At this years BBC TV writers festival Toby Whithouse, the writer of Being Human, spoke of"creating characters with an inherent contradiction or placing them in a contradictory situation; such as a policeman from a family of criminals or a city cop moving to a rural police station. This creates conflict and thus potential storylines in a long running series."
The ironies and contradictions in "Ray Donovan" arise from the fact that as a profession Ray is a Fixer for the rich and famous. This is a man who is capable of easily fixing other people's problems, but is unable to fix the problems in his own family.
Almost instantly in the show we have a character who is anachronistic within this environment. Ray is a primeval force that is at odds sometimes with the clients that have tasked him to serve them. He comes from the wrong side of the tracks in Boston and is now trying to fit into Hollywood high society, but this is character that walks to the beat of his own drum. It is out of this contradiction that conflict and drama springs.
At the heart of the character is his immediate and extended family. Ray wants to better his family and be nothing like the father that he grew up hating, a violent criminal who now (on release from 20 years in prison) has intruded on his new life. Again the contradictions in the character provide conflict and drama as the more Ray tries to protect and better his family, the more he commits violent acts that bring his morality, his children and his relationship with his father into more peril.

On this side of the pond there are numerous great writer creating characters that are utterly compelling, but I'd like to finish this post with the writer who made the comment above, Toby Whithouse. "Being Human" uses the horror comedy genre to create instant conflict through using contradictions as a vampire, werewolf and ghost strive to live a normal human life, though their condition always throws up barriers to their attempts to do so.
