[srean]

>Your function r = r(pp, red shirts, race of offender, etc) exists. A model of the form a x r + b x something_else + ... will detect the bias you've described, assuming of course the biasing variable is either present or redundantly encoded in the data set.

No no no. Had to respond to this because this such a common confusion (not to say that you personally have this).

That such a model exists within the class of models being used says absolutely nothing about whether the statistical/ML algorithm will find it with any degree of confidence from a sample. The science is still grappling with the question of how to do model selection. There are two, sort of, equivalent class of methods, regularization (this can be a regularization over the dependency structure too, not just a simple penalty) and prior. Its only when you get those right that you have decent chance of estimating well, from reasonable amount of data.

Short answer: universal approximation property of a class of models says nothing about learnability.