Bias in aggregations of subjective probability and utility

Subjective estimates of probability or utility are prone to two kinds of error: random and systematic (bias). The usual approach to reducing random error is averaging. How to reduce systematic error is not clear. This paper deals with the question of bias propagation when the estimates that are averaged are bias prone. Both simple and weighted averages are examined. The idea of using averaging as a bias reduction technique is explored. When the weights used in the averaging process are themselves biased, the random error in the average is also affected, possibly adversely. A balance has to be struck between bias reduction requirements and random error reduction requirements.