Moser et al. provide a formalization of heresthetics, the "art of political strategy", in collective choice settings. In doing so they introduce the heresthetically stable set as the set of outcomes least susceptible to manipulation of issue dimension. In this note we correct a small error in the original paper, and close several open questions asked there in. We examine the heresthetically stable set as a tournament solution, establishing some basic properties it possesses, and many it does not posses. In addition, we relate the heresthetically stable set to other tournament solutions, notably the weak uncovered and refinements thereof. We find lack of vulnerability to heresthetic manipulation is contrary to many desirable properties of choice functions, notably majoritarian support.