But even if we had a good explanatory mathematical model, it could not be used to predict anything because of a technical reason, although one that seems to be -- as far as we know -- limited by theoretical constraints: our mathematical techniques simply do not allow us to predict the behaviors of systems with so many variables and so many interactions. Even numerical simulations (the kind used in weather forecasting) would diverge very quickly. In fact, measurement alone would likely take more time than the validity duration of the prediction.
The problem is not unique to the social sciences. Even if biologists could understand the evolutionary mechanism in its entirety, it seems like prediction is beyond our means. All we can do is work back from results to causes, and figure out which evolutionary pressures were more powerful. Computer science is limited by similar constraints: we can explain how a bug came to be, but working forward in time and preventing all bugs requires a computational effort that is probably out of our reach. So the social sciences -- except for very special cases in psychology, where the number of variables is kept artificially low -- is content, like biology and computer science, to provide historical explanations only.
But we don't need perfect models. Sometimes its enough just to get a idea over what influence the outcome. The popular science book freakonomics has a famous example where its describe crime and what influenced the outcome. Interestingly, it involved neither actions done to the criminals nor victims.
In the case of race we are both in agreement that there exist a power difference, ie that the outcome is not identical. What we have not talked about it what influence it. For example, is it the material starting point that causes ripple effects and influencing the outcome? If so there should be some validating data from isolated local areas where the material starting point is smaller or greater, result in a detectable effect. If we can't find such support, it would strongly hint towards invalidating such theory.
Sure, this is very common in the social science.
> there should be some validating data from isolated local areas where the material starting point is smaller or greater, result in a detectable effect
Absolutely. What do you think sociology/history/anthropology journals publish? They're full of such studies.
You say that the social science concentrate on areas where it is meaningful, but much of what we have discussed is focused on the end result. Do the property owners have, in the average, the upper hand in negotiations and do they get their way most of the time. Its an odd place to stop asking further question and not ask the question that really matter, which is what model can predict the price tomorrow.
The big benefit of such model is that such theories can be tested, and later used in prescribing ways to influence the outcome.