Just a few P’s that I have the privilege to point out: Purple, Property, Protection, and Principle. All part of Socrates’s select sophisticated sample of a stellar society. The fourth book of the Republic deals with the matter of deciding what virtue best embodies the ideas of the classes, of which he has 4: Wisdom, Courage, Moderation and Justice.
Wisdom, is obviously attributed to the rulers, for it is through that virtue in which the entire city shall reflect such values. Wisdom will reflect on the city through the rulers.
Courage is the virtue for the Auxiliaries, there duty is to defend the city, and fight for it, and it is the Auxiliaries alone who bear such courage. As it would be useless for a Producer or a Ruler to be courageous.
Moderation not so much as great as sounding as the former, is best described an acceptance of the city itself. Meaning the Producers, who must remain subservient under this entire hierarchy.
Lastly, there is Justice, which has already seen its fair share of appearances in this entire book. Justice is a virtue that embodies all three, and is the understanding that each shall have their own purpose and virtue within the city, and for one to accept and to mind their own business for lack of a better term.
Socrates refers back to the individual, just as how the city has its three divisions, so does the soul. The rational part that carries out the calculations, the irrational which is the source of desires and lust, and then the spirit, which keeps the appetites in check (does not apply to food).
For this all to work together, the rational part would rule over the spirit and the irrational, with the help of the spirit should be an easier task. In the exact same way in which the city shall be ruled over by a just man, and therefore make the city, a just city.