Parameterized Complexity Results for the Kemeny Rule in Judgment Aggregation

We investigate the parameterized complexity of computing an outcome of the Kemeny rule in judgment aggregation, providing the first parameterized complexity results for this problem for any judgment aggregation procedure. As parameters, we consider (i) the number of issues, (ii) the maximum size of formulas used to represent issues, (iii) the size of the integrity constraint used to restrict the set of feasible opinions, (iv) the number of individuals, and (v) the maximum Hamming distance between any two individual opinions, as well as all possible combinations of these parameters. We provide parameterized complexity results for two judgment aggregation frameworks: formula-based judgment aggregation and constraint-based judgment aggregation. Whereas the classical complexity of computing an outcome of the Kemeny rule in these two frameworks coincides, the parameterized complexity results differ.