I do not think there is a great way to do this, but this would work:
[connections limit=1 order_by='id|SPECIFIED']
Randomization occurs every hour on the hour (according to the time set on the server, not necessarily the time on your clock) for every user based on IP address. As an example, lets say user A and user B both visit the site at the same time, they would both see the entries in a different random order for the remainder of the hour in which they visited. After that remainder of the hour has expired, they would both see a different random order.
I hope this helps!