When citizens hold multiple values relevant to their policy opinions, they might experience value conflict, value reconciliation or make a value trade-off. Yet, it is unclear which individuals are able to manage their multiple values in these ways. We posit a sophistication-interaction theory of value pluralism where the most politically sophisticated individuals are able to reconcile the existence of multiple values, thus increasing the stability of their policy opinions. We test this hypothesis using a series of heteroskedastic graded item response theory models of public opinion toward policies related to climate change. We find that people structure their policy preferences toward climate change policies in values toward the environment and the economy, but only the most sophisticated citizens are able to reconcile the potential conflict between these values.