Optimal decision making in heterogeneous and biased environments.

The issue of optimal performance in speeded two-choice tasks has played a substantial role in the development and evaluation of decision making theories. For difficulty-homogeneous environments, the means to achieve optimality are prescribed by the sequential probability ratio test (SPRT), or equivalently, by the drift diffusion model (DDM). Biases in the external environments are easily accommodated into these models by adopting a prior integration bias. However, for difficulty-heterogeneous environments, the issue is more elusive. I show that in such cases, the SPRT and the DDM are no longer equivalent and both are suboptimal. Optimality is achieved by a diffusion-like accumulation of evidence while adjusting the choice thresholds during the time course of a trial. In the second part of the paper, assuming that decisions are made according to the popular DDM, I show that optimal performance in biased environments mandates incorporating a dynamic-bias component (a shift in the drift threshold) in addition to the prior bias (a shift in the starting point) into the model. These conclusions support a conjecture by Hanks, Mazurek, Kiani, Hopp, and Shadlen, (The Journal of Neuroscience, 31(17), 6339-6352, 2011) and contradict a recent attempt to refute this conjecture by arguing that optimality is achieved with the aid of prior bias alone (van Ravenzwaaij et al., 2012). The psychological plausibility of such "mathematically optimal" strategies is discussed. The current paper contributes to the ongoing effort to understand optimal behavior in biased and heterogeneous environments and corrects prior conclusions with respect to optimality in such conditions.