# Are standard discrete choice models based on ordinal utility or cardinal utility?

Suppose we model consumer's choice between three brands Honda(choice 1), Toyota(choice 2) and BMW(choice 3) using a standard discrete choice model, with the utility of choice $$j\in\{1,2,3\}$$ being specified as $$U_j=V_j+\epsilon_j$$ where $$\epsilon_j$$ is unobserved error term and $$V_j=X\beta_j$$ with $$X$$ being some observed covaraites. Suppose consumer choose choice $$j$$ if and only if it gives the highest utility. My question is, are we implicitly assuming the consumer being maximizing cardinal utility or ordinal utility? I feel it seems like ordinal utility because in identification and estimation, we do location and scale normalizations which implies that the actual utility number do not matter.