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.



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