Randomization capability

This may be the craziest request ever, but I've come across a situation where I need to have the sort order of the list as RANDOM by name.

Is there any way to implement an additional switch that will allow for "RANDOM" sort order instead of ascending or descending?

ie, an example of one of the queries on my site would be:

/search-members?query=Lower Mainland&by=&type=&sort=wpum_designation&order=desc

but instead the order could be 'rand' instead of 'desc'.   

The reason I need this is, the directory is showing in alphabetical order, but due to the nature of what the directory is representing, the members don't believe it's fair that the fellow with the last name beginning with "A" is always the first person showing up when people search this directory.   The rest of the members want a fair shot at their name being presented - so every page refresh, the list would "jumble up" so it gave others a chance to get some traffic.

I'd be more than willing to compensate for your time to implement this additional capability.

cheers
Tavis