Collective identity model
This is a model of asexual identity put forth by David Jay. Rather than trying to define a common sexual classification for all asexual people, this model frames asexuality in terms of collective identity. Asexual people have something in common because they have all chosen to actively disidentify with sexuality, a socially dominant framework for thinking about everything from pleasure to attractiveness to intimacy.
Under this model an asexual person is anyone who uses the term "asexual" to describe themselves. The label can only be applied internally, no one has the power to create a set of criteria which determine who "is" and "is not" asexual. The desire to identify as asexual comes from occupying a particular social position relative to culturally dominant ideas about sexuality. This common social position is the one thing which unifies all asexual people.
Imagine a person who does not experience sexual attraction. Imagine they are put in an environment where they are free to talk about desire and pleasure, pursue relationships, and go about their lives without their lack of sexuality ever becoming an issue. This person would feel sexually "normal", they would feel no desire to identify as asexual or participate in a community. Under the collective identity model this person would not be asexual, because they would not use the term "asexual" to describe themselves.
Now imagine that same person in a different environment, where they are reminded of their lack of sexuality constantly. In this environment things like intimacy and attraction are entangled in a set of sexual ideas which have nothing to do with the person's life. The person is constantly expected to be thinking and feeling things which they are not. This second environment could create feelings of confusion and isolation leading to the formation of an asexual identity and make the person asexual.
The collective identity model implies that asexuality as we know it is a direct result of culturally dominant ideas about sex which are incompatible with our lifestyle. By growing as a community and becoming visible in the public sphere asexual people will challenge those ideas, changing what it means to be sexual and what it means to be asexual.