Despite widespread interest in neural mechanisms of decision-making, most investigations focus on decisions between just two options. Here we adapt a biophysically plausible model of decision-making to predict how a key decision variable, the value difference signal-encoding how much better one choice is than another-changes with the value of a third, but unavailable, alternative. The model predicts a surprising failure of optimal decision-making: greater difficulty choosing between two options in the presence of a third very poor, as opposed to very good, alternative. Both investigation of human decision-making and functional magnetic resonance imaging-based measurements of value difference signals in ventromedial prefrontal cortex (vmPFC) bore out this prediction. The vmPFC signal decreased in the presence of low-value third alternatives, and vmPFC effect sizes predicted individual variation in suboptimal decision-making in the presence of multiple alternatives. The effect contrasts with that of divisive normalization in parietal cortex.