Identical Cousins
When a show is created and produced, it usually has a number of different people for most of the behind the scenes roles. A show has producers, writers, directors, and of course those who were responsible for creating it. But on this show, the two men who created the show, William Asher and Sidney Sheldon, were also the ones who wrote most of the episodes.
Sheldon had noticed that Patty often had erratic mood swings — to the point that she almost had dual personalities — and the concept of two “identical cousins” (both played by Patty) was born from this observation. It wasn’t until later in life that Duke was diagnosed as bipolar.