This paper addresses the problem of agent preference aggregation for collective decision-making, a crucial issue in diverse fields. Considering the challenges of designing aggregation rules with specific properties (axioms) in social choice theory, we propose a method for learning aggregation rules, specifically voting rules, from data. To overcome the limitations of existing studies' large-scale models or preference representations, we reframe the problem as a probabilistic function learning problem that outputs a probability distribution over a set of candidates. We learn the probabilistic social choice function using a neural network and demonstrate the effectiveness and learning ability of preference profile encoding using standard embeddings from social choice theory. We demonstrate that the rules can be learned faster and with a smaller network than previous studies. Furthermore, we demonstrate that axiomatic properties can be used to fine-tune the learned rules to create new voting rules, and that this approach enhances resistance to certain types of attacks (e.g., the probabilistic non-response paradox).
