Another approach is to ignore problem people. Tell everyone else to ignore their problems and focus on their strengths.

Read this: http://strengths.gallup.com/110242/About-Book.aspx

You're there to get things done, not make each other feel happy and have neat lunches. If you're more interested in going to fun parties and having fun lunches, go work at Google or Facebook or another dying company.

If you want to get things done, focus on the strengths needed to get things done.