On Christmas, we had History Repeating the one that makes you discard 1d6 cards from your hand. All four of us rolled high and had no cards for several turns.
The History Repeats Itself states that the player who opens the seal cannot escape the Disaster's effect. This implies that the other players CAN escape the effects.
In this post
http://forums.sjgames.com/showpost.p...24&postcount=3 Andrew states that a Militia player can cancel it for just himself. Thus, each player, except the player who opened the seal, could cancel their own copy of the Disaster.