In psychology, metrics about psychological states like happiness are seldom assessed as a single question. The reason is that people's response to a simple question like "Are you happy?" is greatly influenced by many factors that might be unrelated to the particular goals of the person asking the question. So a survey might ask a variety of questions and then "happiness" is a composite of the answers from eight of the twenty questions.

How do you define happiness and how is current department behavior unhappy? How will you measure success, or report success to administration? 

You can also look at the task as an attempt to correct problems or as an opportunity to augment things that are already good. So why would anyone ever work in your department?