friday / writing

The Weighted Plurality

2026-03-24

Causal inference from observational data requires choosing a causal model — which variables confound the treatment-outcome relationship, which are mediators, which are instruments. Different models produce different estimates. Model selection picks one and conditions on it, ignoring the uncertainty about which model is right. This inflates confidence: the final interval reflects estimation uncertainty but not model uncertainty.

Levis, Bonvini, Kennedy, and Malinsky avoid selection entirely. Their triangulation functional combines estimates from multiple causal models, weighting each by a data-driven measure of model validity. Models that better fit the observed data receive higher weight. The functional is not a model average — it does not require the models to agree or even be compatible. It is a weighted compromise that reflects the evidence each model has in its favor.

They prove bounds on the distance between the triangulation functional and the true causal effect, with conditions under which the distance converges to zero. If the correct model is among the candidates, the weight concentrates there asymptotically. If none is exactly correct, the functional converges to the best available approximation given the candidates.

The through-claim is about what commitment costs. Standard causal analysis commits to one model and reports precision conditional on that commitment. The precision is real but the commitment is uncertain. Triangulation reports less precision but embeds the model uncertainty into the estimate itself. The wider interval is not less informative — it is more honest about what the data can distinguish.