This article studies the effects of sampling the alternative values from different distributions when studying the performance of surrogate weight methods in the additive model in multi-criteria decision analysis. The aim is to demonstrate surrogate weights' performance invariance regarding underlying actual distributions. Multiple distributions are characterised and examined through extensive simulation to evaluate their influence on the efficacy of surrogate weight approaches. It was found that employing the presently accepted standard distributions for alternative values led to outcomes from the surrogate weight methods that were remarkably consistent, barring a few notable deviations—-suggesting considerable robustness. In contrast, drawing samples from more extreme distributions resulted in greater divergence. Overall, the observed patterns of the surrogate weight approaches align, to a substantial degree, with findings reported in prior research. We conclude that the performance of the surrogate weight methods is generally stable under a wide variety of reasonable alternative value distributions and show a case when the distribution is too skewed.