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.