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(1/2), Poisson(1/3)... hence probably even if N_i are ranked in order, their sizes would be like 1, 1/2, 1/3 etc.
Manjunath Krishnapur
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