Kuhn argued that scientific theory choice is, in some sense, a rational matter, but one that is not fully determined by shared objective scientific virtues like accuracy, simplicity, and scope. Okasha imports Arrow’s impossibility theorem into the context of theory choice to show that rather than not fully determining theory choice, these virtues cannot determine it at all. If Okasha is right, then there is no function (satisfying certain desirable conditions) from ‘preference’ rankings supplied by scientific virtues over competing theories (or models, or hypotheses) to a single all-things-considered ranking. This threatens the rationality of science. In this paper we show that if Kuhn’s claims about the role that subjective elements play i...