The Bradley--Terry condition is $L_1$--testable
  We provide an algorithm with constant running time that given a weighted tournament $T$, distinguishes with high probability of success between the cases that $T$ can be represented by a Bradley--Terry model, or cannot even be approximated by one. The same algorithm tests whether the corresponding Markov chain is reversible. 
Agelos Georgakopoulos and Konstantinos Tyros
math.CO