Let $P$ be an $n\times n$ stochastic matrix, then coefficient of ergodicity $\tau(P)$ is defined as follows:
$$\tau(P) = \frac{1}{2}\max_{i,j} \sum_{k=1}^n|P_{ik}-P_{jk}|=1-\min_{i,j} \sum_{k=1}^n \min(P_{ik},P_{jk})$$
Can someone give me an intuitive insight of this coefficient?