Averaging distributions or averaging quantiles

Within the Classical Model, the approach of combining experts’ assessments is by averaging distributions. That is, it is the experts’ distributions that are combined.

Note that by averaging, we generally refer to weighed averaging and not necessarily having equal weights. The Classical Model promotes performance-based weights. We have seen that equal weights are used in the same approach of combining experts’ distributions.

You might wonder though, isn’t averaging distributions the same as averaging quantiles?

Well, averaging quantiles means that we average only the quantiles, with performance-based or equal weights.

We will discuss this subject in more detail next.

We will explore, using the Dutch eating habits example, the differences between averaging distributions and averaging quantiles.

Recall the questions of interest

6) What percentage of Dutch adults will eat fruit on a daily basis by 2025?
7) How many liters of milk will be consumed on a yearly basis by the average Dutch adult in 2025?

Note that, as beforehand, the data are purely fictional.

Question	Realization	Expert 1 5% 50% 95%	Expert 2 5% 50% 95%	Expert 3 5% 50% 95%
6		61  68  75	45  55  70	43  52  63
7		67  71  80	50  61  68	55   65  73

Consider first Question 6. From the solution of the performance-base weights, the best estimate is 57 (the median).

Also, recall that the performance-based weights are 0.009 (for Expert 1), 0.417 (for Expert 2) and 0.574 (for Expert 3).