Complexity of the Winner Determination Problem in Judgment Aggregation: Kemeny, Slater, Tideman, Young

Judgment aggregation is a collective decision making framework where the opinions of a group of agents is combined into a collective opinion. This can be done using many different judgment aggregation procedures. We study the computational complexity of computing the group opinion for several of the most prominent judgment aggregation procedures. In particular, we show that the complexity of this winner determination problem for analogues of the Kemeny rule, the Slater rule and the Young rule lies at the Θp 2-level of the Polynomial Hierarchy (PH). Moreover, we show that the problem has a complexity at the ∆p 2-level of the PH for the analogue of Tideman’s procedure with a fixed tie-breaking rule, and at the Σp 2-level of the PH for the analogue of Tideman’s procedure without a fixed tie-breaking rule. Categories and Subject Descriptors F.2 [Analysis of Algorithms and Problem Complexity]: General General Terms Theory Keywords Judgment Aggregation; Winner Determination; Comp...

• Type: Journal
• Year: 2015
• Where: ATAL
• Authors: Ulle Endriss, Ronald de Haan
• Keywords: ATAL 2015, Intelligent Agents