"But the real problem with this subroutine is that it does not sample the space of permutations uniformly."
It is certainly true that the method described initially does not sample the space of permutations uniformly because the permutations utilized are all a product of $n transpositions, so in particular they all have the same parity (even if $n is even, etc). Zaxo's comment that there may be some difference between a "fair shuffle" and a uniformly distributed selection over permutations" is perceptive. A shuffle might be considered "fair" if it tends to remove specific orderings that exist (e.g. in playing cards, one wants to nullify the effect of various groupings that have occurred in previous hands.) On the other hand, if one wants to model what actually occurs in a sequence of "random" shuffles, then restricting to permutations of fixed parity seems objectionable. It's a bit hard to define what "randomizing" shuffle means; Perci Diaconis (a highly respected mathematician) has studied this and written some good articles on the subject which should be found easily by web search.
chas
Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
Read Where should I post X? if you're not absolutely sure you're posting in the right place.
Please read these before you post! —
Posts may use any of the Perl Monks Approved HTML tags:
 a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)

For: 

Use: 
 &   & 
 <   < 
 >   > 
 [   [ 
 ]   ] 
Link using PerlMonks shortcuts! What shortcuts can I use for linking?
See Writeup Formatting Tips and other pages linked from there for more info.

