Choosing the number of conditioning events in judgemental forecasting

One method for judgemental forecasting involves use of decomposition; i.e. estimating the conditional means of an unknown quantity of interest for a finite number of conditioning events, and weighting these estimated conditional means by the estimated marginal probabilities of the corresponding conditioning events. In this paper we investigate how the level of decomposition (i.e. the number of conditioning events) affects the precision of the resulting forecast. Previous analyses assume that key parameters (the informativeness of the decomposition, and the precision of estimation for the conditional means and the marginal probabilities) remain constant as the number of conditioning events increases. However, this assumption is unreasonable, and for some parameters mathematically impossible; the values of these parameters are likely to change significantly even for small numbers of conditioning events. Therefore, we introduce models for how these key parameters may depend on the level of decomposition. We then investigate the implications of these models for the precision of the resulting forecast. In particular, we identify cases in which decomposition is never desirable, always desirable, or desirable only near the optimal number of conditioning events. This second case was not observed previously. We focus throughout on the situation likely to be of greatest interest in practice; namely, the behaviour of decomposition for relatively small numbers of conditioning events.