@article {28155,
title = {When 2 + 2 should be 5: The summation fallacy in time prediction},
journal = {Journal of Behavioral Decision Making},
year = {2022},
publisher = {Wiley},
abstract = {Predictions of time (e.g., work hours) are often based on the aggregation of estimates of elements (e.g., activities, 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). This can be a potential source of bias in predictions of time, as shown in Studies 1 and 2, where 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 over- and underestimation{\textemdash}and also time prediction intervals that are far too wide. Study 4 suggests that the results may reflect a more general fallacy in the aggregation of probabilistic quantities. Our observations are consistent with that inconsistencies and biases are driven by a tendency towards applying a na{\"\i}ve summation (2+2=4) of probabilistic (stochastic) values, in situations where this is not appropriate. This summation fallacy may be in particular consequential in a context where informal estimation methods (expert-judgment based estimation) are used.},
author = {Halkjelsvik, Torleif and J{\o}rgensen, Magne}
}