Parameterized computational complexity of Dodgson and Young elections

We show that the two NP-complete problems of Dodgson Score and Young Score have differing computational complexities when the winner is close to being a Condorcet winner. On the one hand, we present an efficient fixed-parameter algorithm for determining a Condorcet winner in Dodgson elections by a minimum number of switches in the votes. On the other hand, we prove that the corresponding problem for Young elections, where one has to delete votes instead of performing switches, is W[2]-complete. In addition, we study Dodgson elections that allow ties between the candidates and give fixed-parameter tractability as well as W[2]completeness results depending on the cost model for switching ties. Key words: computational social choice, voting systems, winner determination, fixed-parameter tractability, W[2]-completeness

• Type: Journal
• Year: 2010
• Where: IANDC
• Authors: Nadja Betzler, Jiong Guo, Rolf Niedermeier
• Keywords: Condorcet Winner, Dodgson Elections, Efficient fixed-parameter Algorithm, IANDC 2010