We propose a general approach for developing liquid activity coefficient models based on the concept of local composition that satisfy at least two important physical conditions: (1) the total number of neighboring molecules around one molecule of species A must be a constant at any temperature for all possible mixture compositions, and (2) the number of pairs between any two species A-B determined from the local composition of B around A must be the same as that of A around B. Most commonly used liquid activity coefficient models (such as UNIQUAC) satisfy condition (1) but fail to meet condition (2), and thus are considered as fundamentally flawed. We propose a general formulation for the local composition equation containing a symmetric function of species A and B which ensures condition (2) be always satisfied. We show that the composition and temperature dependence of the symmetric functions can be completely obtained from condition (1), resulting in a new class of excess Gibbs free energy models. It is found that such a model can quantitatively reproduce the results of Monte Carlo simulation for various types of lattice fluids, while conventional models are merely qualitative. Furthermore, such a model is more accurate than the UNIQUAC model in correlating experimental data, especially in the dilute regime. Therefore, models developed based on this approach are theoretically sound and potentially applicable to a broader range of conditions.