[rachofsunshine]

I don't know how OP does it, but Elo ratings are a pretty good tool for this kind of thing. In each pairwise comparison, the selected option "wins", the other option "loses", and ratings are adjusted accordingly.

You can incorporate priors by setting initial ratings differently, or force correlations between items by treating a win against option X as something like 0.8 wins against option X and 0.2 wins against options correlated with X.