  For a finite poset $P=(X,\prec)$, let $\mathcal{L}_P$ denote the set of
linear extensions of $P$. The sorting probability $\delta(P)$ is defined as
  \[\delta(P) \, := \, \min_{x,y\in X} \, \bigl| \mathbf{P} \, [L(x)\leq L(y) ]
\ - \ \mathbf{P} \, [L(y)\leq L(x) ] \bigr|\,, \] where $L \in \mathcal{L}_P$
is a uniform linear extension of $P$. We give asymptotic upper bounds on
sorting probabilities for posets associated with large Young diagrams and large
skew Young diagrams, with bounded number of rows.
