On the safety of group manipulation

Groups of voters have more possibilities to influence the voting result than separate individuals. However, there is a problem with coordinating their actions. This paper considers manipulation by groups of voters who have the same preferences. If a voting result is more preferable for voters of a particular group provided that all its members use the same strategy (report the same insincere preference), then each of these members has an incentive to manipulate. If there is a chance that they will become worse off in case only a subset of the whole group manipulates, then manipulation is unsafe. For several voting rules we study conditions on the numbers of voters and alternatives which allow for an unsafe manipulation or which make manipulation always safe.