The per-diem is up to $75 depending on your area, which can buy a pretty nice lunch. Pharma studies are just some of the studies we have that show a real-world scenario. Politics would be harder to study, as bills are harder to quantify than prescriptions. This study on sales (for instance, and note this isn't my field so I don't know anything about this journal) shows that a gift worth about $7.70 has a large effect, depending on timing: "We find that small gifts matter. On average, sales representatives generate more than twice as much revenue when they distribute a small gift at the onset of their negotiations. However, we also find that small gifts tend to be counterproductive when purchasing and sales agents meet for the first time, suggesting that the nature of the business relationship crucially affects the profitability of gifts."

This review article in the Journal of Bioethics comments that "[t]he presumption is that large gifts, such as extravagant vacations, have the capacity to influence behavior, but gifts of de minimis monetary value, such as donuts and penlights, do not. Yet, while it might seem both logical and practicable to distinguish small gifts from larger, seemingly more problematic gifts, a large body of evidence from the social sciences shows that behavior can be influenced by gifts of negligible value."

Overall, there are many studies showing that small gifts influence behavior, especially in certain contexts. I wouldn't be so sure that a turkey sandwich wouldn't influence my behavior. I am not aware of many of my own biases, and most people are not.