Criticism of the value-free ideal has motivated attempts to formulate a criterion for the legitimacy of non-epistemic value influence in science. I argue that this search aims to protect two main components of legitimacy, scientific integrity and justice. While integrity is primary, justice remains important, especially in setting scientific goals. One of the main proposals for setting legitimate goals is to rely on democratic endorsement (Intemann 2015). I critically assess four interpretations of this criterion, finding that all are problematic. I then propose and evaluate three alternative models that seek to better balance respect for the public with scientific expertise