Properties of the Mallows Model Depending on the Number of Alternatives: A Warning for an Experimentalist

The Mallows model is a popular distribution for ranked data. We empirically and theoretically analyze how the properties of rankings sampled from the Mallows model change when increasing the number of alternatives. We find that real-world data behaves differently from the Mallows model, yet is in line with its recent variant proposed by Boehmer et al. [IJCAI '21]. As part of our study, we issue several warnings about using the classic Mallows model. For instance, we find that one should be extremely careful when using the Mallows model to generate data for experiments with a varying number of alternatives, as observed trends in such experiments might be due to the changing nature of the generated data.