Let’s create \(N\) menus \(U_{1} … U_{N}\). And let’s write a decision rule \(U_{j} = u_{j} + \varepsilon_{j}\) (“each person picks some best available option \(u_{j}\) their menu \(U_{j}\), up to noise”)

The logit model asks that \(\varepsilon\) comes from a Gumbel distribution.

An alternative model probit model where \(\varepsilon \sim \mathcal{N}\qty(0, \Sigma)\)