The Right has never been a friend of democracy. Pick any period of history you like. Examine any struggle from below and you will find a slew of Right-wing arguments attacking the idea of collective self-rule. Mostly, these arguments seek to insulate or protect some powerful group from any democratic challenge by the people. Early liberal thought is concerned to defend the freedom and power of the rising mercantile class from threats from above as well as from below. The main goal of liberal politics was to restrain the State, as much as the people, from negatively interfering with the capitalist economy. On the one hand, liberals wanted to protect the business interests of the emerging capitalist class from the old Aristocratic elite. But, on the other, liberals wanted to protect those same propertied businessman from any challenge from the majority of the population who quite obviously had no basic interest in maintaining the capitalist status quo. This dual attack on both feudal power as well as the democratic power of the people gestures toward the sense in which Marx saw the anti-feudal bourgeois revolutions as both progressive as well as regressive. They tore asunder the repressive contours of feudalism at the same time that they created and consolidated new forms of exploitation and elite rule.
The American Revolution was no exception. It was progressive in rejecting many of the feudal aspects of Old Europe. But the new "republic" was by no means an experiment in genuine democracy. Nor was it intended to be. On the contrary, the founders were explicitly skeptical of democratic self-governance and sought to insulate themselves from any challenge from below, whether from unpropertied whites, indentured white servants, white women, or black people. After all, if a majority of the human beings in the US had been allowed to have a genuine voice in government, neither slavery nor the existing distribution of property would have survived for long. The early American ruling class was every bit as hostile to the monarchical power of England as they were to laboring majority of the population.
This is a clear theme among the authors of the Federalist Papers. The authors aren't worried about some abstract majority that could impose its will on some abstract minority. They weren't in the business of designing ideal societies in the realm of pure theory. They were talking about concrete groups of people, with conflicting interests borne out of their conflicting class positions, colliding in the political arena. In good bourgeois fashion they were worried that the majority of the population, over whom they presided, could overpower them if allowed to have unrestricted democratic power. Hence the need for all sorts of restrictions on what democratic bodies may do, restrictions on the pace of change, "checks and balances", etc. All of these fundamentally undemocratic measures were put in place to stabilize and consolidate a particular distribution of power, resources and control. The ignorant rabble must not be allowed to have too much of a say or else the power, expertise and "superior knowledge" of the propertied minority would be threatened.
So, there is a long Right-wing tradition of skepticism about democracy. The masses were either too dumb, too immature, too beholden to base/irrational impulses, too uneducated, or too inferior to be genuinely equal co-legislators in the process of self-rule. For these reasons, some version of elite rule was necessary. The wealth and power of a minority is thereby made "legitimate".
This is the tradition out of which the idea of the "tyranny of the majority" arises.
One version of the argument is as follows. Democracy, if left unfettered, will produce tyranny. In particular, the allegedly sacrosanct property rights of the owners of capital, who are a minority of society by necessity, will be threatened by the envious masses. The wealth of the rich will not be safe if the majority, who has no interest in protecting the power and wealth of the 1%, is allowed to decide matters of public significance. Hence, democracy cannot be unfettered. At the very least, it must be severely constrained by a set of inviolable rights (e.g. the right to property). Or perhaps the economic sphere needs to be walled off from democratic energies entirely. But it's also possible that the threat democracy poses to capitalist property relations is so great in certain periods that democracy itself has to be eliminated or severely restricted. This is the lesson on Chile in 1973. See Friedrich Hayek for versions of this anti-democratic argument, as well as for various harebrained schemes which aim to empower a "wise elite" to insulate capitalism from any democratic challenge.
Another version of the "tyranny of the majority" argument, which is far more plausible on the face of it, is the following. Democracy means that the will of the majority prevails over the minority. But if that is so, what is to stop a dominant group from using democracy to further entrench the oppression of minority groups? Worse yet, how will the interests of oppressed minorities ever be taken seriously if they can always be overruled by the votes of the majority?
