The Minister, or "Frederick" to his family and friends (if he has any), is the figurehead for the government. He pioneers the Ludovico technique as a form of government intervention. Prisons are overcrowded and not rehabilitating the prisoners, so the government steps in.
He single-handedly picks Alex for this procedure because Alex is "enterprising, aggressive, outgoing. Young. Bold. Vicious." By doing this, the Minister transforms Alex into a figurehead, too. Neither of them have power of their own. The Minister must act for government's interest, and Alex becomes a pawn of sorts for people who want to rally against the government and their mind-control techniques.
The Minister speaks for the government, and he has to face the consequences when their plans backfire, which they do. It's difficult to tell if there's backlash simply because the government intervened in prisoner rehabilitation or if it was the method they used that raised public ire.
In the end, the Minister must undo the damage he caused by undoing the damage to Alex's brain. Like an expert politician, he's able to spin it as the government saving young Alex, winning public approval again. Alex is the one who had surgery on his brain, yet it's the public with the short-term memory problems.