Both men strongly believe that they have done the right thing. Their manner of self-justification highlights the difference in their mental makeup.
The Duke's late wife was a sweet woman of a charming nature who found joy in life and in the things around her. She loved the Duke with all his trappings of power and wealth, but she also enjoyed the simpler pleasures of life. She was sweet and charming with her husband the Duke, but to the Duke at least, it seemed that she was no less sweet and charming to anyone else. He feels that she ranked "My gift of a nine-hundred-years-old name/With anybody's gift." No doubt, she would have mended her ways if he had asked her to, but "E'en then would be some stooping, and I choose/Never to stoop." He resorts to the only course he has ever known-the exercise of his power: "I gave commands;/Then all smiles stopped together."
The Duke does not even dream that anyone could think that he had done any wrong. That is why he makes a plain revelation of all the grim facts to an ambassador who has come with a new proposal of marriage to the daughter of a Count well known for his "munificence." This reputation even emboldens the Duke to suggest that he would expect a substantial dowry.