Is there a name for the psychological mechanism according to which a person is more likely to act when provided with proof of information they are already convinced about? Information which is often also trivial: e.g., smoking causes cancer. In fact, some studies find that graphical warning labels in cigarette packages affect implicit smoking attitudes (especially among the new smokers). Although comparatively smaller, text labels (compared to no labels) are also shown to have a similar effect.
Probably best considered as an example of the availability heuristic: people tend to make decisions based on information that is most readily accessible/recent.
In plainer terms, the label is just a reminder.