Equality is an ideal upheld by a number of ideologies, but nowadays it is seldom associated with libertarianism or classical liberalism. Indeed, both libertarians and their critics typically think of equality as an ideal in tension with the ideal of liberty as libertarians understand it.
But what is meant by “equality”? Some thinkers draw a distinction between formal equality and substantive equality, where formal equality means something like mere equality before the law—the same laws applying equally to everyone—while substantive equality requires abolishing, or at least greatly reducing, differences in wealth, opportunity, or influence.
The latter sort of equality—we might also call it socioeconomic equality—is obviously incompatible with libertarianism, at least if such equality is sought through coercive legislation.  Legislation aiming at socioeconomic equality is rejected by libertarians as an unwarranted and socialistic interference with the property rights of individuals.
Equality before the law, by contrast, is generally embraced by libertarians. But by itself there is nothing especially libertarian about it. Anatole France once wryly remarked that the law in its majestic equality forbids the rich as well as the poor to sleep under bridges, a line often invoked by socioeconomic egalitarians scornful of merely formal equality. But libertarians have equal reason to find such formal equality inadequate. As economist Murray Rothbard noted: “[T]he justice ofequality of treatment depends first of all on the justice of the treatment itself. Suppose, for example, that Jones, with his retinue, proposes to enslave a group of people. Are we to maintain that justice requires that each be enslaved equally? And suppose that someone has the good fortune to escape. Are we to condemn him for evading the equality of justice meted out to his fellows?” 
If neither substantive socioeconomic equality nor formal equality before the law captures what libertarians think matters in politics, it’s tempting to conclude that equality is not a central libertarian value at all.
Yet earlier thinkers in the libertarian tradition placed far more emphasis on equality. Thomas Jefferson in the Declaration of Independence famously wrote that “all men are created equal”; in the original draft he went still further, writing that ‘from that equal creation they derive rights inherent & inalienable,” thereby making equality the basis and foundation of our rights.  What sort of equality is Jefferson talking about?
It is generally recognized that John Locke’s Second Treatise of Government stands foremost among those “elementary books of public right” on which Jefferson relied in writing the Declaration; and Jefferson’s notion o f equality is indeed derived directly from Locke’s. Locke defines a “state . . . of equality” as one “wherein all the power and jurisdiction is reciprocal, no one having more than another, there being nothing more evident than that creatures of the same species and rank, promiscuously born to all the same advantages of nature, and the use of the same faculties, should also be equal one amongst another, without subordination or subjection . . . .” 
In short, by the equality of men Locke and Jefferson meant not that all men are or ought to be equal in material advantages, but that all men (today it would be all persons, regardless of gender) are equal in authority. To subject an unconsenting person to one’s own will is to treat that person as one’s subordinate—illegitimately so, if we are all naturally equal. Hence any interference with another person’s liberty violates the Lockean conception of equality: “[B]eing all equal and independent, no one ought to harm another in his life, health, liberty or possessions. . . . And, being furnished with like faculties, sharing all in one community of nature, there cannot be supposed any such subordination among us that may authorise us to destroy one another, as if we were made for one another’s uses, as the inferior ranks of creatures are for ours.” 
No wonder, then, that Jefferson should find it natural to maintain, a century later, that human equality is the foundation of our rights against one another.
Locke in turn was simply developing the ideas o f an earlier group of English radicals with the decidedly egalitarian name Levellers. These Levellers, whose leaders included John Lilburne, William Walwyn, and Richard Overton, emerged during the English Civil War of the 1640s as the first mass libertarian movement. “Levellers” was not actually their preferred name for themselves; indeed, they penned tracts with titles like A Manifestation from [Those] Commonly (Though Unjustly) Styled Levellers and The Levellers (Falsely Socalled) Vindicated. Their discomfort with the name stemmed from the fear that they might be interpreted as demanding the forcible abolition of inequalities in wealth, a goal they expressly repudiated: “We profess therefore that we never had it in our thoughts to level men’s estates, it being the utmost of our aim that the commonwealth be reduced to such a pass that every man may with as much security as may be enjoy his propriety [i.e., his own property].” 
Yet the name “Leveller” suited them nonetheless, for while they did not seek socioeconomic equality, they were passionately devoted to equality in authority. Overton, for example, maintained that “by natural birth all men are equally and alike born to like propriety, liberty and freedom,” so that “bellows-menders, broommen, cobblers, tinkers, or chimney-sweepers” are “all equally freeborn” with “the greatest peers in the land.” John Locke Hence, Overton inferred, ” No man has power over my rights and liberties, and I over no man’s,” and every man is “a king, priest and prophet in his own natural circuit and compass, whereof no second may partake but by deputation, commission, and free consent from him whose natural right and freedom it is.” 
This form of equality goes well beyond mere equality before the law. If the rulers of a state require that everyone worship Shiva, then in some sense they are treating all the citizens equally (assuming they also worship Shiva themselves); but they are nevertheless not respecting equality in authority, because they are arrogating to themselves, and denying to others, the authority to decide whether Shiva will be worshipped. Rather than merely requiring the equal application of the laws, equality in the libertarian sense places restrictions on the content of those laws as well, ruling out forcible subordination of any kind. This point of view is entirely consistent with the legitimate defensive use of force; such force restores equality in authority rather than violating it. But any initiatory use of force involves treating other people as though they were “made for one another’s uses,” and so is forbidden as an affront to human equality. Those who see only two forms that equality can take—substantive socioeconomic equality and formal equality before the law—have neglected the possibility of libertarian equality, which is substantive but not socioeconomic.
