Revealed preferences are a potentially powerful tool for conducting welfare analyses, but due to forces such as behavioral biases, ‘irrational behaviors’ such as non-transitivity (i.e., cycles of preferences) can appear in revealed preferences, which render them useless for welfare purposes. In this work, we provide the first empirical application of a leading proposal for welfare analysis in the presence of behavioral biases, presented in Bernheim and Rangel (2009), called the Strict Unambiguous Choice Relation (hereafter Strict UCR). However, there are two potential problems in the application of this approach: Strict UCR can be cyclic on consumption data, which are incomplete, and Strict UCR is very conservative, which may make it overly coarse, and thus, useless (Rubinstein and Salant 2012). We address these concerns using a dataset of package grocery purchases by 397 households over a two years period in the United States. We find that the Strict UCR relation is cyclic on incomplete data, but much less than revealed preferences (8% against 99% of agents exhibit cycles). It is also almost complete, as in our application, almost all bundles are comparable. In addition, we introduced two new relations based on the idea of the Strict UCR, but that guarantee acyclicity. One is shown to be equivalenton complete data, and the other is in the same flavor than Strict UCR, but is more conservative.