Voting systems have a wide range of applications including recommender systems, web search, product design and elections. Limited by the lack of general-purpose analytical tools, it is difficult to hand-engineer desirable voting rules for each use case. For this reason, it is appealing to automatically discover voting rules geared towards each scenario. In this paper, we show that set-input neural network architectures such as Set Transformers, fully-connected graph networks and DeepSets are both theoretically and empirically well-suited for learning voting rules. In particular, we show that these network models can not only mimic a number of existing voting rules to compelling accuracy --- both position-based (such as Plurality and Borda) and comparison-based (such as Kemeny, Copeland and Maximin) --- but also discover near-optimal voting rules that maximize different social welfare functions. Furthermore, the learned voting rules generalize well to different voter utility distributions and election sizes unseen during training.
翻译:投票系统有各种各样的应用,包括推荐系统、网络搜索、产品设计和选举。由于缺乏通用分析工具,因此很难对每种使用案例进行手工设计适当的投票规则。因此,它呼吁自动发现针对每种情况的投票规则。在本文中,我们显示,定点输入神经网络结构,如Set变换器、完全连通的图形网络和DeepSet等,在理论上和经验上都适合于学习投票规则。特别是,我们显示这些网络模式不仅可以模仿现有的一些投票规则,以强制准确性 -- -- 既基于位置(如多功能和博尔达),又基于比较(如凯梅尼、科普兰和马克林) -- -- 但也可以发现接近最佳的投票规则,从而最大限度地发挥不同的社会福利功能。此外,在培训期间,学到的投票规则一般适用于不同的选民效用分配和选举规模。