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The phase stability of superstructures based on the fcc lattice in the Au-Pd and Ag-Pt alloy systems are examined from the fully relativistic electronic density functional theory. The electron-ion interaction is described by the projector augmented-wave (PAW) method and the exchange-correlation effects are treated in the generalized gradient approximation (GGA). The cluster expansion method is used to obtain effective cluster interactions on the fcc lattice and is used also to guide a systematic ground state search for both alloy systems. The ground state analysis reveals a multitude of ground states in Au-Pd, especially at the Au-rich side. Possibly long-period super-structures occur near the ${\mathrm{Au}}_{70}{\mathrm{Pd}}_{30}$ composition. The ground state analysis indicates a uniquely stable AgPt compound with the $\mathrm{L}{1}_{1}$ structure (CuPt prototype) and it also suggests a marginally stable ordered compound for ${\mathrm{Ag}}_{3}\mathrm{Pt}$. However, our ab initio study rules out the existence of the remarkably stable ${\mathrm{Ag}}_{3}\mathrm{Pt}$ phase with $\mathrm{L}{1}_{2}$ structure, reported first more than half a century ago and since then included in many assessments. We also find no indication for a stable ordered state at the $\mathrm{Ag}{\mathrm{Pt}}_{3}$ composition. The cluster variation method (CVM) with a large maximal cluster is used to compute the enthalpy of mixing of the disordered solid solutions and the solid portion of the Au-Pd and Ag-Pt phase diagrams. These results are critically compared with experimental data and phase diagram assessments. It is shown that cluster expansions cannot account for the high-temperature miscibility gap in the Ag-Pt system when the effective cluster interactions do not reach beyond the second nearest neighbor. Only when third nearest neighbors are included in the cluster expansion is it possible to obtain a phase diagram that agrees qualitatively with the assessed Ag-Pt phase diagram.