It's well known that all other settings being the same, larger sensor translates into a shallower DOF.
However, for the same number of pixels, doubling linear size of the sensor size would quadruple size of the pixels, and therefore increase ISO by 2 stops. This allows reduction of aperture by 2 stops on the larger camera, while maintaining the same ISO.
It's also well known that all other things being equal smaller aperture translates into a deeper DOF.
Thus the question: if you linearly increase sensor size 2x and reduce aperture by 2 stops would you get a deeper DOF (as lower aperture would suggest) or a shallower DOF (as the larger sensor would suggest)?