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Several studies propose that exemplar retrieval contributes to multi-attribute decisions. The authors have proposed a process theory enabling a priori predictions of what cognitive representations people use as input to their judgment process (Sigma, for “summation”; P. Juslin, L. Karlsson, & H. Olsson, 2008). According to Sigma, exemplar retrieval is a back-up system when the task does not allow for additive and linear abstraction and integration of cue-criterion knowledge (e.g., when the task is non-additive). An important question is to what extent such shifts occur spontaneously as part of automatic procedures, such as error-minimization with the Delta rule, or if they are controlled strategy shifts contingent on the ability to identify a sufficiently successful judgment strategy. In this article data are reviewed that demonstrate a shift between exemplar memory and cue abstraction, as well as data where the expected shift does not occur. In contrast to a common assumption of previous models, these results suggest a controlled and contingent strategy shift.