Outline Part IX: Imperfect Societies.
Socrates and Glaucon briefly review the traits of the ideal state. The salient points are that men and women should be equal in education and occupations. Further they should be governed by those rare individuals who are best at philosophy and war. These philosopher rulers shall not possess private property and shall accept their annual wages as sufficient for acting as Guardians of the state.
Adeimantus expresses interest in having Socrates expand on his previous allusion to four types of states or societies. The four are named as the Cretan or Spartan type, oligarchy, democracy, and tyranny. Socrates indicates that he will discuss those states as well as the corresponding individual character. He proposes to take each one at a time starting with the Spartan form and the competitive, ambitious man that is analogous to it. He will proceed through oligarch and democratic man to the worst, the tyrant, which will allow comparisons with the best man and the answer to Thrasymachus" earlier assertions.
2. Timarchy.
Socrates begins by indicating that social change happens when there is dissension among the ruling class. As long as they are in accord no change is possible, but as all material things decay so do societies. He proposes to outline the steps by which that happens.
The whole break down begins with a generation of Guardians who are not properly conceived according to a complicated mathematical equation which Socrates puts forth in this section. He revisits the myth of the metals. Strife occurs when there is no longer balance between reason (gold) and desires and spirit (iron and bronze). That occurs when the previously described ideal breeding practices are violated. A compromised individual is produced composed of varying amounts of the competing metals or motives.
The society resulting from the ill-breeding is somewhere between the perfect society and oligarchy.