# A subjective estimate of a discrete quantity

An expert will sometimes be called upon to provide an estimate of the probability of occurrence of a discrete event. This is a difficult task for the expert. It requires that s/he has some feel for probabilities that is both difficult to acquire and to calibrate. If the discrete event in question has occurred in the past, the analyst can assist by presenting the data and a Beta distribution of the probabilities possible from that data (see here). The expert can then give her opinion based on the amount of information available.

However, it is quite usual that past information has no relevance to the problem at hand. For example, the political analyst cannot look to past general election results for guidance in estimating whether The Labour Party will win the next general election. S/he will have to rely on gut feel based on his/her understanding of the current political climate. In effect, s/he will be asked to pick a probability out of the air - a daunting task, complicated by the difficult of having to visualise the difference between, say, 60% and 70%. A possible way to avoid this problem is to offer the expert a list of probability phrases, for example:

• almost certain

• very likely

• highly likely

• reasonably likely

• fairly likely

• even chance

• fairly unlikely

• reasonably unlikely

• highly unlikely

• very unlikely

• almost impossible

The phrases are ranked in order and the expert told of this ranking. S/he is then asked to select a phrase that best fits his/her understanding of the probability of each event that has to be considered. At the end of the session, s/he is also asked to match as many of the phrases as possible to visual representations of probability. For example, matching a phrase to the probability of picking out a black ball at random from the trays of the figure on the right. Since we know the percentage of black balls in each tray, we can associate a probability with each phrase and thus with each estimated event.

For example, matching a phrase to the probability of picking out a black square at random from the trays of the figure on the right. Since we know the percentage of black squares in each tray (A = 1%, B = 5%, C = 10%, D = 20%, E = 30%, F = 40%, G = 50%, H = 60%, I = 70%, J = 80%, K = 90%, L = 95%, M = 99%), we can associate a probability with each phrase and thus with each estimated event.