This note provides two corrections to the pseudo-code of the algorithm for the Bayesian estimation of the multinomial logit model using auxiliary variables as developed by Homes and Held (2006). After incorporating the two corrections, the algorithm works correctly for the multinomial as well as the binary logit model.
"Bayesian estimation of the multinomial logit model: a comment on Holmes and Held, "Bayesian auxiliary variable models for binary and multinomial regression"." Bayesian Anal. 6 (2) 353 - 355, June 2011. https://doi.org/10.1214/11-BA613