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It has been difficult to quantify the postulated role of social influence on nutrition using traditional methods such as surveys, due to the typically small scale and short duration of studies. To overcome these limitations, we leverage a novel source of data: logs of 38 million food purchases made over an 8-year period on the Ecole Polytechnique Federale de Lausanne (EPFL) university campus, linked to anonymized individuals via the smartcards used to make on-campus purchases. In a longitudinal observational study, we ask: How is a person's food choice affected by eating with someone else whose own food choice is healthy vs. unhealthy? To estimate causal effects from the passively observed log data, we control confounds in a matched quasi-experimental design: we identify focal users who at first do not have any regular eating partners but then start eating with a fixed partner regularly, and we match focal users into comparison pairs such that paired users are nearly identical with respect to covariates measured before acquiring the partner, where the two focal users' new eating partners diverge in the healthiness of their respective food choice. A difference-in-differences analysis of the paired data yields clear evidence of social influence: focal users acquiring a healthy-eating partner change their habits significantly more toward healthy foods than focal users acquiring an unhealthy-eating partner. We further identify foods whose purchase frequency is impacted significantly by the eating partner's healthiness of food choice. 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