The formulation of the log-likelihood ratio in Dunning (1993) is a two-tailed statistical test that if p 1 and p 2 significantly diverge from each other, the −2 log λ would get a high value.
as mentioned above, we are just interested in the cases that p 1 is much higher than p 2 , because, otherwise, coreference links among the mentions which have the relation r in common are less frequent than expected.