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The organic mesogens RM734 and DIO are members of separate molecular families featuring distinct molecular structures. These families, at the present time, are the only ones known to exhibit a ferroelectric nematic liquid crystal (LC) phase. Here we present an experimental investigation of the phase diagram and electro-optics of binary mixtures of RM734 and DIO. We observe paraelectric nematic (N) and ferroelectric nematic (NF) phases in both materials, each of which exhibits complete miscibility across the phase diagram, showing that the paraelectric and ferroelectric are the same phases in RM734 as in DIO. Remarkably, these molecules form ideal mixtures with respect to both the paraelectric-ferroelectric nematic phase behavior and the ferroelectric polarization density of the mixtures, the principal order parameter of the transition. Ideal mixing is also manifested in the orientational viscosity, and the onset of glassy dynamics at low temperature. This behavior is attributable in part to the similarity of their overall molecular shape and net longitudinal dipole moment (~ 11 Debye), and to a common tendency for head-to-tail molecular association. In contrast, the significant difference in molecular structures leads to poor solubility in the crystal phases, enhancing the stability of the ferroelectric nematic phase at low temperature in the mixtures and making possible room temperature electro-optic effects. In the mixtures with excess DIO, an intermediate phase appears via an ultraweak, first-order transition from the N phase, in a narrow temperature range between the paraelectric and ferroelectric nematics., Comment: main paper has 24 pages with 5 figures; supplementary information has 14 pages with 8 figures