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Not sure if this model is natural enough, but if $\pi$ is a random permutation of $\{1,2..n\}$, and $N_i$ is the number of cycles of size $i$ in $\pi$, then, $(N_1, N_2...)$ are approximately independent Poisson($1$), Poisson($\frac{1}{2}$), Poisson($\frac1{3}$)... hence probably even if $N_i$ are ranked in order, their sizes would be like $1, \frac1{2}, \frac1{3}$ etc.