Non-binary social choice preference profile's properties and its application

When the rational social choice function is been studied, it is usually been assumed that the social preference domain is complete. In reality, the social preference some times can not be complete, which gives rise to problem of non-binary social choice, and the concept of determining set has been the important concept in the study of social choice. Based on these this paper tries to analyze the properties of determining set of non-binary social choice function which meets certain constraint conditions, and deduct two property theorems on preference profile of non-binary social choice function. These property theorems can provide a new way to prove Arrow's impossibility theorem.