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As opposed to the Lilliputian Emperor, who primarily uses Gulliver as a weapon against Blefuscu, the Brobdingnagian King wants Gulliver to teach him English governance in case there's something worth imitating there. Gulliver describes the English monarchy, Parliament, religion, and the judicial system. Upon hearing these descriptions, the Brobdingnagian King answers that he cannot understand how the English avoid bribery, corruption, influence peddling, or hypocrisy, when there are no safeguards against these sins in their government system. In fact, the King concludes, most Englishmen must be "the most pernicious race of little odious vermin that nature ever suffered to crawl upon the surface of the earth" (2.6.18). In other words, the English = nasty.
Again, the King of Brobdingnag is not a well-rounded character. We know nothing of his feelings, origins, any of that stuff that might make him seem more like a real person. That's not the point. His purpose is to direct the satire of the novel at England in an even more pointed way than the Lilliput chapters did.
The Lilliput chapters present English politics through a kind of Alice in Wonderland lens, distancing the reader from the topics under discussion. Here, the King of Brobdingnag is a tool to turn that same lens on the narrator himself, Gulliver, and his country. Just as the magnification of a beautiful lady's moles suddenly makes her ugly, the magnification of the weakness of England (and Gulliver) make them seem all the more pathetic.