When 2 + 2 should be 5: The summation fallacy in time prediction

Abstract

Predictions of time (e.g., work hours) are often based on the aggregation of estimates of elements (e.g., activities and subtasks). The only types of estimates that can be safely aggregated by summation are those reflecting predicted average outcomes (expected values). The sums of other types of estimates, such as bounds of confidence intervals or estimates of the mode, do not have the same interpretation as their components (e.g., the sum of the 90% upper bounds is not the appropriate 90% upper bound of the sum). The present research shows that this can be a potential source of bias in predictions of time. In Studies 1 and 2, professionals with experience in estimation provided total estimates of time that were inconsistent with their estimates of individual tasks. Study 3 shows that this inconsistency can be attributed to improper aggregation of time estimates and demonstrates how this can produce both overestimation and underestimation—and also confidence intervals that are far too wide. Study 4 suggests that the results may reflect a more general fallacy in the aggregation of probabilistic quantities. The inconsistencies and biases appear to be largely driven by a tendency to naïvely sum (2 + 2 = 4) probabilistic (stochastic) values. This summation fallacy may be consequential in contexts where informal estimation methods (expert judgment) are used.