Set-Theoretic Multimethod Research

The distinction is defined by set membership relative to a solution term and the outcome. A typical case is a member of a sufficient term and shows the outcome, so it is where the hypothesized mechanism should be observable and is chosen to test and uncover that mechanism. A deviant case for consistency is a member of the term but lacks the outcome, signaling that something — an omitted condition, miscalibration, or measurement error — is missing; it is studied to diagnose why the sufficiency relation failed. Deviant cases for coverage show the outcome but are not covered by any term, pointing to unexplained pathways.

Because in a set-theoretic framework a case's value for revealing or disconfirming a mechanism depends on its relation to the solution term. Random or convenience selection wastes the cross-case information already obtained and may pick cases that cannot speak to the relevant hypothesis. By choosing typical cases to confirm a mechanism and deviant cases to expose model failures, SMMR ensures that within-case work directly tests and refines the cross-case claim, making the inferential contribution of each chosen case explicit and defensible.

Plain QCA delivers cross-case configurational results but cannot demonstrate the mechanism inside any case; plain process tracing illuminates mechanisms within a case but offers little cross-case generalization and no principled basis for case selection. SMMR integrates the two: QCA supplies the solution terms and the case typology that guide selection, while process tracing supplies within-case mechanismic evidence that confirms or revises the QCA. The integration — and its grounding in set theory — is what distinguishes SMMR from simply running the two methods independently.