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To get his personal quest, players must know the true identity of his father as well as have a decent approval rating with him. This makes him much more willing to become king. Basically, a hardened Alistair has more confidence and is willing to put duty above feelings.
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Most guides advise hardening him if the player wants to make him king.
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Alistair, like Leliana, is a character that can be hardened during his personal quest.
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