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 En-tropy. 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 analysing 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.