Abstract: How to aggregate individual rational preference into collective rational preference is the main problem faced by the cognitive study of social rationality. The research about judgment aggregation brings about new ideas for analyzing preference aggregation questions. The close connection between judgment aggregation and preference aggregation was investigated from the logic perspective. After the analysis of the judgment aggregation logic JAL,it was proved that the modal logic JAL(LK) of preference aggregation could be constructed based on JAI in the language of first order logic,thus preference aggregation ctuestions could be changed into judgment aggregation questions,and the generality of the judgment aggregation model was illustrated.

Key words: Rationality, Preference aggregation, Judgment aggregation, Modal logic