On ‘Maxwell's laws’ of individual behaviour

Any theory of choice under uncertainty in which choice depends on locally linear evaluations of univariate probability density functions has precisely two testable implications. These are 1. (a) d ũ = Ω 2. (b) ★d★ ũ = φ. Here φ, ũ , and Ω are differential forms, φ a zero-form, ũ a one-form, and Ω a two-form. d is the exterior derivative operator on forms, and ★ is the Hodge star operator. In this letter we explain in a non-technical way the meaning and import of equations (a) and (b). A fuller treatment will be found in Russell (1989).