Non-parametric ranking and rating functions

Non-parametric ranking and rating using various competitive and consensual methods, as well as an analysis of concordance between rankings.

FUNCTIONS
---
Competitive ranking and rating methods
ranking.m - Massey, Colley, Centroids
ensemble.m - Ensemble voting methods: ratio of offensive and defensive strength, Markov, Perron

Consensual ranking and rating method
majority_judgement.m - Majority Judgement

Optimization of ranking
ranking.m - Local Kemenization

Analysis of rankings
kcc.m - Kendall’s coefficient of concordance between rankings

Utilities
ratings2scores.m - Transform ratings of single items to scores between two items

Demo
ranking_demo.m - Demonstration of the functions on sample data

ACKNOWLEDGMENTS
---
* Implements methods published in the references below.
* Includes open source code by Amy N. Langville (pagerank.m) and Aravind Seshadri (perron.m).

REFERENCES
---
Michel Balinski, Rida Laraki (2010). Majority Judgment Measuring, Ranking, and Electing, Cambridge, MA: MIT Press.

Cynthia Dwork, Ravi Kumar, Moni Naor, D. Sivakumar (n.d.). "Rank aggregation revisited", CiteSeerX, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.2507.

John G. Kemeny (1959). "Mathematics without Numbers", Daedalus, 88 (4): 577–591.

Maurice G. Kendall (1970). Rank Correlation Methods, New York, NY: McGraw-Hill, 4th ed, pp. 94–116. [Summary and additional details.]

Amy N. Langville, Carl D. Meyer (2006). Google’s PageRank and Beyond: The Science of Search Engine Rankings, Princeton, NJ: Princeton University Press.

Amy N. Langville, Carl D. Meyer (2012). Who’s #1?: The Science of Rating and Ranking, Princeton, NJ: Princeton University Press.

Aravind Seshadri (2020). Perron root computation (https://www.mathworks.com/matlabcentral/fileexchange/22763-perron-root-computation), MATLAB Central File Exchange. Retrieved July 19, 2020.