In many surveys, the goal is to estimate the proportion of the population within different domains with a certain characteristic of interest. This estimation problem is often complicated by survey non-response and the difficulty in modeling the non-response mechanism. In this paper we develop a new method for analyzing categorical data with non-response when there is uncertainty about ignorability, which incorporates the idea that there are many a priori plausible ignorable and non-ignorable models. We consider saturated submodels of the full model, which may have a mixture of ignorable and non-ignorable components, and use Bayesian averaging to incorporate model uncertainty. This method is illustrated using data from the 2000 Accuracy and Coverage Evaluation Survey. A simulation study is used to evaluate the performance of the model and to compare the partition model to other popular non-ignorable Bayesian models.