The averages agree.
The lives might not.
Four national service averages can describe very different societies. Are the same people missing everything, or are gaps spread across the population?
Why averages are not enough
Imagine two fictional societies. Every service reaches 50% of people in both. In one, half the population has all four services and half has none. In the other, every person has exactly two services. The same four averages hide a different concentration of deprivation.
With equal weights and the concave valuation below, the first society scores 25/100 and the second 50/100. This example is synthetic. It illustrates the model’s distributional preference, not observed country statistics.
What the calculation does
A person’s access bᵢⱼ is either zero or one for each of four services. Weighted adequacy qᵢ lies between zero and one. The square-root transformation gives more value to improvements for people with fewer services. Its strength is an explicit ethical choice.
We do not observe which services each person has. Instead, a linear program considers all 16 possible access combinations, constraining their population shares to match the four national source estimates. Minimizing and maximizing expected square-root adequacy gives sharp bounds under those constraints.
“Sharp” means both endpoints are achievable by some joint distribution consistent with the inputs. It does not mean the inputs are error-free. The source estimates, population alignment and normative transformation still matter.
Assumptions you can inspect
- Observation year: 2023. Coverage requires all four service estimates.
- Services: basic water, basic sanitation, electricity, and clean cooking.
- Equal weights are 25% each. Cooking priority uses 20%, 20%, 20%, 40%. Water/sanitation priority uses 40%, 30%, 15%, 15%.
- These three scenarios are examples, not a complete range of reasonable ethical choices.
- National access estimates are treated as fixed marginals for a common total population. Survey/model uncertainty is not included in the interval.
- No joint household data are fabricated. No independence assumption is imposed.
- Access does not capture affordability, service reliability, water safety beyond the source definition, or household experience.
Evidence and reproducibility
Download results and extremal joint distributions · Download reproduction code · Source register · Read the framework
Source: World Bank World Development Indicators, SH.H2O.BASW.ZS, SH.STA.BASS.ZS, EG.ELC.ACCS.ZS, EG.CFT.ACCS.ZS. Retrieved November 1, 2026. Calculations: Pluraterra research 0.2.