Which major sociological theory addresses cultural deficiency & cultural bias?
This is a very intelligent question. There are many great sociologists out there that write about how cultural deficiencies and biases work to create unjust advantages and systems in our society. Unfortunately, often times they write in a way that is very difficult to understand. One of these great minds is Pierre Bourdieu. He is a giant in the field of how culture and power works.
The social theory of Pierre Bourdieu called "Cultural Capital," as described in his book Cultural Reproduction and Social Reproduction (1973), in which he explains his theory, concerns what he calls cultural capital. Cultural capital are those things which gives a person the ability to succeed and excel. Also much of this is passed down in the home. For example, if a person speaks very well, it is most likely because that person has grown up in a household where such things were common. This is no little thing, because it allows that person to have an advantage in education, the work place, and other areas, where speech matters. The same goes for tastes in other areas, such as art, music, dress, social etiquette, and education. The more cultural capital a person has, the greater the chance for success.
All of this is to point out that some people have social capital and other do not. This creates cultural deficiencies. Moreover, there is a strong bias in favor of those who already have a lot of social capital. So, those in power stay there.