A theoretical and numerical analysis of a GHZ-type experiment is presented, where linear polarization measurements on three entangled photons are modeled through a sigmoid-based threshold mechanism that violates the fair-sampling assumption. Numerical simulations examine how closely this local construction can approximate quantum correlations for GHZ tripartite states. Through setting-dependent detection efficiency, the model reproduces violations of both the Mermin and Svetlichny inequalities with statistical significance. The results describe how this local model can approximate quantum tripartite correlations and show how the detection mechanism shapes the statistical behavior of outcomes across entanglement regimes.