Somehow pass a three-column matrix of dummy-encoded columns to brms? Like
bf(choice_matrix ~ 0 + seat + ...). That doesn’t work, though, because brms isn’t designed for that kind of input data
This should work if you use family = multinomial(). You would need an outcome matrix that is N × 3. It looks like you only have 1 trial, so you’d have 1 trial per row.
See here for an example of multinomial data.
Hope that helps with this specific problem. Also, discrete choice models suck 😀