Question

When constructing a decision tree, why is the Expected Monetary Value (EMV) calculated by multiplying outcome values by their probabilities rather than using a simple average?

Accepted Answer

A simple average assumes that every possible outcome is equally likely to happen, which is rarely true in real-world decision-making. Expected Monetary Value (EMV) uses a weighted average that accounts for the specific likelihood of each scenario, known as the probability. By multiplying the value of an outcome by its probability, you assign more mathematical importance to outcomes that are more likely to occur and less importance to those that are unlikely. For example, if you are considering a business project where there is a 90 percent chance of earning 100 dollars and a 10 percent chance of losing 500 dollars, a simple average would suggest a loss of 200 dollars, which ignores the high likelihood of success. The EMV calculation, which is 90 dollars minus 50 dollars, results in an EMV of 40 dollars. This figure provides a statistically sound representation of the long-term average outcome if the same decision were made many times. Using probabilities ensures that the decision-maker can compare options based on their true risk-adjusted potential rather than treating rare events and common events as having the same impact.

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When constructing a decision tree, why is the Expected Monetary Value (EMV) calculated by multiplying outcome values by their probabilities rather than using a simple average?

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