用图神经网络和对抗训练，让选举规则更抗操纵、更公平。

In the face of adverse motives, it is indispensable to achieve a consensus. Elections have been the canonical way by which modern democracy has operated since the 17th century. Nowadays, they regulate markets, provide an engine for modern recommender systems or peer-to-peer networks, and remain the main approach to represent democracy. However, a desirable universal voting rule that satisfies all hypothetical scenarios is still a challenging topic, and the design of these systems is at the forefront of mechanism design research. Automated mechanism design is a promising approach, and recent works have demonstrated that set-invariant architectures are uniquely suited to modelling electoral systems. However, various concerns prevent the direct application to real-world settings, such as robustness to strategic voting. In this paper, we generalise the expressive capability of learned voting rules, and combine improvements in neural network architecture with adversarial training to improve the resilience of voting rules while maximizing social welfare. We evaluate the effectiveness of our methods on both synthetic and real-world datasets. Our method resolves critical limitations of prior work regarding learning voting rules by representing elections using bipartite graphs, and learning such voting rules using graph neural networks. We believe this opens new frontiers for applying machine learning to real-world elections.