experimental-design
Randomize the villages, not the people
It is the 1980s, and a public-health team testing a new sanitation program faces a problem individual randomization cannot solve: if one household gets clean water, its neighbors benefit too, so treated and control individuals in the same village contaminate each other's outcomes. Randomize whole villages instead, and design the study so the spillover between neighbors becomes a feature you can measure rather than a bias that hides the effect. Account for the fact that people within a village are correlated, which shrinks your effective sample far below the head count. Get it wrong and you overstate your certainty by treating correlated villagers as independent, or you miss the very community-level benefit the program was built to deliver.
Who this problem belongs to
The two figures whose methods fit it best, out of 33 in contention.
This problem attacks the exact assumption Rubin's potential-outcomes framework (1974, building on Neyman 1923) made explicit and famous: SUTVA, the Stable Unit Treatment Value Assumption, which requires that one unit's outcome not depend on another unit's treatment. Village-level spillover in a sanitation trial is a textbook SUTVA violation, and Rubin's own writing, along with his students' extensions into partial-interference and network-based causal models, directly addresses randomizing at a coarser level (the village) so the assumption holds at that level even though it fails at the individual level. His framework also supplies the language for treating spillover as an estimand to measure rather than a nuisance to eliminate. The score is not perfect only because the specific cluster-design machinery (intracluster correlation, effective sample size) was built out by biostatisticians extending his framework rather than by Rubin himself.
Pearl's causal graphical models and do-calculus (developed from the 1980s-90s onward) give a formal language for exactly what this problem needs: representing which units causally influence which other units' outcomes, so that spillover between neighboring households is drawn explicitly into the causal diagram rather than assumed away. His framework handles interference naturally by adding edges between units, letting an analyst read off from the graph what estimand is actually identified by village-level randomization. That is a more general and more explicit treatment of interference than the potential-outcomes SUTVA violation framing. He sits below Rubin because his major causal-graph publications (Causality, 2000) arrive after this 1980s scene and were built primarily for single-unit causal questions before being extended to networks, a later development relative to the problem's setting.
Fought here
In the mind map
The same ideas, as concepts rather than history — in John's ML knowledge map.
33 figures are scored on this problem. Draw it in a battle to see where you land.