A central puzzle for theories of choice is that people's preferences between options can be reversed by the presence of decoy options (that are not chosen) or by the presence of other irrelevant options added to the choice set. Three types of reversal effect reported in the decision-making literature, the attraction, compromise, and similarity effects, have been explained by a number of theoretical proposals. Yet a major theoretical challenge is capturing all 3 effects simultaneously. We review the range of mechanisms that have been proposed to account for decoy effects and analyze in detail 2 computational models, decision field theory (Roe, Busemeyer, & Townsend, 2001) and leaky competing accumulators (Usher & McClelland, 2004), that aim to combine several such mechanisms into an integrated account. By simulating the models, we examine differences in the ways the decoy effects are predicted. We argue that the LCA framework, which follows on Tversky's relational evaluation with loss aversion (Tversky & Kahneman, 1991), provides a more robust account, suggesting that common mechanisms are involved in both high-level decision making and perceptual choice, for which LCA was originally developed. (Contains 12 figures, 3 tables and 12 footnotes.)