Recent results have established that a variety of voting rules are computationally hard to manipulate in the worst-case; this arguably provides some guarantee of resistance to ma- nipulation when the voters have bounded computational power. Nevertheless, it has become apparent that a truly dependable obstacle to manipulation can only be provided by voting rules that are average-case hard to manipulate.

In this paper, we analytically demonstrate that, with re- spect to a wide range of distributions over votes, the coali- tional manipulation problem can be decided with overwhelm- ing probability of success by simply considering the ratio between the number of truthful and untruthful voters. Our results can be employed to significantly focus the search for that elusive average-case-hard-to-manipulate voting rule, but at the same time these results also strengthen the case against the existence of such a rule.