Exact results on manipulability of positional voting rules

We consider 3-candidate elections under a general scoring rule and derive precise conditions for a given voting situation to be strategically manipulable by a given coalition of voters. We present an algorithm that makes use of these conditions to compute the minimum size M of a manipulating coalition for a given voting situation. The algorithm works for any voter preference model — here we present numerical results for IC and for IAC, for a selection of scoring rules, and for numbers of voters up to 150. A full description of the distribution of M is obtained, generalizing all previous work on the topic. The results obtained show interesting phenomena and suggest several conjectures. In particular we see that rules “between plurality and Borda” behave very differently from those “between Borda and antiplurality”.