How do we choose when confronted with many alternatives? There is surprisingly little decision modelling work with large choice sets, despite their prevalence in everyday life. Even further, there is an apparent disconnect between research in small choice sets, supporting a process of gaze-driven evidence accumulation, and research in larger choice sets, arguing for models of optimal choice, satisficing, and hybrids of the two. Here, we bridge this divide by developing and comparing different versions of these models in a many-alternative value-based choice experiment with 9, 16, 25, or 36 alternatives. We find that human choices are best explained by models incorporating an active effect of gaze on subjective value. A gaze-driven, probabilistic version of satisficing generally provides slightly better fits to choices and response times, while the gaze-driven evidence accumulation and comparison model provides the best overall account of the data when also considering the empirical relation between gaze allocation and choice
