Bayesian statistics assumes that there are specific parameteric distributions for the unknown parameters. It fits the probability model of interest by incorporating prior information regarding the unknown parameters and the likelihood function of the observed data. Moreover, Bayesian statistics as well as non-Bayesian methods produce good asymptotic results. Using WinBUGS and R language, a binomial logistic regression model of voting choice in the 2002 Taipei mayoral election is developed. Adding the prior information from the first panel to the estimation of the second panel, the Bayesian model yields sharper estimates concerning the election outcome. Additionally, the replication of data provides a model check and the baseline of the new observations. The methodological contribution of this paper is the ability to fit a binary logistic regression model with the observed data using the Bayesian inference.