Generalized scoring rules and the frequency of coalitional manipulability

We introduce a class of voting rules called generalized scoring rules. Under such a rule, each vote generates a vector of k scores, and the outcome of the voting rule is based only on the sum of these vectors--more specifically, only on the order (in terms of score) of the sum's components. This class is extremely general: we do not know of any commonly studied rule that is not a generalized scoring rule. We then study the coalitional manipulation problem for generalized scoring rules. We prove that under certain natural assumptions, if the number of manipulators is O(np ) (for any p < 1 2 ), then the probability that a random profile is manipulable is O(np- 1 2 ), where n is the number of voters. We also prove that under another set of natural assumptions, if the number of manipulators is (np ) (for any p > 1 2 ) and o(n), then the probability that a random profile is manipulable (to any possible winner under the voting rule) is 1 - O(e-(n2p-1 ) ). We also show that common...

• Type: Journal
• Year: 2008
• Where: SIGECOM
• Authors: Lirong Xia, Vincent Conitzer
• Keywords: ECommerce, Generalized Scoring, Natural Assumptions, SIGECOM 2008, Voting Rules