At a closed-door meeting in Stockholm this week, each paragraph of a document written by scientists is being projected onto large screens. Delegations from scores of nations participate in the editing: Words will be substituted, emphasis will be added, entire sentences may well be inserted or deleted.

After four days of haggling, the media will be summoned by the United Nations' Intergovernmental Panel on Climate Change to a news conference on Friday where the final version of the document—known as the "Summary for Policymakers"—will...