The local operations manager for the Internal Revenue Service must decide whether to hire one, two, or three temporary tax examiners for the upcoming tax season. She estimates that net revenues (in thousands of dollars) will vary with how well taxpayers comply with the new tax code just passed by Congress, as follows: $$\begin{array} { | l | l | l | l | }
\hline { \begin{array} { l }
\text { NUMBER } \
\text { OF } \
\text { EXAMINERS }
\end{array} } & { \text { COMPLIANCE } } \
\hline & \text { LOW } & \text { NORMAL } & \text { HIGH } \
\hline \text { One } & 50 & 50 & 50 \
\hline \text { Two } & 100 & 60 & 20 \
\hline \text { Three } & 150 & 70 & - 10 \
\hline
\end{array}$$ If she uses the minimax regret criterion, how many new examiners will she decide to hire?
A) one
B) two
C) three
D) either one or two
E) either two or three

Question

The local operations manager for the Internal Revenue Service must decide whether to hire one, two, or three temporary tax examiners for the upcoming tax season. She estimates that net revenues (in thousands of dollars) will vary with how well taxpayers comply with the new tax code just passed by Congress, as follows: $$\begin{array} { | l | l | l | l | } 
\hline  { \begin{array} { l } 
\text { NUMBER } \
\text { OF } \
\text { EXAMINERS }
\end{array} } &  { \text { COMPLIANCE } } \
\hline & \text { LOW } & \text { NORMAL } & \text { HIGH } \
\hline \text { One } & 50 & 50 & 50 \
\hline \text { Two } & 100 & 60 & 20 \
\hline \text { Three } & 150 & 70 & - 10 \
\hline
\end{array}$$ If she uses the minimax regret criterion, how many new examiners will she decide to hire?
A) one
B) two
C) three
D) either one or two
E) either two or three

Quizplus · Accepted Answer

The minimax regret decision rule requires us to find the maximum regret for each possible decision, and then choose the decision with the minimum maximum regret.

We start by calculating the regret for each possible outcome, which is the opportunity loss of not choosing the best option for each state of nature (compliance level). We subtract each revenue value from the maximum revenue value for that compliance level. For example, if one examiner is hired and compliance is low, the maximum revenue is 50, so the regret for that outcome is 50 - 50 = 0. The following table shows the regrets for each decision:

$$\begin{array} { | l | l | l | l | } 
\hline  { \text { DECISION } } &  { \text { COMPLIANCE } } \
\hline & \text { LOW } & \text { NORMAL } & \text { HIGH } \
\hline \text { One } & 0 & 0 & 0 \
\hline \text { Two } & 50 & 10 & 30 \
\hline \text { Three } & 100 & 20 & 60 \
\hline
\end{array}$$

To apply the minimax regret criterion, we need to find the maximum regret for each decision, and then choose the decision with the minimum maximum regret. The maximum regrets are:

- Decision 1: Maximum regret is 0.
- Decision 2: Maximum regret is 50.
- Decision 3: Maximum regret is 100.

Therefore, the decision with the minimum maximum regret is to hire two tax examiners.

The Local Operations Manager for the Internal Revenue Service Must