The area of choice under uncertainty represents the heart of decision theory. Known from the 17th century (Blaise Pascal invoked it in his famous wager, which is contained in his Pensées, published in 1670), the idea of expected value is that, when faced with a number of actions, each of which could give rise to more than one possible outcome with different probabilities, the rational procedure is to identify all possible outcomes, determine their values (positive or negative) and the probabilities that will result from each course of action, and multiply the two to give an “expected value”, or the Average expectation for an outcome; the action to be chosen should be the one that gives rise to the highest total expected value. In 1738, Daniel Bernoulli published an influential paper entitled Exposition of a New Theory on the Measurement of Risk, in which he uses the St. Petersburg paradox to show that expected value theory must be normatively wrong. He gives an example in which a Dutch merchant is trying to decide whether to insure a cargo being sent from Amsterdam to St Petersburg in winter. In his solution, he defines a utility function and computes expected utility rather than expected financial value.
In the 20th century, interest was reignited by Abraham Wald’s 1939 paper[8] pointing out that the two central procedures of sampling-distribution-based statistical-theory, namely hypothesis testing and parameter estimation, are special cases of the general decision problem. Wald’s paper renewed and synthesized many concepts of statistical theory, including loss functions, risk functions, admissible decision rules, antecedent distributions, Bayesian procedures, and minimax procedures. The phrase “decision theory” itself was used in 1950 by E. L. Lehmann.
The revival of subjective Probability theory, from the work of Frank Ramsey, Bruno de Finetti, Leonard Savage and others, extended the scope of expected utility theory to situations where subjective probabilities can be used. At the time, von Neumann and Morgenstern theory of expected utility[10] proved that expected utility maximization followed from basic postulates about rational behavior.
The work of Maurice Allais and Daniel Ellsberg showed that human behavior has systematic and sometimes important departures from expected-utility maximization. The prospect theory of Daniel Kahneman and Amos Tversky renewed the empirical study of economic behavior with less emphasis on rationality presuppositions. Kahneman and Tversky found three regularities – in actual human decision-making, “losses loom larger than gains”; persons focus more on changes in their utility-states than they focus on absolute utilities; and the estimation of subjective probabilities is severely biased by anchoring.
PERT
PERT is an acronym for Program (Project) Evaluation and Review Technique, in which planning, scheduling, organising, coordinating and controlling of uncertain activities take place. The technique studies and represents the tasks undertaken to complete a project, to identify the least time for completing a task and the minimum time required to complete the whole project. It was developed in the late 1950s. It is aimed to reduce the time and cost of the project.
PERT uses time as a variable which represents the planned resource application along with performance specification. In this technique, first of all, the project is divided into activities and events. After that proper sequence is ascertained, and a Network is constructed. After that time needed in each activity is calculated and the critical path (longest path connecting all the events) is determined.PERT uses time as a variable which represents the planned resource application along with performance specification. In this technique, first of all, the project is divided into activities and events. After that proper sequence is ascertained, and a network is constructed. After that time needed in each activity is calculated and the critical path (longest path connecting all the events) is determined.
ERT was developed by the U.S. Navy in the 1950s to help coordinate the thousands of contractors it had working on myriad projects. While PERT was originally a manual process, today there are computerized PERT systems that enable project charts to be created quickly.
The only real weakness of the PERT process is that the time required for completion of each task is very subjective and sometimes no better than a wild guess. Frequent progress updates help refine the project timeline once it gets underway.
CPM
Developed in the late 1950’s, Critical Path Method or CPM is an algorithm used for planning, scheduling, coordination and control of activities in a project. Here, it is assumed that the activity duration are fixed and certain. CPM is used to compute the earliest and latest possible start time for each activity.
The process differentiates the critical and non-critical activities to reduce the time and avoid the queue generation in the process. The reason behind the identification of critical activities is that, if any activity is delayed, it will cause the whole process to suffer. That is why it is named as Critical Path Method.
In this method, first of all, a list is prepared consisting of all the activities needed to complete a project, followed by the computation of time required to complete each activity. After that, the dependency between the activities is determined. Here, ‘path’ is defined as a sequence of activities in a network. The critical path is the path with the highest length.
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Decision making under uncertainty is a complex process that requires careful consideration of all available information. There are a number of factors that can contribute to uncertainty, including:
The lack of complete information about the problem or situation.
The presence of multiple possible outcomes, each with its own probability of occurrence.
The presence of risk, which is the possibility of loss or harm.
The presence of uncertainty about the future, which can make it difficult to predict the consequences of different decisions.
Despite the challenges, it is possible to make effective decisions under uncertainty by following a systematic approach. The first step is to define the problem or situation. This involves identifying the key Elements of the problem, such as the goals, objectives, and constraints. The next step is to identify the possible courses of action. This can be done by brainstorming, listing all possible Options, or using a decision tree.
Once the possible courses of action have been identified, the next step is to evaluate them. This involves assessing the risks and benefits of each option, as well as the likelihood of different outcomes. The final step is to select the best course of action. This can be done by using a decision matrix, which compares the different options based on their risks, benefits, and likelihood of success.
Decision making under uncertainty is a challenging task, but it is possible to make effective decisions by following a systematic approach. By carefully considering all available information and evaluating the risks and benefits of different options, it is possible to select the best course of action and achieve desired outcomes.
Here are some additional tips for making effective decisions under uncertainty:
Be flexible. The best course of action may change as new information becomes available or as the situation evolves. Be prepared to adapt your decision as needed.
Be prepared to take risks. Some decisions will inevitably involve some degree of risk. If you are not willing to take risks, you will likely never achieve your goals.
