  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 that 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 3- and 4-candidate cases.
