Why was Kate crossed off the list?

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Why is Kate off the list if the likes of Sawyer are still on it? The worst she has done is kill her father to protect her mother. Sawyer killed a guy in Australia and then when on the Island he killed Locke's father and the member of the others who was unarmed on the beach after Hurley had driven the VW van in to save the day. If Jacob was watching for the decisions the candidates made after they were on the Island as he told Richard, why would Kate's name have been crossed off in the cave and not Sawyer's name?