Conventional survey tools such as weighting do not address non-ignorable nonresponse that occurs when nonresponse depends on the variable being measured. This paper describes non-ignorable nonresponse weighting and imputation models using randomized response instruments, which are variables that affect response but not the outcome of interest. This paper uses a doubly robust estimator that is valid if one, but not necessarily both, of the weighting and imputation models is correct. When applied to a national 2019 survey, these tools produce estimates that suggest there was nontrivial non-ignorable nonresponse related to turnout, and, for subgroups, Trump approval and policy questions. For example, the conventional MAR-based weighted estimates of Trump support in the Midwest were 10 percentage points lower than the MNAR-based estimates.