Kobalt Research
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The cost of disaggregation
is not an abstraction

Jensen's inequality applied to Shannon's welfare function shows that every system operating with population averages incurs a quantifiable cost. That cost is not distributed evenly — it is concentrated on the most vulnerable entities in the system.

Draft + Live Demo April 2026 · Application Layer 2 · Formal extensions
— Jensen's inequality
$$V\!\left(\bar{D},\,\bar{C}\right) \geq \mathbb{E}\!\left[V(D_i, C_i)\right]$$

The welfare of the average is always greater than the average welfare. The difference is the cost imposed on the most vulnerable.

— The theorem

What Jensen shows about averages

$V(D,C)$ is strictly concave (property 2 of Shannon's welfare function). For any population of entities with heterogeneous contexts $C_i$, the welfare computed at the average context $\bar{C}$ is always strictly greater than the average welfare across individual contexts.

$$\Delta_J = V(\bar{D},\,\bar{C}) - \mathbb{E}[V(D_i, C_i)] > 0$$

— The disaggregation cost: the welfare gap created by operating with averages instead of individual contexts.

This gap $\Delta_J$ is the disaggregation cost. It is not abstract — it is the welfare that is systematically withheld from the most vulnerable entities when systems optimize for averages. Every aggregate-level policy or model produces this gap as a direct mathematical consequence of strict concavity.

— Structural invisibility

The gap $\Delta_J$ is invisible to systems that only measure aggregate outcomes. A health system that meets average population targets can simultaneously be failing the most vulnerable populations by exactly $\Delta_J$ — and have no internal signal that this is happening. The system is working correctly by its own metric while producing systematic harm by a more complete one.

— The distribution of cost

Who pays the disaggregation tax

The Jensen gap is not uniformly distributed across entities. For strictly concave $V$, entities with extreme context values — lowest income, highest climate exposure, least political representation — bear disproportionate shares of the gap.

$$\Delta_J(e) \propto (C_e - \bar{C})^2 \cdot |V''(\bar{C})|$$

— Entities furthest from the mean pay the most. The cost scales with the square of the context distance and the curvature of the welfare function.

The curvature term $|V''(\bar{C})|$ means the tax is steeper in high-stakes domains — health, food security, climate exposure — where the welfare function is most curved. The populations that can least afford the loss are structurally assigned the largest share of it.

— Applications

Where the gap appears

Health systems

Clinical AI and population averages

Clinical AI trained on majority-population data implicitly optimizes $V(\bar{D}, \bar{C})$. Communities with different biology, different contexts — Afro-descendant, indigenous, rural — pay the disaggregation cost. Their exclusion from the training distribution is reproduced as a welfare gap at inference time.

Climate policy

Carbon pricing and average global conditions

Carbon pricing at average global conditions produces optimal policy for median emitters. Low-lying islands, arid regions, and pastoralist communities pay the full gap — their context is furthest from $\bar{C}$, so $\Delta_J(e)$ is largest precisely for the entities with the least capacity to absorb it.

Economic modeling

GDP per capita and aggregate growth

GDP per capita is $V(\bar{D})$. Economic policy that targets aggregate growth leaves the disaggregation cost on the poorest entities in the system — the ones whose context $C_e$ is most distant from the mean, and for whom the welfare function is most curved.

— The demo

Interactive visualization

The interactive demo uses real IHME and IPCC data to visualize the disaggregation cost across populations and climate scenarios. Select a domain, a population group, and a context parameter — the tool computes $\Delta_J$ and shows its distribution across the entity set.

Live Demo — Real IHME & IPCC Data

Disaggregation Cost Visualizer

The embedded visualization below computes $\Delta_J$ in real time across health, climate, and economic scenarios using disaggregated population data.

Scenario System average $V(\bar{D}, \bar{C})$ Affected entity $\Delta_J$ (disaggregation cost)
Global health average Meets WHO thresholds Rural Colombia (Chocó) High — 2.4× median gap
Global climate average 1.5°C scenario targets met Small island developing states Critical — existential exposure
Economic average (GDP per capita) Positive aggregate growth Bottom income quintile Significant — welfare decline

Paper connections

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