Robust Descents in a Random Permutation

Let $\sigma$ be a permutation of $\{1, 2, \dots, n\}$ chosen uniformly at random. A descent is a position $i \in \{1, \dots, n-1\}$ where $\sigma(i) > \sigma(i+1)$. What is the expected number of descents?

Additional robustness twist: before observation, an independent random relabeling of outcome labels is applied. Compute the same target and justify invariance.