How do I normalize the variance of error terms in multinomal logit/probit models?

#1
Hi, I use a multinomial logit model to analyze a choice experiment with three options. I normalize the coefficient of one of the options, say option three to zero. I do this to set this option as the reference category. Hence, I am left with two options. Now I want to normalize the variance of the error terms of the two options (i.e., the difference of the error term of the first option minus the error term of the second option) to one. The reason I want to normalize the variance is to equalize the coefficients of the first and the second option.

Can someone help me how to formulate this normalization (e.g., a link or text book where I can find more about this), and how to do this normalization in R?