  In the present paper we show that in P\'{o}lya's urn model, for an
arbitrarily fixed initial distribution of the urn, the corresponding random
variables satisfy a convex ordering with respect to the replacement parameter.
As an application, we show that in the class of convex functions, the absolute
value of the error of Bernstein-Stancu operators is a non-decreasing (strictly
increasing under an additional hypothesis) function of the corresponding
parameter.
  The proof relies on two results of independent interest: an interlacing lemma
of three sets and the monotonicity of the (partial) first moment of P\'{o}lya
random variables with respect to the replacement parameter.
