The Influence of the Number of Voters on Ranking Data Sampled with the Mallows Model

Ranking aggregation algorithms are typically evaluated using synthetic data generated by the Mallows model. Comparisons are often made across profiles with varying numbers of voters under the assumption that their structural properties remain consistent. However, previous empirical studies have shown that this assumption does not always hold, as the number of voters appears to affect profile characteristics such as the Condorcet properties. In this paper, we provide a theoretical explanation of these phenomena by introducing a probabilistic framework that characterises events arising from the Mallows sampling process, including the probability that a given alternative is the Condorcet winner. We demonstrate that the number of voters influences the distribution of sampled profiles and, consequently, their structural characteristics. Building on these theoretical results, we propose methodological guidelines for the fair evaluation of ranking aggregation algorithms, facilitating unbiased comparisons across benchmark instances generated with different parameter configurations.