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Political party preference is a crucial element in the analysis of economics and political science. However, it is often di cult to investigate the dynamic properties of the individual partisanship due to inaccessibility to panel data. This study proposes a Bayesian approach for estimating Markov dynamics of individual-level partisanship with repeated cross-section data in which the history of respondents' choice of favored party cannot be observed. The proposed approach identifies individual heterogeneities that affect transitional patterns of partisanship, and replicates the dynamic patterns of individual partisan mobility. Using the proposed method with American survey data, the study shows that age, education and race significantly influence partisan dynamics among Americans for three decades from 1972.