  By classic results in social choice theory, any reasonable preferential
voting method sometimes gives individuals an incentive to report an insincere
preference. The extent to which different voting methods are more or less
resistant to such strategic manipulation has become a key consideration for
comparing voting methods. Here we measure resistance to manipulation by whether
neural networks of varying sizes can learn to profitably manipulate a given
voting method in expectation, given different types of limited information
about how other voters will vote. We trained over 70,000 neural networks of 26
sizes to manipulate against 8 different voting methods, under 6 types of
limited information, in committee-sized elections with 5-21 voters and 3-6
candidates. We find that some voting methods, such as Borda, are highly
manipulable by networks with limited information, while others, such as Instant
Runoff, are not, despite being quite profitably manipulated by an ideal
manipulator with full information. For the two probability models for elections
that we use, the overall least manipulable of the 8 methods we study are
Condorcet methods, namely Minimax and Split Cycle.
