information:highlighting, structural:reformatting
As a latent-variable model

This latent variable can be thought of as the utility associated with data point i choosing outcome k, where there is some randomness in the actual amount of utility obtained, which accounts for other unmodeled factors that go into the choice. The value of the actual variable Y i {\displaystyle Y_{i}} is then determined in a non-random fashion from these latent variables (i.e. the randomness has been moved from the observed outcomes into the latent variables), where outcome k is chosen if and only if the associated utility (the value of Y i, k ∗ {\displaystyle Y_{i,k}^{\ast }}) is greater than the utilities of all the other choices, i.e. if the utility associated with outcome k is the maximum of all the utilities. Since the latent variables are continuous, the probability of two having exactly the same value is 0, so we ignore the scenario. That is: