Decision Making Under Uncertainty Situation

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Table of Contents

Introduction
A practical example of decision making under uncertainty
The trade-off between accuracy and precision
Decision-making criteria
Conclusion
Reference List

Introduction

Decision making could be defined as the act of committing resources today for results to be gained tomorrow. Decision making, therefore, involves making predictions about the future and therefore it is subject to various uncertainties.

Conditions of certainty are very rare because it is not easy to predict the outcome of the decisions that are made in our everyday life. Prediction of the future outcome of an act, though uncertain, is made possible by the experience that one has concerning similar acts or similar decisions. Mostly, the concept of probability is very useful in predicting what the outcome of a decision will be. The concept of probability, in this case, uses the assumption that the extent to which an outcome was likely to occur or occurred in the past can recur in the future. Probability takes into account the frequency of occurrence of an event in the past and the likelihood of the same happening today.

In this research, we shall consider a practical example in order to demonstrate the concept of decision making under a situation of uncertainty.

A practical example of decision making under uncertainty

Consider the following situation of decision making under uncertainty.

Each of the conditions of uncertainty offers three differently distributed outcomes. Suppose a boy wishes to visit her grandmother where he is expecting three things to happen. He is either paid a trip to Bermuda, gets $1000 or is bought a modern motorbike.

Let A and B denote the two uncertainty alternatives representing January and December which are the only months the boy can be available to visit the grandmother. The three benefits of visiting the grandmother are the possible outcomes of paying the visit in January or December. The boy is wishing to choose the benefit that will best satisfy him. The likelihood of the three events happening differs depending on the alternative that is chosen. In this case, we can use the available data to determine the best of the three alternatives. The probability of getting the benefits under each situation of uncertainty is as shown in the table below.

	Bermuda	$1000	Motorbike
A	0.4	0.3	0.3
B	0.1	0.6	0.3

To determine the best of the uncertain alternatives A and B, we determine the aggregate utilities of the two alternatives based on the utilities of individual outcomes and choose the one with the highest alternative. Suppose we assign values to the three outcomes as a_1, a₂ and a₃to represent a trip to Bermuda, $1000 and a modern motorbike respectively. To get the utility of individual outcomes, we multiply the assigned values by their respective probabilities (Scholz, 1983, 28). To obtain the total utilities of the two uncertain outcomes, we sum up the expected utilities of the individual outcomes.

This is denoted as follows: U (A) = 0.4 a₁+ 0.3 a₂+ 0.3 a₃ and U (B) = 0.1 a₁ + 0.6 a₂ + 0.3 a₃. This means that the higher of the U (A) and U (B) will be the most preferred alternative because it offers more benefits. The sum of probabilities of all outcomes under each uncertain condition is equal to one to indicate that if all the outcomes happen as per the probabilities, the alternative A or B will be satisfied. If we could assign a monetary value to a_1, a₂ and a₃as $900, $1000 and $950 respectively with certainty, then we will be able to compute the value of U (A) and U (B). We need to multiply them by their respective probabilities as shown in the utility functions. We compute them as shown below.

U (A) = 0.4($900) + 0.3($1000) + 0.3($950) = $945
U (B) = 0.1($900) + 0.6($1000) + 0.3($950) = $975.b.

These values may change from one period to another depending on the prevailing conditions.

Alternative B would be the most preferred because it has the highest utility. In most cases, the value of the outcomes is not known and this is what makes the alternatives uncertain. The decision-maker is not aware of what the value of the alternatives will be. However, with the assigned values of the alternatives, the probability concept is applied to obtain the value of the most valuable alternative. In general, the utility functions are maximized subject to V= v (a1, a₂, a₃) where V stands for the values of a_1, a₂ and a₃. If these values were known, then the utilities could be determined with certainty. The utility maximization problem will be to maximize U (A) = 0.4 a₁+ 0.3 a₂+ 0.3 a₃ or U (B) = 0.1 a₁ + 0.6 a₂ + 0.3 a₃. Subject to V=v (a1, a₂, a₃).

A rational decision-maker or consumer would choose A, if and only if U (A)> U (B) and would choose B if and only if U (B)> U (A).

The trade-off between accuracy and precision

Precision could be achieved if the same experiment repeated frequently under the same conditions gives the same result. This could be used to determine the reliability of the probabilities that are used in statistical estimation (Bell & Schleifer, 1995, 25). The accuracy of the data, on the other hand, is a measure of how close the results of an experiment are compared to the actual figures. The trade-off between accuracy and precision is the difference between the results claimed to be correct due to consistency in repeated experiments and the one obtained after doing the experiment. In the above example, the precision will be reached if the boy visits the grandmother repeatedly and chooses the same alternative in all the visits.

The reliance on such a date may not be accurate because getting the same results does not mean that they are the actual results. The results may also differ because of the change in other factors that may not be considered in the experiment. The accuracy of the above decision making will be affected by the use of past experience in predicting the future.

Decision-making criteria

In the above example, the decision reached by the consumer will depend on his preference. The objective of the consumer is to maximize utility subject to the value of the three alternatives he has. The desired alternative is, therefore, the one that will give the maximum utility. The boy is choosing between alternatives A and B and the decision criteria are as under.

A will be chosen if and only if U (A)> U (B) and B is only preferred if and only if U (B)> U (A). Any rational consumer or decision-maker will choose the decision that offers the highest benefit.

Conclusion

Decision making under uncertainty conditions could be done using the concept of probability as shown in the example above. A rational decision-maker chooses the decision that maximizes his preference. Decision making under uncertainty condition uses experience to estimate the outcome of the future. The likelihood that events occurred in the past is used to estimate the likelihood of the same experience happening in the future.

Reference List

Bell, E. & Schleifer, A. (1995). Decision making under uncertainty. Michigan: The University of Michigan. Web.

Scholz, WR. (1983). Decision making under uncertainty: cognitive decision Research, social interaction, development and epistemology. US: Elsevier. Web.

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