Trogdor's Peasants: A Riddle

A v. hard riddle passed on to me from Jon:

Our not-so-friendly Trogdor the Burninator doesn't like peasants. In fact, he has just captured n peasants (where n>=2) and wants to eat them. But, Trogdor is feeling nice today and will give them a chance to live if they can solve this one puzzle. Trogdor decides to put hats of differing colors on all the peasants' heads. The hats are colored in as many colors as peasants and Trogdor has a large supply of any color; thus, all the peasants could be wearing the same color hat, or all the peasants could be wearing a different color hat. The peasants will sit in a circle and write down on a piece of paper the color hat they think is on their head. Trogdor then collects the pieces of paper and if none of the peasants gets his/her hat color right, all the peasants die; BUT, if at least one peasant is right, they all live (yay!).

The peasants discuss strategy before hat-placement, but once the hats are on, no communication whatsoever. (As a point of clarification, the peasants do know the set of colors from which Trogdor chooses. Another point of clarification: once the hats are on, there is absolutely no communication between peasants--eg, they don't know what the other peasants guessed).

So what strategy should the peasants use? Good luck, and email me for confirmation or clarifications.