Improved scaling laws for infrastructure: planning increased access to water and sanitation networks in low- and middle-income countries
Bibliographic record
Abstract
Despite efforts to expand infrastructure, billions of people still lack access to essential services. Traditional scaling-law (power-law) models of infrastructure estimate the size of infrastructure based on a city’s population, obscuring the consequences of inadequate access. Instead, we model infrastructure size as a power-law function of the population served by the infrastructure (not total population). This generalization better fitted data describing 6898 water and sewer networks in 53 countries—improving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="u1" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> by up to 32%. Even in cities with little access to infrastructure, we found economies of scale: infrastructure that serves more people can do so with less per beneficiary. Uniquely, our generalized scaling laws can model the infrastructure needed to expand access. We validate with 16 years of data from 3391 water and sewer networks in Brazil. If economies of scale are exploited at the cost of inter-city equality, sewer access can expand from 54% to 90% of Brazil’s population with 29% (89 000 km) fewer new sewers. Benefit- and equality-maximizing strategies to achieve universal access in Brazil differ by 220 million people-years of access. Our generalized model can estimate the infrastructure needed to expand access and quantify trade-offs between the benefits and equality of access expansions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".