Dodgson's Rule and Young's Rule

Dodgson’s and Young’s election systems, dating from 1876 and 1977, are beautiful, historically resonant election systems. Surprisingly, both of these systems turn out to have highly intractable winner-determination problems: The winner problems of these systems are complete for parallel access to NP. This chapter discusses both the complexity of these winner-determination problems and approaches—through heuristic algorithms, fixed-parameter algorithms, and approximation algorithms—to circumventing that complexity.