When the objective probabilities of the occurrence of various states of nature are not known, the same can be assigned on the basis of the expectations or the degree of belief of the decision-maker. Such probabilities are known as subjective or personal probabilities. It may be pointed out that different individuals may assign different probability values to given states of nature.

This indicates that a decision problem under uncertainty can always be converted into a decision problem under risk by the use of subjective probabilities. Such an approach is also termed as Subjectivists' Approach.

Example : The conditional payoff (in Rs) for each action-event combination are as under:

conditional payoff

(i) Which is the best action in accordance with the Maximin Criterion?
(ii) Which is the best action in accordance with the EMV Criterion, assuming that all the events are equally likely?


(i) The minimum payoffs for various actions are:

Action 1 = –5
Action 2 = –2
Action 3 = 2
Action 4 = –3

Since the payoff for action 3 is maximum, therefore, A3 is optimal on the basis of maximin criterion. Since there are 5 equally likely events, the probability of each of them would be 1/5.
Thus, the EMV of action 1, i.e., EMV1= 4+0-5+3+6/5 = 8/5 = 1.6

Similarly, EMV2 = 20/5 = 4.0, EMV3 = 19/5 = 3.8 and EMV4 = 17/5 = 3.4

Thus, action 2 is optimal.

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Quantitative Techniques for management Topics