I don't think that there is any provision in the Norwegian constitution that allows voluntary renunciation of titles or succession rights. Titles of people in the line of succession are a prerogative of the King under the constitution, so the King (and, in my understanding, only he) can rescind or change those titles at any time. Succession rights, on the other hand, are forefeited when a person in the line of succession marries without the King's consent. In that case, the descendants of the person who married without consent are also excluded from the line of succession.The best possible thing right now would be if the King could convince Martha-Louise to renounce her rights and titles before she gets married without his having to take action against her. It would solve a lot of problems for the royal family, and it would demonstrate to the public how much respect she has for her father and the institution.
A different, and often controversial discussion, is whether "the King" in the constitution means the King personally, or, as some scholars argue, "the King in Council", i.e., the government of Norway. King Harald V has said that, when it comes to royal marriages, he sees Art. 36 of the constitution as his personal prerogative, but, in my personal and irrelevant opinion, in a constitutional monarchy, the task of advising the King to consent to a royal marriage or not should fall on the government. That is why I think that different Norwegian governments in my opinion are equally to blame for any alleged "permissiveness" in the approval of certain royal marriages in Norway, including Haakon's marriage to MM, or ML's two marriages to Ari Behn and Durek Verrett.
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