My boy Henry will always choose my right side, tucking under my arm and his head on my chest. Which is him in a "leftward" position then.

He'll work out some kind of arrangement if I'm laying on my left side and he can't lay on his left, but if I'm lying on my back it's always to the right.

It makes you wonder about cat-person compatibility based on the person's preference for how to lie down and the cat's preference.