Weyl-Taste Utility: Unifying Geometry, Attention, and Dynamic Choice

Classical utility theory assumes that preferences can be represented by a scalar potential function, so that the utility difference between two consumption bundles is independent of the path taken between them. This assumption—equivalent to marginal utility being a gradient—is challenged by extensive evidence on sequence effects and constructed preferences. We develop a unified framework that generalizes classical utility by modeling marginal utilities as a one-form that need not be exact. The failure of exactness is measured by curvature, a gauge-invariant geometric quantity. When curvature is nonzero, utility becomes genuinely path-dependent: identical endpoints can yield different experienced utility depending on the consumption sequence. The paper makes five contributions. (i) We provide complete mathematical foundations with explicit regularity conditions and show that curvature is the unique observable object characterizing path dependence. (ii) We connect the framework to classical demand theory via a reference-path scalar utility, deriving sharp implications such as Slutsky matrix asymmetry and structured revealed-preference violations. (iii) We give a cognitive microfoundation: cross-inhibitory attention dynamics generically induce nonzero curvature, linking geometry to attention-based preference construction. (iv) We prove a separation theorem that enables empirical identification of curvature distinct from taste drift and provide a complete experimental protocol. (v) In a two-good general equilibrium environment, we solve price dynamics and show that curvature can generate oscillatory yet stable adjustment. Keywords utility theory; revealed preference; demand theory; integrability; path dependence; dynamic choice; attention dynamics; constructed preferences; Weyl geometry; differential geometry; one-forms; curvature; holonomy; Slutsky asymmetry; GARP violations; general equilibrium JEL codes D01; D11; D50; D81; D87; D91; C61