This is more of an implementation option, but when I worry about what is active/inactive I put start/end dates on the tables. Then you don't need active indicators. You just look for the record where now() is >= start date and now() <= end date or end date is null. You can even activate/deactivate a badge on a future date. Of course, this complicates the data integrity - you will need some kind of specialized trigger that checks the data and makes sure there are no date overlaps to ensure you don't have two badges active at the same time. But is also gives you a history of badges and their activities.
Partial indexs seem to be "what the doctor ordered!" And your suggest is right on, the idea of the constraint is to allow only one active badge status at a time.
But now that I think about it, using the authors suggestion (if it actually worked), how would would it be possible to change the active status from one badge to another?
Oh well, partial index are obvious the superior solution since the entire table doesn't not have to be scanned to determine if the new badge can be set to active.