Is attentional discounting in value-based decision making magnitude sensitive?

Choices in value-based decision making are affected by the magnitude of the alternatives (i.e. the summed values of the options). Magnitude sensitivity has been instrumental in discriminating between computational models of choice. Smith and Krajbich [(2019a). Gaze amplifies value in decision making. Psychological Science, 30(1), 116–128. https://doi.org/10.1177/0956797618810521] have shown that the attentional drift-diffusion model (aDDM) can account for magnitude sensitivity. This is because the discount parameter on the value of the nonfixated alternative ensures faster choices for high-magnitude alternatives, even in the case of high-magnitude equal alternatives compared to low-magnitude equal alternatives. Their result highlights the importance of visual fixations as a mechanism for magnitude sensitivity. This rationale relies on the untested assumption that the discount parameter is constant across magnitude levels. However, the discount parameter could vary as a function of the magnitude of the alternatives in unpredicted ways; this would suggest that the ability of the aDDM to account for magnitude sensitivity has been misinterpreted by previous research. Here, we reanalyse previous datasets and we directly test whether attentional discounting scales with the magnitude of the alternatives. Our analyses show that attentional discounting does not vary with magnitude. This result further strengthens the aDDM and the role that visual fixations could play as an explanation of magnitude sensitivity.