Models of multi-attribute decision making vary on whether all (or only part of the) information available is being processed. The models also vary on whether the preference formation is based on within-alternative or within-attribute processing. Here we carry out an experimental study in which we rely on lottery-options, and we vary the task complexity, from simple (2 options with 2 attributes each) to complex (4 options with 4 attributes each). In addition we monitor eye-gaze during the decision formation, in order to directly observe the way in which participants attend to decision-relevant information. We then compare a large set of models, of different levels of complexity, by considering the dynamic interactions between uncertainty, attention and pairwise comparisons between attribute values, in their ability to account for the choice data. We find that two models outperform all others. The first is the two-layer leaky-competing accumulator based on prospect theory (LCA-PT), which predicts human choices on the simpler task better than any other model. We call the second model, which is introduced in this study, the Attention and Memory-guided PROMETHEE (AMP) model. It is modified from a previous model (PROMETHEE) developed in management science, designed to deal with highly complex decision problems. Our results show that this model performs best in the complex lottery task. Both of these models use the sequence of observed eye movements for each participant to capture the allocation of attention to specific options and attributes during the decision process, but make different assumptions about the effect of attention on decision making. Our results suggest that, when faced with complex choice problems, people form their preference based on attention-guided pairwise, within-attribute, value-comparisons.