This paper examines the sensitivity of the Local Markovian Consensus method with weak ordinal dominance (LMC-WOD) to changes in the damping factor d. The factor controls the balance between local preferences dominance and global uniform influence. Experiments are conducted on synthetic datasets generated via the Mallows model, covering various levels of ranking noise, dimensionality, and data volume. Aggregation outcomes are evaluated using Kendall tau distance, pairwise agreement, and the WS coefficient, each capturing distinct aspects of ranking consistency. The results show that LMC-WOD is robust to changes in d across all settings, consistently producing high-quality aggregated rankings in non-conflicting environments. Moreover, the method maintains stable consensus rankings even in the presence of preference conflicts or a large number of alternatives.