A decision is a selection of a choice, usually a choice that has important consequences.

You make decisions all of the time.

• Should I go to class?
• Should I study for the exam?
• What is the best answer for this question?
• Why am I reading this?

Sometimes the "best" decision is not clear or obvious.

How do you make decisions? That is, do you have a process for making decisions, or do you just make them.

Simple decision analysis involves making a yes-no decision before something critical to the decision happens that is, called a "State of Nature" outcome, is known. It is called a yes-no "State of Nature" because the outcome is not predictable. But, you must make your decision before you know the outcome of the "State of Nature".

Here as a simple text diagram for the problem.

Even when we might want to have more than two outcomes, the problem and decision process is easier to analyze when there are only two outcomes.

Consider a medical cancer test. These tests are not perfect, so there are some errors involved.

• If the test predicts that you have cancer, and you do have cancer, then there is no logical problem. The test worked, a true-positive. But, for you it might be a personal tragedy.
• If the test predicts that you have cancer, but you do not have cancer, then this is a false-positive (type I error).
• If the test predicts that you do not have cancer, but you do have cancer, then this is a false-negative (type II error).
• If the test predicts that you do not have cancer, and you do not have cancer, then there is no logical problem. The test worked, a true-negative.

Suppose you want to "win big" and decide that the lottery is the way to do it.

• What is the decision?
• What is the state of nature?

• The decision is to either "buy a ticket" or "do not buy a ticket".
• The state of nature is either "you win" or "you lose".

In influence diagram can be used to show the decision process. Here is one way to draw the decision tree. Since if you do not buy a ticket, you cannot win, the diagram might be drawn with only one "no buy" branch.

• Decision: Should I buy a ticket to go to the event?
• State of nature: Will it rain? If it rains, the event is canceled and I do not get my money back?

Here are the four possible outcomes for the above problem.

• If I buy a ticket, and it rains, it is logically not OK. I am upset that I came all this way and did not get to see the event.
• If I go, and it does not rain, it is logically OK. I can see the event I wanted to see.
• If I do not go, and it rains, it is logically OK. I miss the event, but would have missed it anyway.
• If I do not go, and it does not rain, it is logically not OK. I missed the event that I could have attended.

Here are some more decision analysis problems, only from a sports point of view where there are two opposing players each trying to accomplish a goal, and only one of them will win while the other loses.

The same principles would apply to other sports (e.g., a goalie in soccer, a spiker in volleyball, etc.)

In baseball, the batter tries to hit the ball thrown by the pitcher.

From a batter's point of view:

• Decision: Look for a fast ball (instead of curve ball) by the pitcher? Yes/No.
• State of nature: A fast ball is thrown (instead of curve ball) by the pitcher? Yes/No.

From a pitcher's point of view:

• Decision: Throw fast ball (instead of curve ball) to the batter? Yes/No.
• State of nature: Batter looks for a fast ball (instead of curve ball)? Yes/No.

• Decision: Look for a forehand (instead of a backhand) by an opponent? Yes/No.
• State of nature: A forehand is used (instead of a backhand) by an opponent? Yes/No.

Many times, political parties will take one point of view or the other point of view in attempting to minimize (or maximize) one of the logical problems inherent in the decision process.

• Decision: Someone gets welfare assistance? Yes/No.



• State of nature: Does that person needs welfare assistance? Yes/No.

• Decision: The jury decides if a person is guilty? Yes/No.



• State of nature: The person committed the crime. Yes/No.

• Decision: Should a specific person be allowed to get a gun? Yes/No.



• State of nature: That person commits a crime with the gun. Yes/No.

• Decision: Should a convicted person on death row be executed? Yes/No.



• State of nature: That person is guilty. Yes/No.