Wikimedia only works by building consensus, as everyone has equal powers (except for blocking, deletion, and page protection, functions limited to administrators) and therefore can undo any change. Editors build consensus through polite discussion and negotiation.
One description of what consensus is, made on the mailing list, is as follows:
In fact WP's standard way of operating is a rather good illustration of what it does mean: a mixture across the community of those who are largely agreed, some who disagree but 'agree to disagree' without disaffection, those who don't agree but give low priority to the given issue, those who disagree strongly but concede that there is a community view and respect it on that level, some vocal and unreconciled folk, some who operate 'outside the law'. You find out whether you have consensus, if not unanimity, when you try to build on it.”
Specifying exactly what constitutes a reasonable or rational position is difficult. Nearly every editor believes that their position is reasonable; good editors acknowledge that positions opposed to their own are also reasonable. But Wikimedia's consensus practice does not justify stubborn insistence on an eccentric position combined with refusal to consider other viewpoints in good faith. With respect to good faith, no amount of emphasized assertions that you are editing according to the neutral point of view (NPOV) while engaging in biased editing will serve to paper over the nature of your activities.
Consensus should not trump NPOV (or any other official policy). However, a group of editors may be able to shut out certain facts and points of view through persistence, numbers, and organization. This group of editors should not agree to an article version that violates NPOV, but on occasion will do so anyway. This is generally agreed to be a bad thing and to be avoided.