#preference-probability

A reward model is trained under the Bradley–Terry preference model, $P(y_1 \succ y_2 \mid x) = \sigma\big(r(x, y_1) - r(x, y_2)\big)$. For three responses $A$, $B$, $C$ to the same prompt it predicts $P(A \succ B) = 0.8$ and $P(B \succ C) = 0.6$. What probability does it assign to $A \succ C$?