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:

Number of examiners Compliance
Low Normal High
One 50 50 50
Two 100 60 20
Three 150 70 -10

If she uses the Laplace 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

Answer 1

If she uses the Laplace criterion, the number of new examiners she will decide to hire is:

c. three

Explanation:

a) Data:

Number of Compliance

examiners Low Normal High

One 50 50 50

Two 100 60 20

Three 150 70 -10

b) Outcome Calculations:

Number of Compliance

examiners Low Normal High

One 16.65 (50 *.333) 16.65 (50 *.333) 16.65 (50 *.333) = 50

Two 33.3 (100 *.333) 19.98 (60 *.333) 6.66 (20 *.333) = 60

Three 49.95 (150 *.333) 23.31 (70 *.333) -3.33 (-10 *.333) = 70

c) Decision:

Three has the highest payoff condition and is selected.

d) The Laplace criterion assumes that each compliance state is equally likely to happen. Therefore, it assigns the same weight to each state of compliance. Since there are three states of compliance, we shall assign each state a weight of 0.333. The number of examiners that have the highest payoff condition is three, and therefore, the number "three" is selected.