Be confident in your decision. Once you have made a decision, trust your gut and move forward. Don’t second-guess yourself or let others talk you out of your decision.
Learn from your mistakes. Everyone makes mistakes. The important thing is to learn from them and use them to make better decisions in the future.
Decision making under uncertainty is a skill that can be learned and improved with practice. By following these tips, you can become a more effective decision-maker and achieve your goals.
What is decision making under uncertainty?
Decision making under uncertainty is the process of making decisions when there is incomplete or imperfect information about the possible outcomes of those decisions.
What are some examples of decision making under uncertainty?
Some examples of decision making under uncertainty include:
Investing in a new business venture
Deciding whether to take a new job
Choosing a college to attend
Getting married
What are some common biases that can affect decision making under uncertainty?
Some common biases that can affect decision making under uncertainty include:
Anchoring bias: The tendency to rely too heavily on the first piece of information that is presented.
Availability bias: The tendency to judge the probability of an event based on how easily examples come to mind.
Representativeness bias: The tendency to judge the probability of an event based on how similar it is to other events that have occurred in the past.
Confirmation bias: The tendency to seek out information that confirms one’s existing beliefs and to ignore information that contradicts those beliefs.
What are some strategies for improving decision making under uncertainty?
Some strategies for improving decision making under uncertainty include:
Gathering more information: The more information you have about the possible outcomes of your decision, the better equipped you will be to make a decision.
Considering multiple scenarios: When making a decision, it is important to consider multiple possible scenarios and to think about how you would react to each one.
Using decision trees: Decision trees can be a helpful tool for visualizing the possible outcomes of a decision and for making a decision that is most likely to lead to the desired outcome.
Seeking advice from others: Sometimes it can be helpful to seek advice from others who have more experience or knowledge about the situation you are facing.
Making a decision and sticking with it: Once you have made a decision, it is important to stick with it and not second-guess yourself.
What are some common mistakes to avoid when making decisions under uncertainty?
Some common mistakes to avoid when making decisions under uncertainty include:
Making decisions based on gut feeling: It is important to avoid making decisions based on gut feeling alone. Instead, you should gather as much information as possible and carefully consider all of your options before making a decision.
Avoiding making decisions: Sometimes people avoid making decisions because they are afraid of making the wrong choice. However, it is important to remember that even if you make the wrong decision, you can always learn from your mistakes and make a better decision next time.
Procrastinating: Procrastinating can lead to making decisions under pressure, which can increase the chances of making a bad decision. It is important to make decisions in a timely manner so that you have enough time to gather information and consider all of your options.
What are some Resources that can help with decision making under uncertainty?
There are many resources available to help with decision making under uncertainty. Some of these resources include:
Books: There are many books available on decision making, such as “Thinking, Fast and Slow” by Daniel Kahneman and “The Black Swan” by Nassim Nicholas Taleb.
Websites: There are many websites that offer advice on decision making, such as the website of the Decision Sciences Institute.
Courses: There are many courses available on decision making, both online and in person.
Consultants: There are many consultants who specialize in helping people make decisions.
Question 1
A decision tree is a graphical representation of the possible decisions and outcomes of a decision. The branches of the tree represent the possible decisions, and the leaves represent the possible outcomes. The probability of each outcome is represented by the thickness of the branch leading to that outcome.
Which of the following is not a step in creating a decision tree?
(A) Identify the decision to be made. (B) Identify the possible outcomes of the decision. (C) Assign probabilities to the possible outcomes. (D) Calculate the expected value of each outcome. (E) Choose the outcome with the highest expected value.
Answer
The correct answer is (D). The expected value of an outcome is not a step in creating a decision tree. The expected value of an outcome is calculated after the decision tree has been created.
Question 2
A utility function is a function that maps possible outcomes to a measure of their desirability. The utility function is used to make decisions under uncertainty.
Which of the following is not a property of a utility function?
(A) The utility function is increasing in the outcome. (B) The utility function is continuous. (C) The utility function is concave. (D) The utility function is convex. (E) The utility function is bounded.
Answer
The correct answer is (C). The utility function is not necessarily concave. The utility function can be concave, convex, or neither.
Question 3
A risk-averse decision maker is a decision maker who prefers to avoid risk. A risk-neutral decision maker is a decision maker who is indifferent to risk. A risk-seeking decision maker is a decision maker who prefers to take risks.
Which of the following is not a way to measure risk aversion?
(A) The coefficient of risk aversion. (B) The certainty equivalent. (C) The risk premium. (D) The expected utility. (E) The Variance.
Answer
The correct answer is (E). The variance is not a way to measure risk aversion. The variance is a measure of the spread of a probability distribution.
Question 4
A decision under uncertainty is a decision that is made without knowing all of the possible outcomes. A decision under risk is a decision that is made knowing all of the possible outcomes and their probabilities.
Which of the following is not an example of a decision under uncertainty?
(A) Deciding whether to invest in a new business. (B) Deciding whether to buy a new car. (C) Deciding whether to go to college. (D) Deciding whether to get married. (E) Deciding whether to have children.
Answer
The correct answer is (A). Deciding whether to invest in a new business is an example of a decision under risk. The decision maker knows all of the possible outcomes and their probabilities.
Question 5
A decision under ambiguity is a decision that is made without knowing all of the possible outcomes or their probabilities.
Which of the following is not an example of a decision under ambiguity?
(A) Deciding whether to invest in a new business. (B) Deciding whether to buy a new car. (C) Deciding whether to go to college. (D) Deciding whether to get married. (E) Deciding whether to have children.
Answer
The correct answer is (A). Deciding whether to invest in a new business is an example of a decision under risk. The decision maker knows all of the possible outcomes and their probabilities.