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Recent research has investigated the process of integrating perceptual evidence toward a decision, converging on a number of sequential sampling choice models, such as variants of race and diffusion models and the non-linear leaky competing accumulator (LCA) model. Here we study extensions of these models to multi-alternative choice, considering how well they can account for data from a psychophysical experiment in which the evidence supporting each of the alternatives changes dynamically during the trial, in a way that creates temporal correlations. We find that participants exhibit a tendency to choose an alternative whose evidence profile is temporally anti-correlated with (or dissimilar from) that of other alternatives. This advantage of the anti-correlated alternative is well accounted for in the LCA, and provides constraints that challenge several other models of multi-alternative choice.