A close equivalent phrase might be the "collective opinion" of a group, keeping in mind that some degree of variation is still possible among individuals, and certainly if there must be individual commitment to follow up the decision with action, this variation remains important. There is considerable debate and research into both collective intelligence and consensus decision making - discussed in depth in those articles. This article focuses strictly on the idea of consensus in the abstract, not on the implications of consensus for politics or economics (where actual action, not just agreement or decision, is required).
The word 'consensus' also holds implications of compromise. Rather than one opinion being adopted by a plurality, consensus suggests that various different opinions are brought together and adapted until a single (one might say "convergent") statement is reasonably representative of the whole, within tolerances. The articles of Wikipedia are intended to follow this kind of approach.
In mathematical terms, we might naively start by envisioning the distribution of opinions in a population as a Gaussian distribution in one parameter. We would then say that the initial step in a consensus process would be the written or spoken synthesis that represents the range of opinions within perhaps three standard deviations of the mean opinion. Other standards are possible, e.g. two standard deviations, or one, or a unanimity minus a certain tolerable number of dissenters. The following steps then operate both to check understanding of the different opinions (parameter values), and then to find new parameters in the multi-dimensional parameter space of all possible decisions, through which the consensus failure in one-dimensional parameter space can be replaced by a solution in multi-dimensional parameter space.
An alternative, qualitative, mathematical description is to say that there is an iterative process through (m+n)-dimensional parameter space, starting from initial guesses at a solution in (m)-dimensional parameter space, which tries to converge to find a common solution in (m+n)-dimensional parameter space.
Implications and usefulness of such definitions may be discussed in consensus decision making.
A criticism of such modelling is that the opinions or agreements are only theoretical, and that the strength or degree of conviction as measured is not closely correlated to the willingness of any given individual to take action. In direct action politics, the consensus is constantly tested by asking those who agree to immediately place their own bodies 'on the line' and in harm's way, to actually demonstrate that they are committed to a consensus. The ecology movement, peace movement, and labor movement have historically required such demonstrations of commitment. Some have disdained any attempt at formal models or methods, but others have prepared extensive documentation on both formal and informal consensus decision making processes.
Typically, the usefulness of formal models of consensus is confined to cases where followup action is closely and centralled controlled, e.g. in a military hierarchy or a set of similar computer programs executing on hardware that it completely controls. The idea of consensus itself is probably quite different when considering action by a group of independent human agents, or considering action by those taking orders and committed to executing them all without question, or suffering great harm or exile for any disobedience.
Formal models themselves may push consensus into groupthink, by making it harder for those who reject any formal model to have their case heard out in informal terms. A classic example is the peace movement's objection to the logic of mutual assured destruction during the Cold War, which reflected the opinions of a few experts in game theory, and directed vast resources into ultimately-useless weapons of mass destruction, which (in the USSR at least) caused the world's worst toxic waste disposal problem to date, as its nuclear missiles start to decay. Peace activists found the formal models of escalation and military behavior to be significant barriers when they objected to military spending and long term impacts on the environment - without mastering game theory models they were simply not heard.
As this example suggests, the concept of consensus is a particularly important one in the context of society and government, and forms a cornerstone of the concept of democracy. Democracy, in its rawest form, direct democracy, has been criticized since Plato and is sometimes been referred to as the "tyranny of the majority[?]", with the implication that one faction of the society is dominating other factions, possibly repressively.
Others, however, argue that if the democracy adheres to principles of consensus, becoming a deliberative democracy, then party or factional dominance can be minimized and decisions will be more representative of the entire society. This too is discussed in depth in the article on consensus decision making, with many actual examples of the tradeoffs and different tests for consensus used in actual societies and polities.
Business and political analysts have pointed out a number of problems with consensus decision making. A too-strict requirement of consensus may effectively give a small self-interested minority group veto power over decisions. Decision by consensus may take an extremely long time to occur, and thus may be intolerable for urgent matters, e.g. those of executive decisions. In some cases, consensus decision making may encourage groupthink, a situation in which people modify their opinions to reflect what they believe others want them to think, leading to a situation in which a group makes a decision that none of the members individually think is wise. Finally, consensus decision making may fail in a situation where there simply is no agreement possible, and interests are irreconcilable.
Within the IETF, the concept of "rough consensus" (and running code) is the basis for the standardization process. This has proven extremely effective for standardizing protocols for inter-computer communication.
A Wiki can be seen as a machinery for reaching consensus in text form, because a text will continue to be edited until consensus is reached (as is pointed out in Wikipedia:Welcome, newcomers)--a stable text is one sign of consensus. It can also be a sign of disgust by those who no longer care to edit the text to advance an unpopular opinion that is edited out constantly by others. In itself, agreement on text without any need to commit to action is rarely indicative of the kind of agreement required in politics or business. The article on consensus decision making looks at these issues in more depth.