We introduce a method to calculate the probability of discord between any two agents in the multi-state voter model with and without zealots. Our work applies to any directed, weighted graph with any finite number of possible opinions, and allows for various update rates across agents. Under certain topological conditions, their opinions are independent and the joint distribution can be decoupled. Otherwise, the evolution of discord probabilities is described by a linear system of ordinary differential equations. We prove the existence of a unique equilibrium solution, which can be computed via an iterative algorithm. The classical definition of active links density is generalised to take into account long-range, weighted interactions. We illustrate our findings on several real-life and synthetic networks. In particular, we uncover a rich landscape of varied behaviours in polarised networks.