In this paper, we argue that on many important public policy questions, people may be unsure of their preferences because their underlying principles or values are in conflict. We build a simple model of conflicting core beliefs, building on the work of Heider (1958). Using abortion policies as our test case, we develop a test for our theory using heteroskedastic probit, using data taken from the 1988 General Social Survey. The heteroskedastic probit results confirm our model, and in the last section of the paper, we trace the implications of this model for some of the larger questions in public opinion research