  In this paper, we apply a Bayesian perspective to sampling of alternatives
for multinomial logit (MNL) and mixed multinomial logit (MMNL) models. We find
three theoretical results -- i) McFadden's correction factor under the uniform
sampling protocol can be transferred to the Bayesian context in MNL; ii) the
uniform sampling protocol minimises the loss in information on the parameters
of interest (i.e. the kernel of the posterior density) and thereby has
desirable small sample properties in MNL; and iii) our theoretical results
extend to Bayesian MMNL models using data augmentation. Notably, sampling of
alternatives in Bayesian MMNL models does not require the inclusion of the
additional correction factor, as identified by Guevara and Ben-Akiva (2013a) in
classical settings. Accordingly, due to desirable small and large sample
properties, uniform sampling is the recommended sampling protocol in MNL and
MMNL, irrespective of the estimation framework selected.