The two different versions of the argument are worlds apart. The first seeks to insulate the power of an already dominant group from any democratic challenge by the majority. The second expresses a worry that currently dominated and oppressed groups will not be well served by majority rule. Still, although the motivation for both versions are extremely different, the reply to both will be the same.
First of all, democracy is not mere majority rule. The mere fact that a majority of people support something does not mean that democracy endorses it, nor does it mean that its the right thing to do. Everything depends on why people support something, what their reasons are, and who is allowed to participate in the discussion. Democracy is an arrangement in which citizens collectively self-govern themselves through reasoned discussion and deliberation. For that to have any meaning at all, citizens must be substantively equal to one another. That is to say, there cannot be any social relations that exhibit domination, exploitation, subordination or oppression. Otherwise, democratic self-governance is not possible. Exploiters and exploited cannot participate together in a reasoned process of democratic deliberation. Their interests, being diametrically opposed, prevent them from having a reasoned discussion as equals. The arguments of the exploited will fall on deaf ears, and the exploiters will be in a position to issue threats and throw their weight around. Collective self-governance between such groups is impossible. The only way forward is struggle. Since the exploited are the only ones with an undistorted interest in entirely overturning relations of exploitation, they are the group most likely to bring such a social change about. The exploiters, on the other hand, having no interest in altering the status quo, will fight to keep things as they are. The task of those committed to democracy in such a situation is to organize alongside the exploited to fight for a militant, internally democratic movement capable of overturning social relations that exhibit exploitation.
In virtue of what is someone an exploiter? In virtue of her social position in the economic structure of society. A person who owns and controls means of production is in a position to dominate those who don't. Moreover, the owner of means of production has influence and power over society insofar as that person has disproportionate control over such important matters as employment, investment, workplace organization, wages, and so forth. It is a farce to say that the 1%, given their concentrated economic power, are equal co-legislators alongside the rest of us. Collective self-governance is impossible if an unelected group enjoys exclusive control over the basic structure of society. The basic concern of those who defend socialism from below is "who decides?" If the answer is: an aristocratic elite, the capitalist class, the military brass, or state bureaucrats, then we don't have democracy (and neither do we have socialism).
The same goes for other relations of domination. Suppose that a majority of people vote in favor of a racist policy in the contemporary US. Would that be a genuinely democratic outcome? Hardly. Democracy means collective self-governance among equals. If a segment of society push for the exclusion and oppression of another segment of society, that is fundamentally undemocratic. For it means undermining the ideal of collective self-rule in favor of a situation in which one group lords over and dominates another. Real democracy means that citizens participate together as equals in determining what their shared life together should be like. But that equality is impossible in a society marked by racial oppression. Reinforcing racial oppression—by whatever means—is tantamount to increasing the undemocratic character of a social formation. As long as some group is oppressed, its members cannot be said to be equal with others. So, the second version of the argument is correct to worry that oppressed minorities may be ill-served by majority-rule, but majority-rule is not necessarily democratic.
Any action which undermines continued collective self-governance among equals is undemocratic. Thus, restricting free speech isn't wrong because it violates some "natural" right; it is wrong precisely because it makes genuine collective self-governance impossible.
Second, democracy is not identical to voting. Voting is simply one possible way of trying to institutionalize democratic decision making. But the mere act of voting is not the most important part of democracy. Far more important is the discussion that preceded a particular vote. This should be evident to anyone who has participated in a General Assembly at an occupation. A vote is really only as good as the discussion that preceded it. If that discussion was distorted by asymmetrical relations of power and threats by more powerful groups, then the upshot of the vote is unclear. If the discussion was dominated by a powerful misconception propagated from above, the results are similarly dubious. Or, if the voices and concerns of certain groups are not heard or taken seriously in the discussion, this can similarly devalue a vote. Only a discussion which generalizes from the experiences of all, which proceeds on the basis of reasoned deliberation, which takes seriously the interests of all those participating, is likely to produce an outcome with genuinely democratic credentials.
