  This paper studies Markov chains on the symmetric group $S_n$ where the
transition probabilities are given by the Ewens distribution with parameter
$\theta>1$. The eigenvalues are identified to be proportional to the content
polynomials of partitions. We show that the mixing time is bounded above by a
constant depending only on the parameter if $\theta$ is fixed. However, if it
agrees with the number of permuted elements ($\theta=n$), the sequence of
chains has a total variation cutoff at $\frac{\log n}{\log 2}.$
