Application of PageRank Algorithm on Sorting Problem

In the social life, people often face a wide range of scheduling problems, such as appraisal of excellence, race rankings. These are often hot and sensitive issues, so the research of this type of problems has practical and economic value. But due to socio-cultural diversity and pluralism of values, sorting problems would be restricted on a set of priority level or justice principles. As well-known Arrow theory told us: in a certain sense, there are not a set of the justice axiom to satisfy the so called sort rules. This article is stimulated by Google's PageRank algorithm and the example of national college mathematical modeling contest problem B in 1993. Constructing random matrix shows the application of PageRank algorithm on sorting problem.