The Greater Value Assumption asks the question of whether humans are superior, one for one, to other animals.  Those who would say yes accept the Greater Value Assumption. 

Slightly different forms of the Greater Value Assumption are also made.

Furthest philosophically from anthropocentrism are the deep ecologists.  They reject the Greater Value Assumption, saying that humans and animals are equals.  Such people hold an egalitarian-value theory, and obviously reject the Sole Value Assumption as well.

However, some deep ecologists such as Arne Naess want to avoid saying that all forms of life are equal in value.  Others, such as Paul Taylor, instead welcome this implication of their rejection of the Greater Value Assumption.

One major reason for rejecting the Greater Value Assumption is that it leads to bias in favor of people over other species.  Some people oppose this and wish to avoid this assumption because it might lead to mistreatment of other species.  Thus, even if they do not think all species are completely equal in value, some people might reject the Greater Value Assumption.

Peter Singer, the author of Animal Liberation, would not be represented in either the for or the against the Greater Value Assumption group. 

He instead argues that equal consideration should only be given if the level of interests are equal.  Thus, an animal dying is worth more than a human having a meal, and vice-versa.