Being of "two minds": Assessing vacillating and simultaneous ambivalence with the density matrix

Ambivalence is a common experience that permeates a broad range of research. Unfortunately, quantifying ambivalence has proven a daunting task, with researchers limited to studying vacillating ambivalence, VA (i.e., temporal oscillations between favor/disfavor evaluations of an attitude object). Here, we demonstrate the use of the density matrix to measure both VA and what we term "simultaneous ambivalence" (SA): ambivalence that manifests itself as "in the moment" concurrent favor/disfavor evaluations. In a methodological study we gave participants the option of either single-responding or double-responding to questionnaire items regarding a controversial topic (i.e., affirmative action). Since standard statistical procedures provide no means for analyzing double responses, such data are routinely treated as "bad." As demonstrated here, the density matrix provides an unambiguous and relatively easy means of accounting for double responses, which is our indicator of SA. Our data are well explained by a mixture model, with participants divided into two nearly equal groups of SA and non-SA participants, and provide evidence that the general phenomenon of SA transcends differences of gender and ethnicity. Further, the density matrix data are consistent with viewing SA and VA as distinct ambivalence constructs.