Book IX contains a description of the tyrannical man, and three arguments that he will be the least happy of men. Plato/Soc then proceeds to extrapolate from these results to make a case for paternalistism.
In order to characterize the tyrannical man, Plato/Soc introduces a distinction between lawful and lawless desires. Lawless desires are present in everyone, as is evident in the disordered state of even the best people's dreams. The tyrant is the man in whom the lawless desires reign supreme; he does not use reason to organize his life in accordance with the good. This is to say that he is constantly indulging in "feasts, revelries, luxuries, girlfriends, and all that sort of thing" (573d). He shrugs off responsibilities and steals whatever he needs to feed his various appetites.
As his first proof that a tyrant is the most unhappy of men, Plato/Soc argues that such a man should be described as a slave to base and arbitrary desires, to the part of him least human. Furthermore, even when such a man wins political control, he is so hated that in order to protect himself he must pander to the ugliest sorts of people in order to protect himself from the others whom he subjects to continuous abuse. He debases himself and lives in constant fear of his underlings, who he knows would like to see him dead.
The second proof draws on the earlier distinction between the three parts of the soul. Each part, it is now added, acquires from its object a distinctive sort of pleasure. Depending upon which part of the soul holds sway, a person will be profit-loving, honor-loving, or wisdom-loving, and will judge objects accordingly. These pleasures are arranged hierarchically, each more comprehensive than the last. The argument, then, is that the philosopher understands the pleasures of tyranny and can weigh them correctly, but the tyrant does not understand the pleasures of philosophy and uses the wrong standard when he tries to judge them. So if philosophers report themselves as most happy, we are compelled to take their word for it.
The third proof incorporates an additional premise to the second argument in order to get a similar, but more ontologically substantive result. The new premise is that pleasure and pain are always relative one to the other; to give a crude example, intense pain in your past might make pleasurable for you an experience that is painfully boring to someone of a more sheltered upbringing. Hence all of the pleasures have their place on a single continuum and can, at least in principle, be quantitatively assessed, one against the other. We are said to be most pleased by what most fills us as the kind of being that we are, i.e., rational beings. Knowledge of what is is eternal provides a far more substantial pleasure than profit or honor, which pass away and must be continually renewed. These things have more being, Plato claims, and so the pleasures they afford are more truly pleasurable. The majority of people, unacquainted with the forms, live at the low end of the pleasure scale and have a consequently distorted experience of the world. In fact, with the aid of some screwball math, Plato/Soc. is able to inform us that the tyrant lives 729 times less pleasantly than the king. (My translator, for what it's worth, contends that Plato fudges the numbers and that, really, the tyrant lives only 125 times less pleasantly.)
Yet, we must remember, even philosophers must attend to the lower parts of the soul. The appetitive and spirited parts of the soul are to be ruled, not replaced, by the rational part. Furthermore, it needs to be emphasized that rational pleasures, for philosophers, are not simply tacked onto the other kinds of pleasures enjoyed just as much by non-philosophers. Philosophers are able to most effectively direct their lower desires in order to maximize pleasure afforded and to avoid frustration or excess. Disordered desires, as we've seen, lead to unhappiness.
From this, Plato/Soc extrapolates an argument for a strongly paternalistic form of government:
"Therefore, to insure that someone like that [i.e., like those irrational people who are slave to their appetites] is ruled by something similar to what rules the best person, we say that he ought to be the slave of that best person who has a divine ruler within himself. It isn't to harm the slave that we say he must be ruled, which is what Thrasymachus thought to be true of all subjects, but because it is better for everyone to be ruled by divine reason, preferably within himself and his own, otherwise imposed from without, so that as far as possible all will be alike and friends, governed by the same thing." (590c-d).
I've a few questions still to respond to from the previous Book. I'll get to them as soon as I can. Sorry about the delay!