Towards Reality: Smoothed Analysis in Computational Social Choice

Hemaspaandra [22] celebrated the quite close relationship between computational social choice and computational complexity as a two-way street from which both areas benefited in the past, and expressed his hope that the areas become best friends forever. Later on, Rothe [38] celebrated the prominent Borda voting rule and surveyed recent advances on the complexity of problems related to the three most fundamental models of tampering with electionsnamely, via manipulation, control, and bribery-and even related to using Borda beyond voting: in fair division and coalition formation in hedonic games. But now the party is over: no more celebration! Instead, we present a common criticism regarding computational social choice persistently making use of worst-case complexity. To overcome this shortcoming, we propose our blue sky idea of applying to problems from computational social choice the method of smoothed analysis due to Spielman and Teng [43, 44] and also used by Bläser and Manthey [7], as some sort of a middle ground between the worst-case and the average-case analysis of algorithms.