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Social influence is a strong determinant of food consumption, which in turn influences health. Although consistent observations have been made on the role of social factors in driving similarities in food consumption, much less is known about the precise governing mechanisms. We study social influence on food choice through carefully designed causal analyses, leveraging the sequential nature of shop queues on a major university campus. In particular, we consider a large number of adjacent purchases where a focal user immediately follows another user ("partner") in the checkout queue and both make a purchase. Identifying the partner's impact on the focal user, we find strong evidence of a specific behavioral mechanism for how dietary similarities between individuals arise: purchasing mimicry, a phenomenon where the focal user copies the partner's purchases. For instance, across food additions purchased during lunchtime together with a meal, we find that the focal user is significantly more likely to purchase the food item when the partner buys the item, v.s. when the partner does not, increasing the purchasing probability by 14% in absolute terms, or by 83% in relative terms. The effect is observed across all food types, but largest for condiments, and smallest for soft drinks. We find that no such effect is observed when a focal user is compared to a random (rather than directly preceding) partner. Furthermore, purchasing mimicry is present across age, gender, and status subpopulations, but strongest for students and the youngest persons. Finally, we find a dose-response relationship whereby mimicry decreases as proximity in the purchasing queue decreases. The results of this study elucidate the behavioral mechanism of purchasing mimicry and have further implications for understanding and improving dietary behaviors on campus.