Structural Accountability: A Responsibility-Based Framework for Democratic Legitimacy

This work develops a purely structural theory of democratic accountability by formalizing how responsibility flows from individual political agents to collective political outcomes. The paper introduces the concept of a responsibility mapping and demonstrates, using category‑theoretic tools, that proportional representation systems structurally degrade this mapping by allowing responsibility to be absorbed by non‑responsibility‑bearing party entities. When this occurs, the mapping collapses into a zero morphism, rendering accountability invisible and unrecoverable. The analysis does not rely on empirical case studies or country‑specific observations. Instead, it identifies the mathematical conditions under which any electoral system preserves or destroys the visibility of responsibility. The paper further proposes an integrity‑threshold mechanism that restricts proportional participation when evidential doubts arise, ensuring that responsibility remains traceable under conditions of political stress or external shocks. Appendix A provides an intuitive explanation of the structural failure without requiring prior knowledge of category theory, while Appendix B offers a rigorous formalization using functors, zero morphisms, kernels, cokernels, and limits. Together, these components establish a general theoretical framework for evaluating democratic legitimacy based on the recoverability of responsibility.