| Summary: | 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.
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