Foundation and identification of multi-attribute Shannon entropy

Abstract

By weakening Shannon's original axioms to allow for attributes of the choice environment to differ in their associated learning costs, this paper provides an axiomatic foundation for Multi-Attribute Shannon Entropy, a natural multi-parameter generalization of Shannon Entropy. Sufficient conditions are also provided for a simple dataset that provides a closed-form solution for the Multi-Attribute Shannon Entropy cost function for information by analyzing stochastic choice data produced by a rationally inattentive agent that is picking between pairs of options when relatively few states of the world have a positive probability of being realized.