Resistance and conductance in structured Zermelo tournaments

The mathematical model that Zermelo developed for ranking by paired comparisons and that was later popularized by Bradley and Terry has several attractive theoretical properties, but computation of the associated ratings may involve solution of a system of several high-degree polynomial equations in several variables. This paper describes how to define quantities analogous to electrical resistance and conductance for certain generalized tournaments in such a way that these quantities are well-behaved with respect to certain types of decomposition of tournaments and permit comparison of the ratings of pairs of nodes. Application of this theory is illustrated through consideration of specific examples.