Losses due to manipulation of social choice rules

In a companion paper, "Gains from Manipulating Social Choice Rules," we analyzed the incentive to manipulate by considering the maximum number of ranks someone can gain in their preference ordering by manipulation. This paper treats the number of ranks someone else can lose due to manipulation. We find large classes of rules where that loss is very large, a few rules where the loss can be significantly smaller, and even some rules where no one ever loses-even though manipulation will take place.