What is the meaning of the paradoxes and the overall message in the poem "Much Madness is Divinest Sense"?

In this poem, Dickinson presents two paradoxes, or statements that contradict themselves. The first is that people with "much madness," or who are insane, show a great deal of sense. In fact, people who act insane show the type of sense that characterizes the divine. The second paradox is that those who show "much sense," or who seem totally sane, in actuality show "stark madness," or complete insanity. 

The poem's message is that those who "assent," or give into society's rules and norms, are considered sane. On the other hand, those who "demur," or who are reluctant to follow the dictates of society, are considered dangerous and "handled with a chain," or treated with barbarism. In other words, the label of sanity is awarded to those who simply follow the rules, and those who disagree with the rules, even if the rules are themselves insane, are considered mad and handled with brutality. Dickinson expresses the idea that society's rules can be insane and that one who resists these rules is in fact closer to godliness and sanity. 

Emily Dickinson's poem expresses the paradox that what is sometimes regarded as madness or craziness is actually perfectly sensible, and what sometimes seems to make perfect sense is actually madness.  The paradoxes are reversals of each other.  These paradoxes are the statement of the theme of the poem.  The poem goes on to explain her a point a bit further.  She explains that it is the majority (of people) who decide what is "sane" and if one goes along with the majority, then that he/she is considered sane, but that if one demurs (objects) then he/she is considered crazy and will be treated that way.

While we have no expressed idea about what inspired this poem for Dickinson, we can certainly see its relevance in all kinds of big and small examples in our everyday lives.  If the majority of people decide that a certain fashion trend is great, then anyone wearing that trend is considered fashionable; anyone who doesn't, isn't. This could apply to anything that is "popular."  Dickinson's reclusive behavior might have been considered mad, but it made perfect sense to her and how she wanted to live her life.  Dickinson's first and only submission to have her poetry considered for publication ended in a rejection letter, but she knew she wrote great poetry and we certainly know that today!  Who is to say what is mad and what is sane?

In light of the exchanges of the combatants in the political arena, it is not difficult to understand this poem.  In fact, throughout history, those who have been prophetic or who have seen what the real problems exist in the future have been considered "mad."  

Emily Dickinson's clever and ironic poem seems more relevant than in her day.  For, those who truly understand and explain situations or foresee situations to come are scoffed and treated as though they are foolish or narrow-minded or some other pejorative term.  Yet they are those who have "divinest sense," though those adherents of conventional wisdom would call them "mad."

Dickinson's third line compares to what John Stuart Mill called "the tyranny of the majority":

Much Sense--the starkest Madness--

For, this is the thinking of "the Majority" that prevails, Dickinson states in the next two lines,

"Tis the Majority
In this, as All, prevail--

The Majority that prevails is the majority that tyrannizes others with its conventions to which they are forced to adhere or else be "handled with a Chain"; that is, be locked up or ostracized or vilified.

While they may easily be other interpretations to Miss Dickinson's poem, it clearly is about those who think independently and can perceive beyond the present or the appearance of things and assess what real dangers lie ahead for people. But, to the obtuse majority, these few perceptive individuals are "mad," and considered dangerous to the complacency and conventional wisdom of the majority.

What is the claim or meaning of the poem "Much Madness is Divinest Sense"?

A contemporary of Emily Dickinson, Ralph Waldo Emerson, wrote in his essay Self-Reliance,

Society everywhere is in conspiracy against the manhood of every one of its members....The virtue in most request is conformity. Self-reliance is its aversion.  It loves not realities and creators, but names and customs.

Like Emerson, Ms. Dickinson strongly valued her independence of thought, and led a reclusive life, deliberately choosing solitude in which to write her poetry.  In fact, she was often portrayed as a mad recluse; however, in her poem "Much Madness is divinest Sense" she may be presenting a defense of her solitude.  For, her mention of "the Majority" in the fourth line certainly points to Emerson's words about "Society" and its demand for conformity that poses no problems:

Assent--and you are sane--

Demur--you're straightway dangerous--

And handled with a Chain--

These last three lines of Dickinson's also call to mind the poet T.S. Eliot, who was declared insane and institutionalized for a period during World War II because he had "demurred" against the conventional wisdom.

"Society," that body of governing people who set the standards of normalcy, dictates, as Emerson declared, that thinking away from conventional lines is "madness."  But, it is those who think creatively and independently, who often perceive reality and even the future with a "discerning eye," that understand the truth of what happens and will happen.  Because they are a threat to the stability of their societies, these people are often ostracized or declared to be abnormal and "mad."