Randomize groups when one treatment changes another unit’s outcome

Without interference, one often writes a unit’s outcome as a function of its own treatment only. With interference, it can depend on the entire assignment vector or on a specified exposure summary, such as the share of treated neighbors. A direct effect at one neighborhood exposure differs from the effect of switching everyone. The experiment’s treatment saturation and network structure therefore belong to the estimand, not merely to the implementation notes.

An exposure model simplifies the assignment vector into categories that are believed to capture relevant spillovers. For example, full-neighborhood treatment might require both a user and every connected collaborator to receive treatment. Such exposure conditions have probabilities determined by the randomization design, sometimes very small under independent user assignment. The original graph-cluster work derives weighting methods under correctly specified exposure assumptions; it does not claim that every unobserved network pathway disappears when a graph is clustered.

Assigning households, teams, or graph communities together can place strongly interacting units in the same arm. This may make observed exposure more similar to a full rollout within each group. Cross-cluster edges can still transmit spillovers, and very large connected components can make perfect separation impractical. Unequal cluster sizes also complicate the choice between an average person effect and an average cluster effect, so state the weighting rule before analyzing results.

Correlated outcomes inside a cluster reduce information relative to the same number of independent people. An elementary equal-size exchangeable model gives a design-effect expression for a population mean. It illustrates why counting members as independent understates uncertainty, but it is not a universal variance formula for every cluster-randomized treatment contrast. Inference must respect the actual number of randomized clusters, allocation constraints, outcome dependence, and any matching or stratification used.

A social feature may motivate graph clusters, while a shared marketplace may need geographic, time-block, or two-sided designs with explicit carryover assumptions. No design can be selected solely from a convenient traffic split. Write down whether the intended conclusion concerns direct effects at partial adoption, spillovers onto untreated units, or an all-treatment equilibrium. Those quantities can legitimately differ in magnitude and sign, even with impeccable assignment and logging.

Test the network and exposure assumptions through diagnostics and sensitivity analysis. Measure cross-cluster connections, cluster sizes, and treatment saturation rather than assuming the grouping isolates every interaction. Avoid claiming that a small number of large clusters creates a large independent sample just because the user count is high. When interference remains substantial, report the estimand the design actually supports and the limits on extrapolating it to full deployment.