Assessing the extent of strategic manipulation: the average vote example

The average voting procedure reflects the weighted average of expressed opinions in [0,1]. Participants typically behave strategically. We evaluate the discrepancy between the average taste and the average vote. If the population is sufficiently large, it is possible to construct approximations of both the average vote and the average taste which may be readily compared. We construct upper and lower bounds for the limit average vote that depend on the limit average taste. If the average taste is central enough, the range of possible values for the average voting outcome is narrower than the corresponding range for majority voting. For instance, if the average taste is at 1/2, the limit equilibrium outcome is this value plus or minus roughly .2, whereas the weighted median maybe anywhere in the [0,1] interval.