In "A World Of Choice," chapter 1 of No One Makes You Shop at Wal-Mart (via Brad DeLong), Tom Slee shows that the simple aggregation of individual choices can lead to socially undesirable outcomes: outcomes that the individuals exercising their choices themselves see as undesirable. How can this be? The answer is, fundamentally, externalities: everyone's choices affect everyone else's outcomes. Alice's choices affect Bob and Carol's outcomes and choices, Bob's choices affect Alice and Carol, and Carol's affect Alice and Bob. The simplest model of the tension between individual and collective choices is the Prisoner's Dilemma, but Slee shows that much more complicated games can exhibit the same tension. (Yoram Bauman also has a good example using pollution as an externality.) What's important about the Prisoner's Dilemma and Slee's example is that the externalities in both are intrinsic parts of the game. Either we must have true collective decision-making, or we must accept the apparently undesirable outcomes of purely individual decision-making as a consequence of the principle.
Collectivism, i.e. collective decision-making, means that a social group makes a single decision as a whole. The advantage of collectivism is that externalities, both physical externalities such as pollution and game-theoretic externalities like those from the Prisoner's Dilemma, can be included and addressed in the collective decision. The disadvantage of collectivism is that the social decisions are never consensual. Some people will always dissent from the collective decision. In Slee's case (go read it, it's not that long, and I'm too lazy to summarize), some people will not find the variety of the downtown department stores or the experience of walking downtown to be desirable; they are happier overall with only Wal-Mart than they were with only the two downtown department stores. Collectivism is also subject to institutional capture, where some minority gains a disproportionate influence over the collective decision-making process. The analysis of individualism and collectivism is non-trivial.
As noted above, even in a majoritarian system, the long-run collective benefit of the majority will almost always operate to the detriment of some minority. On the one hand, this oppression of the minority is not always bad: clearly, the collective decision to prohibit murder and rape oppresses the interests of killers and and rapists, and most people are fine with that outcome. To simply assert the absolute categorical injustice of the majority imposing its will on a minority contradicts our intuitions and expectations about justice. On the other hand, absolute majoritarianism contradicts strong intuitions and expectations about the value individualism and even eccentricity. There's some wiggle room there: we can have a majoritarian approval of a general principle that leads to specific outcomes that the majority would disapprove of. For example, the majority approves of the general principle of free speech even if the majority would disapprove of some specific outcomes, such as blatantly racist speech. Still, we cannot wholly escape the tension between the benefit of the majority and the benefit of the minority and individual.
Institutional capture is another problem with collectivism. A collective decision must be enforced with actual and threatened violence, and those within the institutions of enforcement can more easily gain influence over the decision-making process itself. Because enforcement is always directed to the specific, to charge the majority themselves with direct enforcement blurs or erases the distinction between the general and the specific necessary to protect the minority and individual. The problem of institutional capture underlies, I think, the main thrust of anarchism: the value of collective decision-making is outweighed by the tendency of the "state," i.e. the set of cooperating institutions with a monopoly on the legitimate use of violence, to capture the decision-making process for the disproportionate or exclusive benefit of the members of those institutions. Like the tension between the majority and minority, we cannot avoid tension between the institutional and majoritarian.
Both anarchism, left and right, as well as intentional institutionalization of a minority in the collective decision-making process are untenable. Even stripped of their vagueness, hypocrisy, and internal contradictions, left- and right-anarchism are impossible simply because people spontaneously institutionalize the use of violence; the "state" did not drop down from outer space to oppress humanity. Minority institutionalization, whether of the minority capitalist ruling class of large property owners or of a bureaucratic and intellectual elite such as a Communist Party is certainly possible, but it is inevitable that those individuals who form the elite will make decisions that, at first disproportionally and later exclusively, benefit only themselves. There is no simple, easy way to cut the Gordian knot of politics.