The article is centered on the problem of inferring the parameters of a majority rule sorting model when large sets of assignment examples are considered. Beside the proposal of an approach for solving this problem, the main focus of the paper lies in the inclusion of veto thresholds inside the majority rule model, which, as we illustrate, increases the expressiveness of the model. However, due to its complexity, an exact approach for inferring its parameters is not practical especially when large datasets are considered. Therefore, we propose a metaheuristic approach to overcome this difficulty. The approach is validated over a set of constructed benchmarks as well as on several datasets containing real data.