What are the political implications of this third kind of equality? The upshot of libertarian equality, equality in authority, is that government can possess no rights that its subjects lack—unless they freely surrender such rights by “deputation, commission, and free consent.” Since I have no right over anyone else’s person or property, I cannot delegate to government a right over anyone else’s person or property. As nineteenth-century French economist Frederic Bastiat eloquently stated:
If every person has the right to defend—even by force—his person, his liberty, and his property, then it follows that a group of men have the right to organize and support a common force to protect these rights constantly. Thus the principle of collective right—its reason for existing, its lawfulness—is based on individual right. And the common force that protects this collective right cannot logically have any other purpose or any other mission than that for which it acts as a substitute. Thus, since an individual cannot lawfully use force against the person, liberty, or property of another individual, then the common force—for the same reason—cannot lawfully be used to destroy the person, liberty, or property of individuals or groups. 
While libertarians disagree with one another as to how much, if any, of one’s natural liberty it is proper or needful to surrender to government, all libertarians agree in seeking to minimize the inequalities in authority existing between the average person on the one hand and the functionaries and privileged beneficiaries of the state on the other.
Neither socioeconomic equality nor equality before the law measures up to the radicalism of libertarian equality, because neither socioeconomic equality nor equality before the law goes so far as to call into question the existing power structure. Both forms of equality call on the rulers to ensure that equality (of the favored form) prevails among the ruled, while assuming all along an inequality in authority between rulers and ruled. (The fact that the ruled are eligible for elective office does not erase this inequality, since those who make it into the ranks of the rulers must necessarily be a small minority of the populace.) As philosopher Antony Flew writes, under a system of governmental regulation “what the various ruling elites determine to be fitting . . . may or may not turn out to be equality between all those who are so dependent. But as between those who give and those who receive the commands . . . there can of course be no equality at all.” 
Libertarian equality, by contrast, involves not merely equality before those who administer the law, but equality with them. Government must be restrained within the Thomas Jefferson moral bounds applicable to private citizens. If I may not take your property without your consent, neither may the state.
Hence it is libertarianism, not statist socialism, that deserves the title radical egalitarianism. Liberty is the truest form of equality. 
 It’s worth remembering that pursuing socioeconomic equality through peaceful and voluntary means is entirely compatible with libertarianism. For a fuller discussion of this point, see Roderick T. Long and Charles W. Johnson, “Libertarian Feminism: Can This Marriage Be Saved?” www.charleswjohnson.name/essays/libertarianfeminism.
 Murray N. Rothbard, Man, Economy, and State: A Treatise on Economic Principles; with Power and Market: Government and the Economy, scholars’ edition (Auburn, Ala.: Ludwig von Mises Institute, 2004), p. 1219, http://mises.org/rothbard/mes/chapl6d.asp.
 Thomas Jefferson, Original Draft of the Declaration of Independence (emphasis added), http://classicliberal.tripod.com/jefferson/origdecind.html.
 John Locke, Second Treatise of Government II. 4, www.lonang.com/exlibris/locke/loc-202.htm.
 Locke, ibid., II. 6.
 A Manifestation from Lieutenant-Colonel John Lilburne, Mr. William Walwyn, Mr. Thomas Prince, and Mr. Richard Overton (Now Prisoners in the Tower of London), and Others, Commonly (Though Unjustly) Styled Levellers (1649),www.constitution.org/lev/eng_lev_ll.htm.
 This passage is from what is perhaps the most delightfully titled political treatise ever written:
Richard Overton, An Arrow Against All Tyrants and Tyranny, Shot from the Prison of Newgate into the Prerogative Bowels of the Arbitrary House of Lords, and All Other Usurpers and Tyrants Whatsoever; Wlierein the Original, Rise, Extent, and End of Magisterial Power, the Natural and National Rights, Freedoms and Properties of Mankind are Discovered and Undeniably Maintained; the Late Oppressions and Encroachments of the Lords over the Commons Legally (By the Fundamental Laws and Statutes of This Realm, As Also By a Memorable Extract Out of the Records of the Tower of London) Condemned; the Late Presbyterian Ordinance (Invented and Contrived by the Diviners, and By the Motion of Mr. Bacon and Mr. Tate Read in the House of Commons) Examined, Refuted, and Exploded, As Most Inhumane, Tyrannical and Barbarous, by Richard Overton, Prerogative Archer to the Arbitrary House of Lords, Their Prisoner in Newgate, for the Just and Legal Properties, Rights and Freedoms of the Commons of England (1646), www.constitution.org/lev/eng_lev_05.htm.
For further discussion of Overton see Peter Kurrild-Klitgaard, “Self-Ownership and Consent: The Contractarian Liberalism of Richard Overton,” Journal of Libertarian Studies, Fall 2000, pp. 43—96, www.mises.org/journals/jls/15_1 /15_l_2.pdf.
 Frederic Bastiat, The Law, trans. Dean Russell (Irvington-on-Hudson, N.Y.: Foundation for Economic Education, 1998 ),www. econlib.org/library/Bastiat/basEss2a. html.
 Antony Flew, The Politics of Procrustes: Contradictions of Enforced Equality (Buffalo, N.Y.: Prometheus Books, 1981), p. 12.
 For a fuller discussion of libertarianism’s egalitarian dimension, see Roderick T. Long, “Equality: The Unknown Ideal,” Mises Daily Article, October 16, 2001, http://mises.org/story/804.