A Method to Evaluate Geometrical Configuration of Candidates from Ranked Preference Data

Ranked preference data arise in the situation that a large number of people (voters) rank several objects (candidates) in order of their extent of preference, for instance, multiple voting with ranking or a questionnaire of preference ranking. Such data are supposed to include the information about similarity among candidates in the sense that those who are highly preferred by the same voter would seem to be similar to the voter. Based on this idea, we have proposed a method to evaluate the geometrical configuration and distance between candidates by applying multidimensional scaling (MDS) on ranked preference data in which each voter votes multiple candidates consistently with their preference ranking. In this paper, we have an experiment in order to investigate the feasibility of this method. Using simulative data, we examine whether our method can retrieve the original configuration. We generate candidates and voters simulatively and apply this method to the data obtained. We also have an application to actual data obtained from students about allocation to advisory professor at undergraduate course (for bachelor degree).