Public Folder Permissions Are Cumulative

Public folder permissions are designed to be optimistic. Optimistic here implies the "least restrictive" set of permissions.

The Permissions that apply to the user include the set of permissions that the user inherits from each of the groups the user belongs to, in addition to the explicit permissions granted directly to the individual user account. A user's permission level is always the least restrictive of that user's explicit permissions and the permissions of any and all groups to which that user belongs.

This means that if different permissions are given to the same mailbox, the summation of all the given rights is what the mailbox will end up with.

For example:

Users A and B exist on a site. The administrator creates two distribution lists (DLs): Manager and Supervisor. Both User A and User B are added to the Supervisor DL; only user A is added to the Manager DL. Then, on folder X, the Manager DL is given the Owner role, and the Supervisor DL is given the Contributor role. User A will ultimately have Owner permissions on folder X, even though user A is a member of the Supervisor DL which only has the Contributor role.