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I don't think they'll like it much - it may look like cloaking.
How about a user-friendly alphabetic list, and a business-friendly "Featured
Site" box at the top that changes each time? That way, the users will be able
to find a business by name, and the businesses will be happier because even
"Zeke's Zebra Shop" will get to be listed first occasionally. In addition,
most of the page will be static, and only the featured site will change between
robot visits.
As a potential user, a random list sounds like a usability nightmare to me...
Jim