User-chosen passwords remain essential to online security, and yet people continue to choose weak, insecure passwords. In this work, we investigate whether prospect theory, a behavioral model of how people evaluate risk, can provide insights into how users choose passwords and whether it can motivate new designs for password selection mechanisms that will nudge users to select stronger passwords. We ran a user study with 762 participants, and we found that an intervention guided by prospect theory -- which leverages the reference-dependence effect by framing selecting weak passwords as a loss relative to choosing a stronger password -- causes approximately 25% of users to improve the strength of their password (significantly more than alternative interventions) and reduced the final number of weak passwords by approximately 25%. We also evaluate the relation between user behavior and users' mental models of hacking and password attacks. These results provide guidance for designing and implementing account registration mechanisms that will significantly improve the strength of user-selected passwords, thereby leveraging insights from prospect theory to improve the security of systems that use password-based authentication.