Judgment Aggregation And The Greedy Algorithm

The judgment aggregation problem is an extension of the group decision-making problem, wherein each voter votes on a set of propositions which may be logically interrelated (such as \( p \), \( p \to q \), and \( q \)). The simple majority rule can yield an inconsistent set of results, so more complicated rules must be developed. Here, the problem is cast in terms of matroids, and the Greedy Algorithm is modified to obtain a “best” result. An NP-completeness result is also presented for this particular formulation of the problem.