The PerronRank family: a brief review

  • Ngoc Mai TranEmail author


Ranking by pairwise comparison is a widely used method in economics, decision analysis, operations research, and machine learning. However, the choice of method used for computing the score vector can strongly influence the outcome. We examine three methods for ranking by pairwise comparison: PerronRank ( Principal Eigenvector), HodgeRank, and TropicalRank. In a previous work, we showed that HodgeRank and TropicalRank are limits of PerronRank, hence the methods belong to the same family. On the other hand, the choice of method can produce arbitrarily different rank order. This paper reviews these results, discusses their implications in practice, and states some open problems.


Pairwise comparison Decision support system Individual preference Analytic hierarchy process Perron-Frobenius Ranking 

JEL Classification

D70 D71 



This work was supported by an award from the Simons Foundation (\(\#197982\) to The University of Texas at Austin). The author would like to thank an anonymous referee for the careful reading and helpful suggestions.


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Copyright information

© Japan Association for Evolutionary Economics 2015

Authors and Affiliations

  1. 1.Department of MathematicsThe University of Texas at AustinAustinUSA

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