  At the core of most random utility models (RUMs) is an individual agent with
a random utility component following a largest extreme value Type I (LEVI)
distribution. What if, instead, the random component follows its mirror image
-- the smallest extreme value Type I (SEVI) distribution? Differences between
these specifications, closely tied to the random component's skewness, can be
quite profound. For the same preference parameters, the two RUMs, equivalent
with only two choice alternatives, diverge progressively as the number of
alternatives increases, resulting in substantially different estimates and
predictions for key measures, such as elasticities and market shares.
  The LEVI model imposes the well-known independence-of-irrelevant-alternatives
property, while SEVI does not. Instead, the SEVI choice probability for a
particular option involves enumerating all subsets that contain this option.
The SEVI model, though more complex to estimate, is shown to have
computationally tractable closed-form choice probabilities. Much of the paper
delves into explicating the properties of the SEVI model and exploring
implications of the random component's skewness.
  Conceptually, the difference between the LEVI and SEVI models centers on
whether information, known only to the agent, is more likely to increase or
decrease the systematic utility parameterized using observed attributes. LEVI
does the former; SEVI the latter. An immediate implication is that if choice is
characterized by SEVI random components, then the observed choice is more
likely to correspond to the systematic-utility-maximizing choice than if
characterized by LEVI. Examining standard empirical examples from different
applied areas, we find that the SEVI model outperforms the LEVI model,
suggesting the relevance of its inclusion in applied researchers' toolkits.
