Building on research in social psychology, we propose a model of survey response in which individuals’ policy preferences are characterized by two parameters: their attitude on an issue, and their attitude strength. Strong attitudes are behaviorally relevant and stable over time while weak attitudes are easily manipulated with only limited behavioral consequences. We assume that the psychological cost to individuals of not reporting their attitude depends positively on the issue strength. We derive predictions about how respondents will answer survey questions under two different survey techniques, Likert scales and Quadratic Voting (QV). The QV method gives respondents a fixed budget to “buy” votes in favor or against a set of issues. Because the price for each vote is quadratic, it becomes increasingly costly to acquire additional votes to express support or opposition to the same issue. We formally show that QV better measures preference strength. This, we argue, is especially true in a polarized two-party system where individuals with weak preferences are more likely to mechanically default to the party policy position. We test these predictions using a survey experiment. QV, as a powerful compromise between a stated and a revealed preference approach, has the potential to affect the way preferences are conceptualized and measured across the social sciences.