Monkeying with Bayes’ theorem

Here's previous discussion on HN that fleshes this out considerably: <a href="http://news.ycombinator.com/item?id=3693447" rel="nofollow">http://news.ycombinator.com/item?id=3693447</a>

The point about hackily downplaying independence by raising the product to a fractional power was nice.<p><a href="http://www.johndcook.com/blog/2012/03/09/monkeying-with-bayes-theorem/#comment-144221" rel="nofollow">http://www.johndcook.com/blog/2012/03/09/monkeying-with-baye...</a>

I'm confused. So should that part of Bayes' Theorem be raised to the 1.5 power?