committees

[jim@hydra.maths.unsw.EDU.AU]

 A small caveat about when it is good to average different estimates
of an unknown quantity:
 If you have a fairly accurate and a fairly inaccurate way of estimating
something, it is obviously not good to take their simple average (that
is, half of one plus half of the other). The correct weighting of the
estimates is in inverse proportion to their variances (that is, keep
closer to the more accurate one). (At least, that is the correct
weighting if the estimates are independent: if they are correlated,
it is more complicated, but not much more). Proofs are easy, and included
in the ref below:

R. Templeton & J. Franklin, `Adaptive information and animal behaviour',
Evolutionary Theory 10 (Dec 1992): 145-155.

(Note that this concerns inaccurate estimates, not biased ones, as some
previous posters have been considering).
Of course, averaging and correlations are very easy calculations for
neural nets.
Some similar ideas have been studied in connection with "sensor fusion"
for robots:

Journal of Robotic Systems 7 (3): (1990), Special issue on multisensor
integration and fusion for intelligent robots, ed. R.C. Luo.

Interesting work on how real committees combine information is reviewed in:

D. Bunn & G. Wright, `Interaction of judgemental and statistical
forecasting methods: issues and analysis', Management Science 37 (1991): 501.


James Franklin
School of Mathematics
University of New South Wales