Value preferences have long been central to research in political science and psychology. Despite their well‐established theoretical importance, however, their measurement is still an open question. Early research on values relied heavily on ranking instruments for data collection, but more recent work calls this measurement technique into question. Specifically, it is argued that traditional ranking instruments are (1) too long, (2) too complex, and (3) may force respondents to make ad hoc differentiations between values of similar importance, behind which there is no systematic preference. As a result, the reliability of the measure is called into question, and measurement error remains a concern. In this article, we discuss the method of triads—a technique used to gather rankings data that affords the researcher the opportunity to assess the extent to which random error affects preference rankings. Using the method of triads to collect preference data on five values central to American political culture, we find that Americans' value preferences are clearly structured and driven by systematic preferences, even when psychological theory suggests they may not. We also compare the predictive validity of the data collected with the method of triads against that of the data collected with traditional importance ratings. We show that models of ideology, party identification, presidential approval, and vote‐choice fit to “triads” data explain more variance than models fit to ratings data.