Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour

We consider the problem of manipulation of elections using positional voting rules under impartial culture voter behaviour. We consider both the logical possibility of coalitional manipulation, and the number of voters who must be recruited to form a manipulating coalition. It is shown that the manipulation problem may be well approximated by a very simple linear program in two variables. This permits a comparative analysis of the asymptotic (large-population) manipulability of the various rules. It is seen that the manipulation resistance of positional rules with 5 or 6 (or more) candidates is quite different from the more commonly analyzed three- and four-candidate cases.