Kahneman and Tversky's Cumulative Prospect Theory (CPT) has proved to be better suited for representing risk preferences than von Neumann and Morgenstern's Expected Utility Theory (EUT). We argue that neglecting this may explain to some extent why farmers do not contract crop insurance as much as they are expected to. We model the decision to contract an individual yield crop insurance for a sample of 186 French farmers. We show that 21% of the farmers who would be expected to contract assuming that their preferences are EUT, would actually not do so if their true preferences were in fact CPT.