Wikipedia:Rough consensus

When closing a discussion, the discussion closer may recognize that despite the participants not reaching a consensus, there is evidence of a rough consensus enough to make a decision and to close the discussion.

Traditionally, this has been most prominently done by administrators in deletion discussions. See Deletion guidelines for administrators, shortcut WP:ROUGH CONSENSUS.

However, experienced non-admin closers are also respected for rough consensus calls, and rough consensus is also used to close a number of non-deletion discussions, such as requested moves, formal requests for comment, and many others.

Who may close a discussion with a decision based on rough consensus
Administrators are generally all considered qualified to close citing a rough consensus. Other editors may be respected in doing the same. No qualifications have been defined, except that the editor should be "experienced". However, closers must be "uninvolved".

Adapted from Administrators

Editors should not close discussion in which they have been involved. Things that may be considered to cause the editor to be too "involved" to close include:
 * A significant interest in the subject being discussed,
 * Participation in the discussion,
 * Participation in directly applicable policy discussions, if contentious
 * A significant history of friendly or unfriendly interactions with the discussion initiator or major participants in the discussion.

Things that do not cause the editor to be considered "involved" include:
 * Clerking of the discussion,
 * Providing assistance, whether information, simple advice or warnings, to involved editors,
 * Other associated but purely administrative roles

Rough consensus closing
Discussion closers must use their best judgment, attempting to be as impartial as is possible for a fallible human, to determine when rough consensus has been reached. Closers can disregard opinions and comments if they feel that there is strong evidence that they were not made in good faith. Such "bad faith" opinions include those being made by sock puppets, or accounts created solely for voting on the deletion discussion. If a rough consensus holds that the nomination was made in bad faith, the page may be speedily kept.

If the major stakeholders have not been notified of the proposed deletion or given time to respond, reliable consensus determinations will rarely be possible.

Consensus is not determined by counting heads, but by looking at strength of argument, and underlying policy (if any). Arguments that contradict policy, are based on opinion rather than fact, or are logically fallacious, are frequently discounted. For instance, if someone finds the entire page to be a copyright violation, a page is always deleted. If an argument for deletion is that the page lacks sources, but an editor adds the missing references, said argument is no longer relevant.

Per "ignore all rules", a local consensus can suspend a guideline in a particular case where suspension is in the encyclopedia's best interests, but this should be no more common in deletion than in any other area.