The point is that democracy is not something that happens merely in the act of voting. It occurs in and through the arguments and deliberations about what to do. To the extent that those deliberations are skewed by threats, self-interested bargaining, private gain or by certain groups throwing their weight around, what results from them is not democratic. To the extent that those deliberations exclude parties that are affected by a decision, they are similarly undemocratic. Moreover, if those deliberations proceed on the basis of ideological manipulation or deception, they are similarly undemocratic. Democracy happens when substantively equal participants collectively and openly discuss together—by exchanging reasons among one another, not by appealing to unexamined "preferences"—how to settle matters of common concern. Thus, a vote may or may not, in this sense, be democratic. The mere fact that a majority supports something does not make it democratic.
It should be clear, then, from what has been said above that democracy is not identical with existing electoral procedures. Democracy, properly understood, is antithetical to these illegitimate procedures and to the society in which they are situated. Democracy is general assemblies, workers' councils, consciousness raising groups, strike committees, mass demonstrations and public speak-outs. The ossified electoral structures in the US—which revolve around around two massive corporate-backed party organizations—are anything but democratic. US elections—especially presidential elections—are little more than opportunities for us to choose which wing of the ruling class will misrepresent us for the next couple of years. To encourage us to choose between the Democrats and Republicans is to do nothing more than attempt to cast a system of, by and for the 1% in a favorable light by making it appear as if it enjoys democratic legitimacy.
One closing thought about "consensus" procedures in social movements. I think those who defend these sorts of procedures do so in part for democratic reasons. That is, the goal of every deliberation should be consensus. Consensus is not compromise. Compromise occurs when parties who have different interests, or at least different views, agree to disagree and bargain rather than try to convince the other of what they take to be correct. Consensus means that a group of people are won to a position because they agree that it is best supported by the relevant reasons.
In democratic deliberations and discussions, consensus should always be the goal. We shouldn't start off the discussion by strategizing about how to bargain, threaten, deceive, or frighten people in to voting one way or another. We should begin by trying to convince them through reasoned argument—and we should be open to having our minds changed by the arguments we encounter in the discussion. Genuine democracy means that all of the relevant arguments are heard, all of the reasons for and against considered. No voices are silenced. After all of that, the hope is that the view best supported by reasons will win out. Of course, real life is hardly ever so clean cut. Sometimes group deliberations about what to do yield deep disagreement. Sometimes that disagreement is over what's best supported by reasons, sometimes not. Sometimes certain groups refuse to seriously consider certain arguments because they threaten their authority or power.
What's more, we never have an unlimited time frame in which to discuss and deliberate. At some point, the need to act intervenes and cuts short the ideal of unconstrained, endless deliberation. So, in the absence of a real consensus, working democratic bodies need a decision procedure that best captures what the will of all is at that moment. Some version of majority rule (whether that's simple majority or super-majority) is unavoidable here for practical reasons. First, genuine consensus is one thing, but so-called "consensus procedures" are another. "Consensus procedures" endow each individual with veto power. That individual need not have good reasons for her veto. She need not convince others that her views are correct. In order to derail a collective discussion all she need do is veto it and the whole thing is shot. This hardly encourages reasoned argument and collective deliberation among equals. Neither does it encourage aiming to achieve real consensus. On the contrary, it encourages threats, raw bargaining (which is not the same as arguing), foot-stomping, and other non-deliberative interactions.
One final thought, just so that the above is not misunderstood. I am not saying that we need "more dialogue" and discussion between oppressor and oppressed, exploiter and exploited. Reasoned argument from below tends to fall on deaf ears when it is aimed at convincing those in positions of power. In these cases, only struggle can carry the day. An all-encompassing democracy isn't possible in social conditions marked by systemic oppression, exploitation and marginalization. The system must be changed in order to lay the groundwork for such a possibility. But, among those organized to fight for a better society, democratic self-governance is key. The movement for a better world has to embody many of the attributes that the future world must exemplify. So my comments about democracy, discussion, deliberation, reasoned argument, etc. should be taken to apply to movements from below that bring together people concerned to fight against all forms of oppression, domination and exploitation. I'll sit down and have a reasoned discussion with the ruling class when they give up all of their wealth and power.