The Smoothed Complexity of Computing Kemeny and Slater Rankings

The computational complexity of winner determination under common voting rules is a classical and fundamental topic in the field social choice. Previous work has established NP-hardness some commonly-studied rules, such as Kemeny rule Slater rule. In recent position paper, Baumeister, Hogrebe, Rothe (2020) questioned relevance worst-case nature choice proposed to conduct smoothed analysis (Spielman Teng 2009) Blaser Manthey’s (2015) framework. this we develop first results for voting. We prove hardness using runtime analysis, parameterized typical-case easiness result Kemeny. also make an attempt applying framework contexts by proving that categorizes always-exponential-time brute force search algorithm being poly-time, natural noise model based on well-studied Mallows statistics. Overall, our show challenging fruitful topic.