We propose a model of moral policy opinion formation that integrates both ideology and cognitive ability. The link from people's ideology to their opinions is assumed to go via a semantic processing of moral arguments that relies on the individual's cognitive ability. An implication of this model is that the relative quality of arguments that justify supporting vs. opposing a moral policy—the policy's “argument advantage”—is key to how opinions will be distributed in the population and develop over time. To test this implication, we combine polling data with measures of the argument advantage for 35 moral policies. Consistent with the opinion formation model, the argument advantage of a moral policy accounts for how public opinion moves over time, and how support for the policy ideologies varies across different ideological groups and levels of cognitive ability, including a strong interaction between ideology and cognitive ability.