Why protecting public funding may not preserve philanthropy’s wider benefits

A donation designated for one public service can benefit other services too, because the budget authority can rearrange its own spending. That creates a question for rules intended to keep philanthropy additional: additional compared with what? Christian Jaag examines this distinction in a theoretical economics preprint posted to arXiv in November 2026. The supplied record lists no journal publication; the findings are mathematical results, not measurements of actual budgets.

Two different promises

The paper calls the first promise “baseline additionality”: protecting a service’s public appropriation before donations arrive. Full protection means government cannot cut that original allocation when the service receives its gift.

The second promise, “portfolio preservation,” uses a different reference. It asks whether a service retains what it would receive after all gifts arrive and the authority freely reallocates its budget. A service can meet the first standard while falling short of the second, losing benefits indirectly generated by other donors.

This portfolio reference is a diagnostic comparison, not a claim that any service is entitled to that allocation.

How the model works

The model includes at least two donor-backed services and a separate category representing other public spending. Each service’s total provision equals its public funding plus its designated donation. The public budget is fixed, and every unit of service costs one unit of money.

The authority values all categories, with diminishing marginal benefits: additional provision remains beneficial, but each extra unit contributes less than the previous one. These assumptions produce a unique preferred allocation.

A separate rule-setter imposes minimum funding requirements. Protection rates range from zero to one. At full protection, a service’s guaranteed total provision equals its original public appropriation plus its own gift. The permitted rules cannot require public funding above that original appropriation, although the authority can voluntarily spend more.

Jaag first holds donations fixed and derives how the authority reallocates resources when these requirements become binding. The analysis uses constrained optimization and mathematical proofs, supplemented by an illustrative calculation rather than empirical data.

The central finding

Under the model’s unrestricted allocation, increasing any gift raises provision in every category. However, only the recipient service gains a corresponding increase in its maximum contractual guarantee.

Other services therefore gain benefits that their own protection rules may be unable to secure. The paper calls this a “cross-donor fiscal externality”: one donor changes another service’s exposure to subsequent budget reallocations.

The main result establishes an exact boundary. If any service’s maximum permitted guarantee falls below its unrestricted post-donation provision, every protection reform that actually changes the allocation reduces that service relative to that reference. Even fully protecting its original public appropriation cannot prevent this loss.

Conversely, a reform can expand at least one donor-backed service while preserving all the others exactly when every service’s maximum guarantee reaches its reference level. Such expansions are financed by reducing the separate category of other public spending. Preserving donor-backed services does not mean preserving the entire budget portfolio.

A numerical illustration

In the paper’s example, a public budget of 30 initially provides 10 units to each of two donor-backed services and 10 to other spending. Gifts of five and one increase total resources to 36. With unrestricted allocation, each category receives 12.

The largest permitted guarantees are nevertheless 15 and 11. The second service’s guarantee cannot reach its reference of 12. One protection reform produces allocations of 13, 11.5 and 11.5. The second service retains more than its original public funding, yet loses provision compared with unrestricted budgeting after the gifts. These numbers illustrate the model; they are not observed outcomes.

Welfare and limits

Preservation is not automatically the best social objective. Using a welfare measure combining the authority’s benefits and donor benefits in comparable units, the paper identifies a unique best reform within the preservation set. Small preserving expansions improve that measure, but larger reallocations can impose substantial costs elsewhere.

The fixed-donation results also have a limited voluntary-giving foundation. With logarithmic preferences and sufficiently high donor valuations, every donor contributes its full authorized capacity under every protection vector, and the authority accepts all gifts. This is a sufficient condition, not evidence that donors generally behave this way.

The conclusions depend on enforceable commitments, observable preferences and capacities, equal provision costs, and a predetermined public budget and baseline. Changing donations, enforcement costs, private information or public matching above original appropriations requires further analysis. The practical lesson is to specify which funding reference an additionality rule is intended to protect.