Let us remember that Jerry's central idea, which gives this essay its title, is as follows:
You tell me whar a man gits his corn pone, en I'll tell you what his 'pinions is.
To paraphrase this idea, we receive our opinions and ideas not from independent thought and careful rumination, but from our society and those that are responsible for feeding us. Our desire for continued preservation outweights our desire for independent thought, so we adopt the thoughts of those who are more important than us as a deliberate strategy to help us survive.
In paragraph six of this essay, Twain considers his own response to this claim, saying:
It was his idea that a man conforms to the majority view of his locality by calculation and intention. This happens, but I think it is not the rule.
The irony in this statement is the way in which we all believe, overtly at least, that our thoughts and feelings are independent and borne out of serious study and reflection. This quote argues that the opposite is true, that all of our views are just a matter of us "conforming" and a careful, calculated and intentional response to our locality and what everybody else thinks. This is the irony that governs the whole essay as Twain unpacks the truth behind "Public Opinion."
The young man who sermonizes for young Mark Twain declares,
"You tell me whar a man gits his corn-pone, en I'll tell you what his 'pinions is."
This observant man has noticed that in the interest of self-preservation and the hope of prospering, men conform to conventional wisdom by thinking and feeling with those around them. In other words, their self-approval is derived from the approval of other people.
In paragraph 6, however, Twain writes of the philosopher,
It was his idea that a man conforms to the majority view of his locality by calculation and intention.
There is irony in this statement because there is an incongruity in it. By conforming, people do not exercise independent thought, and it is independent thought that is connected to the meanings of the words calculation and intention.
To underscore this incongruity, Twain contends that
...a coldly-thought-out and independent verdict upon a fashion in clothes, or manners, or literature, or politics, or religion, or any other matter...is a most rare thing--if it has indeed ever existed.
Further, Twain argues that people derive self-approval from the approval of others. People conform to conventional wisdom, to what is safe to think, to what will preserve them. They do not "calculate" judgments or beliefs; rather, it is simply in the nature of man to conform.