The importance of Perron-Frobenius Theorem in ranking problems

Alberto Peretti

No 26/2014, Working Papers from University of Verona, Department of Economics

Abstract: The problem of ranking a set of elements, namely giving a ``rank'' to the elements of the set, may be tackled in many different ways. In particular a mathematically based ranking scheme can be used and sometimes it may be interesting to see how different can be the results of a mathematically based method compared with some more heuristic ways. In this working paper some remarks are presented about the importance, in a mathematical approach to ranking schemes, of a classical result from Linear Algebra, the Perron--Frobenius theorem. To give a motivation of such an importance two different contexts are taken into account, where a ranking problem arises: the example of ranking football/soccer teams and the one of ranking webpages in the approach proposed and implemented by Google's PageRank algorithm.

Keywords: Ranking scheme; Linear transformation; Eigenvalue; Dominant eigenvalue (search for similar items in EconPapers)
JEL-codes: C65 C69 (search for similar items in EconPapers)
Pages: 16
Date: 2014-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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