Additivity of information value in two-act linear loss decisions with normal priors

Information about two uncertainties is superadditive in value if the value of information for resolving both uncertainties together exceeds the sum of the value of information for resolving each uncertainty alone. For the two-act linear loss decision problem with normal priors, conditions are derived for which the expected value of perfect information about two independent risks is superadditive. An approximate condition is also presented. The level of additivity of information value has implications for how risk-management resources should be allocated to acquisition of information. Several applications show how a variety of decision problems can reduce to the basic problem, and how the general results obtained here can be translated simply to prescriptions for specific situations.