The dynamics of self-evaluation

Abstract

We investigate a situation where qualification values are to be attributed to n persons, based on a matrix A of cross-ratings and a so-called calibration function describing the dependence between qualification and competence of judging. An appropriate vector of qualification values is obtained as the solution of a certain fixed point equation. Motivated by the aim to compute this fixed point as the limit of an iterative procedure of qualification assignments, we study the dynamics of this procedure. Sufficient conditions for the existence of a unique, globally attracting fixed point are derived. Furthermore, it is shown that there are cases where only repelling fixed points exist and hence the procedure does not converge.