Bradley-Terry model in brms or rstanarm (lme4 notation)?

Thanks, @andymilne ! I have tried to parse what the article recommends, but cannot seem to get the gist of what the the authors are suggesting.

I have a set of paired comparison data, in which no preference was an option.

Each row has Option A (3 possibilities), Option B (also 3 possibilities) and the Preference either A, B or No Preference. Each subject did all possible comparisons, in both directions, under a set of other conditions.

How should I code the factors for a glmm approach to a Bradley-Terry model?