  An observer wants to understand a decision-maker's welfare from her choice.
She believes that decisions are made under limited attention. We argue that the
standard model of limited attention cannot help the observer greatly. To
address this issue, we study a family of models of choice under limited
attention by imposing an attention floor in the decision process. We construct
an algorithm that recovers the revealed preference relation given an incomplete
data set in these models. Next, we take these models to the experimental data.
We first show that assuming that subjects make at least one comparison before
finalizing decisions (that is, an attention floor of 2) is almost costless in
terms of describing the behavior when compared to the standard model of limited
attention. In terms of revealed preferences, on the other hand, the amended
model does significantly better. We can not recover any preferences for 63% of
the subjects in the standard model, while the amended model reveals some
preferences for all subjects. In total, the amended model allows us to recover
one-third of the preferences that would be recovered under full attention.
