Convergence analysis of a family of Zermelo-type iterations for the Bradley--Terry model

תקציר מקורי באנגליתarXiv:2607.22221v1 Announce Type: cross Abstract: Zermelo's algorithm is a classical method for computing the maximum likelihood estimator in the Bradley--Terry (BT) model, but its convergence can be slow in practice. To accelerate computation, Newman introduced a family of Zermelo-type fixed-point iterations parameterized by $\alpha$, with Zermelo's algorithm recovered at $\alpha=1$. Empirical evidence suggests that the choice $\alpha=0$ often converges substantially faster, making it a promising alternative, yet the mechanism underlying this acceleration remains elusive. This paper provides theoretical insight into this phenomenon through a systematic local convergence analysis. We derive closed-form expressions for local convergence factors under synchronous and asynchronous updates and