A Federation provides a standard, pre-negotiated set of contracts that allow organizations to recognize identities issued by one another. A federation agreement might specify user roles, governance, security and verification policies, or specific technical methods. The federation is organized around a Contract Hub, which is responsible for the agreements. Organizations with similar goals or structure create a standard agreement rather than negotiating individually.
When to Use: A large number of organizations can agree upon roles and governance, and can create a standard contract.
Advantages: Organizations can recognize identities that one another issue without having to negotiate individual agreements with every party.
Disadvantages: Not customized for individual member organizations. Because of the need to create an agreement that a large number of parties can agree to, the federation might be limited to lowest common denominator roles.
Ability to Scale: Very high.
The full papers is downloadable [Field-Guide-Internet-TrustID] Here is a link to introduction of the paper and a at the bottom of that post is a link to all the other models with descriptions. Below are links to all the different models.