Abstract

The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes are extended into complete ones in a favorable way. POSSIBLE WINNER is NP-complete for common voting rules such as Borda, many other positional scoring rules, Bucklin, Copeland etc. We investigate how three different parameterizations influence the computational complexity of POSSI-BLE WINNER for a number of voting rules. We show fixed-parameter tractability results with respect to the parameter “number of candidates ” but intractability results with respect to the parameter “number of votes”. Finally, we derive fixedparameter tractability results with respect to the parameter “total number of undetermined candidate pairs ” and identify an interesting polynomial-time solvable special case for Borda. 1

Citations