After yet another series of devastating wars that have caused tremendous destruction (and resulted in yet another trilogy from Tolkien), the inhabitants of Middle Earth have decided to set up a Security Council to maintain peace and harmony. This security council is to be comprised of five members; each member is appointed for a term of one year. The goal is to have the council be composed in as fair a manner as possible, in order that it accurately reflect the population of Middle Earth. Assuming that the population of Middle Earth is as follows:

1. What properties would you like the security council to satisfy, in order that it be truly considered "fair?"
2. Suggest a possible composition for the security council for the first five terms.
3. At the end of the first five years, the goblins and the orcs decide they want out of the security council; the rest of the species remain in.

• Suggest a possible composition for the security council for the next five terms.
• Had you known at the beginning of the first year that goblins & orcs were going to quit after five years, would you have composed your security council differently in the first five years?

1. Repeat parts 2. and 3. above, under the additional constraint that Goblins, Dragons, and Orcs never be allowed to form a majority in the council, lest they be tempted to form an alliance, take over the council, and deliver all of Middle Earth over to the Dark Lord Sauron.