Good points. Just as it is prudent to begin with objective measures, and then slowly add more complex subjective factors, it is also useful to recognize that mathematical models are only one approach, and are often insufficient for the problem at hand.

In complex systems and computational social science, mathematical models (e.g. equations) are often used as a first approximation or an early step in modeling a system. Mathematical models are often insufficient if the system is complex enough, so once a mathematical models have been built, folks can move to agent-based models to replicate the mathematical model and extend it to capture and track dynamics and heterogenous features of interest over time and across simulations. And even more so than in traditional modeling, agent-based models must be built and run with care - or you can find anything you want to find.