To randomize the member search results go to: 

Content » Edit Post Settings

Click Edit on the Member Listing Feature.

Go to the Search Results Design tab.

Scroll down and expand the "Additional Settings"; Go to "Order Results By", select Random:

Finally, click on Save Changes and visit the website.

Keep in mind that the random sort order works based on each browser session. To make sure the user is viewing different results they must close the current browser session and open a new one or use a different browser.