Bradley-Terry choice probability in maximum likelihood and eigenproblem solutions

The Bradley-Terry model (BT) is commonly used for evaluation of choice preferences by paired comparison data in various areas of applied psychology, advertising, and marketing research. The estimation of BT parameters of preference is usually achieved in an iterative procedure based on the maximum likelihood approach. In this paper an easier way of finding these parameters via an eigenproblem is considered. This approach corresponds to solving a Chapman-Kolmogorov system of equations to estimate the steady-state probabilities of the compared items. Both techniques produce very similar results, but the eigenvector solution is simpler for applications and suggests an interpretation of BT preferences as the choice probabilities. The suggested approach can facilitate the paired comparison estimations and be utilized in various practical aims of managerial decision making.