When a group agrees to support and commit to the decision of the group, they have reached

When a group agrees to support and commit to its decision, it has reached a consensus.

Consensus means broad agreement that every member is willing to back and act upon.

The word census means an official headcount of a population, unrelated to group agreement.

The word solution means an answer to a problem, which may be adopted with or without full agreement.

An analysis is a careful breakdown of a matter, a step before deciding rather than the shared commitment.

Consensus in group communication grows through discussion, compromise and tests of agreement.