A different version of the preceding model uses the complementary log-log link function:

\[
\log \left(-\log \left(1-\operatorname{pr}\left(Y_{i, j} \leq right)ight)ight)=\gamma_{r}+\alpha_{i}-\alpha_{j}
\]

depending on two threshold parameters \(\gamma_{1} \leq \gamma_{2}\) plus player strength parameters \(\alpha_{1}, \ldots, \alpha_{n}\).

In what sense is this model inconsistent? How do you modify it to resolve the inconsistency?