  Inspired by Aldous' conjecture for the spectral gap of the interchange
process and its recent resolution by Caputo, Liggett and Richthammer, we define
an associated order on the irreducible representations of S_n. Aldous'
conjecture is equivalent to certain representations being comparable in this
order, and hence determining the "Aldous order" completely is a generalized
question. We show a few additional entries in this order.
