Ranking Psychology: LL. Thurstone(1928)(scaling) Statistics: M. Kendall(1930s, rank corellation), F Mosteller, Bradley-Terry, .. P. Diaconis(group theory), etc Economics: K Arrow, A Sen(voting and social choice theory, Nobel Laureates Computer Science: Google' s PageRank, HITS, etc We shall focus on ranking in the sequel as the construction of abstract simplicial complex is more natural and easier than point cloud dataRanking Psychology: L. L. Thurstone (1928) (scaling) Statistics: M. Kendall (1930s, rank corellation), F. Mosteller, Bradley-Terry,…, P. Diaconis (group theory), etc. Economics: K. Arrow, A. Sen (voting and social choice theory, Nobel Laureates) Computer Science: Google’s PageRank, HITS, etc. We shall focus on ranking in the sequel as the construction of abstract simplicial complex is more natural and easier than point cloud data