The Metropolis choice is to maximize the $A$ values, that is $$A_{j \rightarrow i} = \min \left ( 1, \frac{p_iT_{i\rightarrow j}}{ p_jT_{j\rightarrow i}}\right ).$$ Other choices are possible, but they all correspond to multilplying $A_{i\rightarrow j}$ and $A_{j\rightarrow i}$ by the same constant smaller than unity.\footnote{The penalty function method uses just such a factor to compensate for $p_i$ that are evaluated stochastically and are therefore noisy.}