"Bayesian anchoring" and the fourfold pattern of risk attitudes

Experiments on decision making under uncertainty are known to display a classical pattern of risk aversion and risk seeking referred to as "fourfold pattern" (or "reflection effect"), but recent experiments varying the speed and order of mental processing have brought to light a more nuanced phenomenology. We model experiments though a Bayesian formalization of the anchor-and-adjust heuristic observed in empirical studies on cognitive bias. Using only elementary assumptions on constrained information processing, we are able to infer three separate effects found in recent observations: (1) the reported enhancement of the fourfold pattern for quicker decision processes; (2) the observed decrease of fluctuations for slower decision-making trials; (3) the reported dependence of the outcome on the order in which options are processed. The application of Bayesian modeling offers a solution to recent empirical riddles by bridging two heretofore separate domains of experimental inquiry on bounded rationality.