Well, Jeremy gets more cake. The real question is how does he maximize it? If Marie takes the smaller portion of the first cake and chooses her portion of the second cake, Jeremy will cut the second cake in half. If she chooses the larger portion of the first cake, she’ll only get a crumb of the second cake.
So Jeremy cuts the first cake in the ratio 3:1, and no matter which portion Marie picks, she’ll end up with 3/4 of a cake (neglecting crumbs).
If Jeremy cuts a smaller piece than 1/4 from the first cake, Marie chooses the bigger portion and gets more than 3/4, so he’s not going to do that.
If Jeremy cuts a bigger piece than 1/4 (up to 1/2), Marie will take the smaller (but >1/4) plus half of the second cake, so she’ll end up with >3/4.
So: 1 1/4 cake for Jeremy–assuming Marie consents to the entire arrangement.