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.

翻译：根据社会选择理论中的经典结论，任何合理的偏好投票方法有时都会使个体有动机报告不真实的偏好。不同投票方法对抗策略性操纵的程度已成为比较投票方法的关键考量因素。本研究通过衡量不同规模的神经网络能否在预期收益上学会针对给定投票方法进行有利操纵，来测度其抗操纵能力，其中神经网络需基于关于其他选民投票行为的不同类型有限信息。我们训练了超过7万个26种不同规模的神经网络，针对8种投票方法、在6种有限信息类型下、面向5-21名选民和3-6名候选人的委员会规模选举进行操纵。研究发现，某些投票方法（如波达计数法）在有限信息条件下极易被神经网络操纵，而另一些方法（如即时决选投票制）则难以被操纵，尽管在全知全能的理想操纵者面前它们能带来可观收益。在我们采用的两种选举概率模型中，所研究的8种方法中整体抗操纵性最强者为孔多塞方法，即最小最大法和分裂循环法。