The Allocation Gap: A Simple Index for Measuring the Distance Between Public Will and Public Spending

Public budgets are usually judged by their size, their efficiency or their legality. They are rarely judged by a simpler question: do they match what the public says it values and needs? I propose a communicable, auditable way to ask that question. The Allocation Gap, G, is half the sum of absolute differences between a community's priority shares (the Public Will, p) and its actual spending shares (s) across n categories or areas: G = ½ Σ |p − s|. G lies between 0 and 1 and has a direct reading: it is the fraction of a budget that would have to be moved to make spending match priorities. The formula is mathematically identical to the Index of Dissimilarity (Duncan and Duncan, 1955), the Hoover or "Robin Hood" index (Hoover, 1936) and the total variation distance. My contribution is the application and framing: pairing the index with an explicit method for stating public priorities, a public-facing visual grammar, and a testable research agenda for small, open economies, with Barbados and the wider Caribbean as the motivating setting. This is a conceptual and methodological paper, with illustrative figures only. It is open for peer review.