Economic decisions are noisy due to errors and cognitive imprecision. Often, they
are also systematically biased by heuristics or behavioral rules of thumb, creating behavioral anomalies which challenge established economic theories. The interaction of noise and bias, however, has been mostly neglected, and recent work suggests that received behavioral anomalies might be just due to regularities in the noise. This contribution formalizes the idea that decision makers might follow a mixture of rules of behavior combining cognitively-
imprecise value maximization and computationally simpler shortcuts. The model delivers new testable predictions which we validate in two experiments, focusing on biases in probability judgments and the certainty effect in lottery choice, respectively. Our findings suggest that neither cognitive imprecision nor multiplicity of behavioral rules suffice to explain received patterns in economic decision making. However, jointly modeling (cognitive) noise in value maximization and biases arising from simpler, cognitive shortcuts delivers a unified framework which can parsimoniously explain deviations from normative prescriptions across domains.