A statistical analysis of bias in a personnel assignment problem: stable solutions vs. multiplicative utility solutions

Abstract

<p>Fairness or bias in selecting employees is an important issue which is widely discussed in the literature dealing with human resources. In this paper we study a different type of bias. This bias stems from the type of mathematical algorithm used to determine an optimal match between two groups. We compare two different solution concepts for the matching assignment problem: the stable solution vs. the multiplicative utility approach. For a very small scale problem the multiplicative utility approach was found by Mehrez, Yuan and Gafni (1988) to be more fair compared to the stable approach. Using a simulation model we study the following questions: (a) Does the size of the problem affect the degree of the bias when using different approaches to solve the problem? (b) If yes, in what direction? Our main findings are: With respect to all sizes compared in our experiment the outcome was always more fair when using the multiplicative utility approach compared to the stable approach. When using an absolute measure to determine the scope of these discrepancies we find a size effect the bigger the size of the problem the bigger is the performance discrepancy between two parties when using the stable approach. No such size effects were found when the multiplicative utility approach was used. When using a relative measure to determine the scope of the discrepancies, no size effects were found for both approaches.</p>