Need to automatically rotate the result of a view once a week (Sunday night)
The problem with that solution is it relies on the view's cache lifetime which might not sync up to Sunday (e.g. a manual cache clear it will reset the lifetime clock on the view cache and expire it 6 days from the manual cache clear). 

A better solution would rely on hook_cron() and do the following: 


Trigger every Sunday 
Set all node fields to false
Randomly select a node and update its field to true.


This could be accomplished with a custom module hook_cron or, I think, the Elysia Cron module.