Before revision:  Using these results, we show that a set (possibly a singleton) of strict preference orderings compatible with RAM is identifiable from the decision maker's choice probabilities, and establish a representation of this identified set of unobserved preferencesas a collection of inequality constrains on her choice probabilities. Given this nonparametric identification result, we develop uniformly valid inference methods for the (partially) identifiable preferences. We showcase the performance of our proposed econometric methods using simulations, and provide general-purpose software implementation of our estimation and inference results in theR software package\texttt{ramchoice .
After revision:  Using these results, we show that a set (possibly a singleton) of strict preference orderings compatible with RAM is identifiable from the decision maker's preferences. To illustrate the applicability of our results and their concrete empirical content in specific settings, we also develop revealed preference theory and accompanying econometric methods under additional nonparametric assumptions on the consideration set for binary choice problems. Finally, we provide general purpose software implementation of our estimation and inference results in theR software package\texttt{ramchoice .