What do you do when you're in a lose/lose?

Interesting story over at TV squad. Today the Writer's Guild of America (WGA) went on strike.
This creates an issue for three of the actors on The Office. BJ Novack, Mindy Kaling (Kelly) and Paul Lieberstein (Toby) are all actors and writers on the show. The Screen Actors Guild (SAG), which all three also belong to are requiring all actors to show up.

It's a tough thing when two things you are committed to and passionate about are at complete odds with each other.

I posted earlier today about how important it is to go for multiple wins, but what do you do when you are in a situation where you are going to have a significant lose no matter which choice you make?

In my experience these situations have less to do with what choice you make, and much more to do with the character and manner in which you go about your choice.