BGP Protocol Theory – VRP vs BGP Protocols

My question then is, what would the purpose be of sending an unordered list? In what cases would you be better off sending an unordered list as opposed to an ordered list?

as-set is commonly used when aggregating routes downstream of an autonomous system; so the use case for an unordered list is bgp aggregation.

EXAMPLE:

In the example below, AS65500 aggregates the eBGP announcements from AS65000 and AS65001 into 10.1.0.0/23. After aggregating the announcements from AS65000 and AS65001, AS65500 sends NETWORK: 10.1.2.0/23 AS-PATH: 65500 and NETWORK: 10.1.0.0/23 AS-PATH: 65500 {65000, 65001} (the aggregate). Typically, an AS will aggregate when it has delegated portions of a larger address block to customers.

It doesn't make sense to build an ordered list when you aggregate space for multiple ASNs; for instance, an ordered AS-PATH for the aggregate below would be either 65500 [65000, 65001] or 65500 [65001, 65000]. However, both of those ordered lists are non-sense because ordering is irrelevant to the aggregate (i.e. both autonomous systems are directly connected to AS 65500). Ordering implies a sequence which is meaningless to the aggregate.

Unordered lists (i.e. mathematical sets) make the most sense for an AS_SET.

          _.------------.
      ,-''               `--.
    ,'                       `.
   (         AS65000           )
    `.       10.1.0.0/24     ,'
      `--.               _.-'
          `------------''
                    \          ------> NETWORK: 10.1.2.0/23   AS-PATH: 65500
                     \         ------> NETWORK: 10.1.0.0/23   AS-PATH: 65500 {65000, 65001}
           _.--------------.        router bgp 65500
       ,-''                 `--.     no sync
     ,'                         `.   no auto-summary
    (          AS65500             ) neighbor 10.1.0.2 remote-as 65000
     `.        10.1.2.0/23      ,'   neighbor 10.1.1.2 remote-as 65001
       --.                 _.-'      network 10.1.2.0 mask 255.255.254.0
           `--------------''         aggregate-add 10.1.0.0 255.255.254.0 summary-only as-set
                    /
                   /
          _.--------------.
      ,-''                 `--.
   ,'                         `.
  (           AS65001           )
   `.         10.1.1.0/24     ,'
     `--.                 _.-'
         `--------------''

You have to remember that models like OSI are just that, models. They are theoretical. The real world doesn't fall neatly into these models. For the most part, routing is a layer-3 function, but, as you pointed out, BGP uses a layer-4 protocol to communicate with other BGP speakers in order to do what is normally considered a layer-3 function.

Many network protocols fall into a gray area, or are considered in one layer while using another layer. Take ARP for instance. It resolves layer-3 addresses to layer-2 addresses. Which layer should it be considered to be in?

Understanding the models is useful, but the models are not mandated by any organization, and you are free to create protocols and functions that do not follow any model.