What does it assume?
ACT rests on the main assumption that all individuals understand and conceptualize events in the world in a manner in keeping with the sentiments that they hold about all individuals' identities in a given situation: people want the world to reflect the way that they see the world, so that the "does" of human behavior matches the "should" of human behavior as they see it.
If behaviors don't work to keep reality in line with expectations, people will re-conceptualize or redefine behaviors or identities of self or other in the situation.
Emotions reflect your sentiments and the levels and types of validation you are or are not experiencing in the moment.
As you work to create and structure events that confirm your sentiments, you perform social roles, and these social roles make up the basic institutions of society.
What it can do:
ACT can tell us in what light society will likely view a particular course of action, occasion, or person. It can tell us in what society this will hold true (for ACT can map the expectations and predict how the interactions will differ in different cultures). It can tell us what behavior people expect from certain types of people, and how perspectives differ by subgroup inclusion. ACT can tell us how people will treat and label a person based on that person's demeanor, and it can predict behaviors and emotions of particular actors. The theory has extraordinarily flexible utility, and its predictions have been affirmed in many empirical studies.
How it works:
ACT can be expressed entirely by mathematics, or be translated into words. The equations of the theory essentially work to decrease deflection. Deflection is the distance between the transient impression and the fundamental sentiment of an identity or an event. Every identity, behavior, mood, object, etc. has a cultural sentiment. Just as a computer can express everything in binary code by using ones and zeros, ACT can define everything using numerical points along three explanatory dimensions: Evaluation, Potency, and Activity. These dimensions are universal and fully descriptive using direction and magnitude combinations along the three dimensions. For instance, a very good, very powerful, very active identity might be someone like a hero, firefighter, or winner, while a very bad, very powerful, very active identity might be someone like a drug dealer or a brute. People seek to observe harmony between all elements of an event. A mother kissing a child is in keeping with cultural sentiments. A mother insulting and demeaning a child is not in keeping with cultural sentiments, and causes deflection. She has just done something much less good, powerful, and active than a mother normally does to a child. You may, as an observer, now have more negative feelings about this particular mother, but it does not change your sense of how positive, powerful, and active "a mother" in general is supposed to be. Your cultural sentiment about mothers remains stable, and is the reference point against which you unfavorably compare this particular mother. ACT expresses these culture-specific sentiment confirmations mathematically, using weights for cultural terms, and markers and modifiers for things like emotion and setting. These equations allow predictions of likely and unlikely ways that an interaction may play out in a given culture.