We consider optimal stopping problems with loss function q
depending on the rank of the stopped random variable. Samuels asked whether
there exists an exchangeable sequence of random variables $X_1, \dots, X_n$
without ties for which the observation of the values of the $X_i$'s gives no
advantage in comparison with the observation of just the relative ranks of the
variables. We call distributions of the sequences with this property
q-noninformative and derive necessary and sufficient conditions for this
property. Extending an impossibility result of B. Hill, we show that, for any
$n > 1$, there are certain losses q for which q-noninformative
distributions do not exist. Special attention is given to the classical problem
of minimizing the expected rank: for n even we construct explicitly
universal randomized stopping rules which are strictly better than the rank
rules for any exchangeable sequence.