  A {\it superpattern} is a string of characters of length $n$ that contains as
a subsequence, and in a sense that depends on the context, all the smaller
strings of length $k$ in a certain class. We prove structural and probabilistic
results on superpatterns for {\em preferential arrangements}, including (i) a
theorem that demonstrates that a string is a superpattern for all preferential
arrangements if and only if it is a superpattern for all permutations; and (ii)
a result that is reminiscent of a still unresolved conjecture of Alon on the
smallest permutation on $[n]$ that contains all $k$-permutations with high
probability.
