The effectiveness of imperfect weighting in advice taking

We investigate decision-making in the Judge-Advisor-System where one person, the ``judge'', wants to estimate the number of a certain entity and is given advice by another person. The question is how to combine the judge's initial estimate and that of the advisor in order to get the optimal expected outcome. A previous approach compared two frequently applied strategies, taking the average or choosing the better estimate. In most situations, averaging produced the better estimates. However, this approach neglected a third strategy that judges frequently use, namely a weighted mean of the judges' initial estimate and the advice. We compare the performance of averaging and choosing to weighting in a theoretical analysis. If the judge can, without error, detect ability differences between judge and advisor, a straight-forward calculation shows that weighting outperforms both of these strategies. More interestingly, after introducing errors in the perception of the ability differences, we show that such imperfect weighting may or may not be the optimal strategy. The relative performance of imperfect weighting compared to averaging or choosing depends on the size of the actual ability differences as well as the magnitude of the error. However, for a sizeable range of ability differences and errors, weighting is preferable to averaging and more so to choosing. Our analysis expands previous research by showing that weighting, even when imperfect, is an appropriate advice taking strategy and under which circumstances judges benefit most from applying it