Granular Ambiguity and the Value of Resolution

Two finite sets of priors can share a convex hull while differing in resolution. Maximin expected utility treats them as equivalent. We axiomatize Variational Information-Structure (VIS) preferences over acts paired with finite prior sets, for which the convex hull is not a sufficient informational state variable. Value equals the maximin value over the convex core minus the product of the act's ambiguity exposure and a coefficient that depends on the core and on granularity, the Hausdorff distance between the prior set and its core. Under structural richness and a resolution Archimedean axiom, the coefficient vanishes as granularity approaches zero along granularities attainable at a fixed core. Differences in resolution can reverse the maximin ordering induced by core inclusion, and we characterize when the representation satisfies statewise monotonicity.Supports with the same core and the same granularity are behaviorally equivalent, which distinguishes the model from α-maximin with a structure-specific pessimism index.