178 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Past selection decision could be analysed according to contract value, expected profit, number and type of competing companies, whether or not a panel test was used, etc., and the recommended selection procedure based upon this analysis. Suppose, for the sake of simplicity, it appears reasonable to assume the likelihood of winning a contract is independent of the number of firms competing, and also the value of the contract. (If these assumptions are not valid, the same subsequent analysis may be performed but considera- tion restricted to, and based upon data from contracts within a value range, say oe8 000-oe10 000, and with a specific number of competing firms.) We have, therefore, information such as Number of contracts where the number of successful and unsuccessful tenders selected on the basis of a panel test (Xs) and a specific welfare function W are ns and ms etc. Based upon this information, the probabilities of successful tenders using and not using a panel test are respectively P(s Ixs)- ns p(slx)- ns . ns + go ns + ms On the basis of these probabilities the same cost analysis as before may be performed. Non-panel decision Under policy Xs, the selection of the tender sample is made within the company without recourse to a panel test. Presumably the decision or selection criterion is some function of the considered opinion of perhaps a (•) the chief perfumer a © the marketing manager and a © the produc- tion manager. Each of these individuals has his own opinion as to the most likely candidate to submit as a tender and this opinion is based on his or her own subjective understanding and knowledge of perhaps current trends and fashions in perfumery, or even upon some subconscious consideration. If the individual

DECISION ANALYSIS 17 9 preferences of these experts have been recorded along with the actual group choice Xs, --or was to be recorded over a period of time, information of the following nature would be available. Number of occasions Number of occasions a(O and X• agreed a(i) and X• disagreed Result of tender a(t) S S x unknown X• 7 18 0 a(x) 5 6 14 a(a) 6 7 11 a (a) 4 1 20 This table indicates the number of times each individual agreed with a selection which was subsequently found to be either successful or unsuccess- ful, or to have disagreed with a selection decision which was unsuccessful. Accordingly it is possible to associate a prediction measure to each of the individuals and so identify, on historic grounds, the 'best' predictor. One possible such measure is to give, say, one mark to each correct prediction, 0 to a known incorrect prediction and perhaps 1In (where n is the number of competing firms) in the case of an unknown result. Thus, if n -- 4 we have for a preference measure Xa=7 a (O = 8.1/2 a % = 8.3/4 a (a) = 9. In this particular instance, the current practice of using X• could be super- seded by any a (ø with an anticipated increase in successful tenders. The best apparent predictor is, of course, a (a), or in this case the production manager. With a © the prior probability measure of success is 9/25 = 0.36 as opposed to 0.28 with ,Y•.. Clearly such a prediction measure could and should be updated as results of each tender become available. Care must be taken when deciding upon a 'measure' of prediction performance. Above we used the principle of Insufficient Reason to assign equal probabilities to a set of events of unknown probability. Equally well one may have reasoned as follows: the production manager has made 25 selections, five of which we know split into four successful selections and