer Diagnostic Architecture

Human participation in interactive systems is typically analyzed through either system-level design features or latent psychological states, creating an explanatory gap between objective mechanics and subjective experience. We develop a design-theoretic taxonomy that bridges this gap through a dual-layer diagnostic architecture: separating objective system properties (Signal Source) from agent perception (Decoder). We establish a seven-dimensional orthogonal vector space decomposing participatory propensity into: Output, Cost, Temporal Commitment, Extrinsic/Intrinsic Motivation, Failure Cost, and Risk Structure. Through largescale empirical validation on 𝑁 = 14,717 player reviews, we demonstrate three fundamental properties: (1) Orthogonality-dimensions exhibit weak correlation (modal |𝜌 | < 0.1) and function as independent design levers; (2) Minimal Completeness-24 of 28 components required for 90% variance capture, with each dimension explaining unique behavioral variance; (3) Behavioral Validity-96.08% coverage of substantive feedback, with systematic identification of residual categories falling outside structural design scope. We establish two critical theoretical advances: (1) The Structural Asymmetry of Failure-demonstrating that engagement success follows conjunctive logic (all dimensions must satisfy thresholds) while failure follows disjunctive logic (any single dimension violation triggers churn), explaining the systematic differences in user feedback complexity and correlation patterns; (2) Recursive Structural Applicability-evidence that the taxonomy applies recursively across micro (action), meso (session), and macro (lifecycle) granularities, validating cross-domain transferability beyond gaming to education, workplace, and civic systems. The taxonomy exhibits strong structural properties: low inter-dimensional correlation, linear PCA variance decay indicating genuine high-dimensionality, and empirical necessity of rare dimensions. These results establish that engagement can be treated as a structurally auditable behavioral product, with the dual-layer architecture enabling precise diagnosis of whether system failure lies in signal source (design deficiency), decoder (user expectation mismatch), or interface mapping (perceptual misalignment). This framework transforms abstract motivational theories into operationalizable design guidance by characterizing the objective signal space within which psychological mechanisms operate.