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Researchers introduce the Attentional Interference Model to study how external cues — like ads, displays, or recommendations — change which options people consider before choosing. The paper asks what can be learned about attention when analysts observe only choices and how often different cues are shown, not direct measures of attention. This matters because marketers and policymakers often want to know whether a stimulus actually reached a person’s consideration set or simply appeared without effect.
The model builds on two opposing psychological forces. Proactive interference means earlier information can block new stimuli from entering a person’s consideration. Retroactive interference means a new stimulus can push out options the person would otherwise have thought about. The authors capture these effects with two parameters. The permeation parameter β is the probability that an external stimulus successfully enters the consideration set. Conditional on entry, the displacement parameter α is the probability that the stimulus displaces internally generated considerations. After this two-stage process, the decision maker chooses their most preferred available option.
Using this setup, the paper asks which values of α and β are consistent with observed choice data and observed frequencies of external stimuli. In a general setting the authors show that only an upper bound on permeation (β) can be recovered from choice and stimulus data alone. They study three benchmark cases — Perfect Displacement (α = 1), Perfect Retention (α = 0), and Unified Attention Interference (α = β) — and show that these cases order the bounds in a predictable way. The upper bound tells analysts the maximal extent to which stimuli could have entered consideration; for example, a frequently displayed but rarely chosen promoted option implies that it must have entered consideration only rarely.
The authors also study what extra assumptions buy you. By imposing a nonparametric monotonicity condition on the unobserved internal attention rule (an assumption used in earlier work by Cattaneo and colleagues), they obtain a lower bound on permeation as well as a tighter upper bound. The key idea is that certain violations of regularity in choice behavior — patterns that would not occur under monotonic internal attention alone — must be due to external stimuli. Those violations let the analyst infer a minimal level of permeation that the data require.
To illustrate their results, the paper reports simulations. The simulations generate choice data from attention processes that satisfy the monotonicity assumption and then show how the added restriction narrows the revealed range for β. The authors find that the lower bounds produced under monotonicity track the true permeation values in their simulated examples. They also report that the model can reject many incorrect preference orderings and recover a substantial part of the underlying preference relation, even with limited data.
Important caveats remain. Attention is not directly observed and the main theoretical result is one of partial identification: without extra assumptions the model typically yields only an upper bound on how often stimuli enter consideration. The lower bound depends on the monotonicity assumption, which may or may not hold in every setting. The paper’s conclusions rest on the specific two-stage modeling choices and on simulated illustrations; empirical application will require careful matching of assumptions to the setting. In short, the model clarifies what can and cannot be learned from choices and observed exposure, but it does not fully solve the hard problem of measuring attention from observational data.