Groups, information theory, and Einstein's likelihood principle

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.

Rational choice, social identity, and beliefs about oneself

Social identity poses one of the most important challenges to rational choice theory, but rational choice theorists do not hold a common position regarding identity. On one hand, externalist rational choice ignores the concept of identity or reduces it to revealed preferences. On the other hand, internalist rational choice considers identity as a key concept in explaining social action because it permits expressive motivations to be included in the models. However, internalist theorists tend to reduce identity to desire—the desire of a person to express his or her social being. From an internalist point of view, that is, from a viewpoint in which not only desires but also beliefs play a key role in social explanations as mental entities, this article rejects externalist reductionism and proposes a redefinition of social identity as a net of beliefs about oneself, beliefs that are indexical, robust, and socially shaped.