Political Incoherence: an application of κ-uncolourable hypergraphs to the theory of democracy

摘要

Preservationist paraconsistent logicians have demonstrated the, utility of κ-uncol-ourable hypergraphs when it comes to formalizing non-trivial but classical inference from inconsistent premise sets. Here it is shown how this application can be extended to the deontically dual political context in which elected officials form u-nified policies which putatively represent, incohe-sive interest groups. By exploiting the logical duals of κ-uncolourable hypergraphs. a non-statistical model for a democratic polling technique is designed whose aim is to preserve electoral representativeness through deliberative legislative processes of policy formation. Moreover, it is proven that the mathematical technology required to instantiate the polling technique exists, and would not be too dif-ficult to implement. In particular, it is shown to be a theorem that any κ > 1, any j > κ, "exist" H : H is a hypergraph, with x(H) = κ + 1, and any E ∈ H, the restriction of H to ∪H ― E has chromatic number κ ― 1.