In Puccini's Turandot, after Calaf successfully answers her riddles, Turandot begs her father not to make her marry him. (That's pretty rich given that the opera implies that she had at least 26 people killed for not being able to answer the riddles, but that's an issue for a different question). In response, Calaf states that he wants her to love him too and offers to call the whole thing off if she can discover his name by dawn. Why does he offer this? I understand that he wants her to love him, but why does he think that that would help?
In one sense, it's a counter to her own riddles: for the suitors, who were unable to answer Turandot's riddles, their punishment is death. Calaf however knows that Turandot's greatest fear isn't death, but to submit herself to a foreign suitor- and hence, or so she believes, risk reliving the tragedy which befell her ancestor, Princess Lo-u-Ling, who ruled peacefully until one day she was raped and killed by a foreign prince ("In questa reggia", from Act II) - and hence, he offers her a chance to save herself from her fear as well with a riddle, just as she offered her suitors a chance.
When Calaf sees that Turandot loathes him and begs her father to annul the marriage, he realises that should he take her then and there, he would be doing it as an act of force in some sense. So when she asks of him, Mi porterai con la forza?, he tells her instead ("Tre enigmi m'hai proposto") that he wants her "burning of love" for him (ti voglio ardente d’amor). He offers her a chance to refuse him once again, and puts his own life on the line in order to show her that his love is truly sincere and genuine, in a way that fairly honours her agency.