We present a statistical model for voter choice that incorporates a consideration set stage and final vote intention stage. The first stage involves a multivariate probit model for the vector of probabilities that a candidate or a party gets considered. The second stage of the model is a multinomial probit model for the actual choice. In both stages we use as explanatory variables data on voter choice at the previous election, as well as socio-demographic respondent characteristics. Importantly, our model explicitly accounts for the three types of "missing data" encountered in polling. First, we include a no-vote option in the final vote intention stage. Second, the "do not know" response is assumed to arise from too little difference in the utility between the two most preferred options in the consideration set. Third, the "do not want to say" response is modelled as a missing observation on the most preferred alternative in the consideration set. Thus, we consider the missing data generating mechanism to be non-ignorable and build a model based on utility maximization to describe the voting intentions of these respondents. We illustrate the merits of the model as we have information on a sample of about 5000 individuals from the Netherlands for who we know how they voted last time (if at all), which parties they would consider for the upcoming election, and what their voting intention is. A unique feature of the data set is that information is available on actual individual voting behavior, measured at the day of election. We find that the inclusion of the consideration set stage in the model enables the user to make more precise inferences on the competitive structure in the political domain and to get better out-of-sample forecasts.