On optimality conditions for the likelihood difference

Nelson J.D., Szalay C., Meder B., Crupi V., Gigerenzer G., and Tentori K., On optimality conditions for the likelihood difference heuristic, 46th Annual Meeting of the Society of Mathematical Psychology (Potsdam, August 5).


Abstract. Consider the task of selecting a medical test to determine whether a patient has a disease. Normatively, this requires considering the base rate of the disease, the true and false positive rate for each test, and the payoffs and costs for correct and incorrect diagnoses. Due to multiple sources of uncertainty, however, these quantities are seldom precisely known. Are there shortcuts or heuristic strategies that could approximate calculation of tests’ objective value, if the precise payoffs are unknown? Can pure information strategies (which disregard the objective utilities) sometimes identify the objectively most useful test? We study the performance of the likelihood difference heuristic for test selection. This extremely simple heuristic selects the test with the highest likelihood difference, or difference between true and false positive rate, ignoring all other information. We prove that despite its simplicity, the likelihood difference heuristic identifies the objectively most useful test under certain conditions. This holds if the base rate of the disease equals the threshold probability above which it is best to act as if the patient has the disease. In other circumstances, the likelihood difference heuristic is not in general optimal but can perform remarkably well. In further simulation studies we explore the circumstances under which other pure information strategies, such as information gain and probability gain, also tend to identify the objectively more useful test.


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