Chapter 4, Problem 59E

This exercise refers to the apportionment of social workers in Happy Rivers County introduced in Exercise 19. The answers to parts (a) and (b) in Exercise 19 are an illustration of which paradox? Explain. [You will need to work out parts (a) and (b) of Exercise 19 if you haven't done so yet.]

19. Happy Rivers County consists of three towns: Dunes, Smithville, and Johnstown. Each year the social workers employed by the county are apportioned among the three towns based on the number of cases in each town over the previous calendar year. The number of cases in each town in 2016 is shown in Table 4-29.

Table-4-29

Town	Dunes	Smithville	Johnstown
Number of cases	41	106	253

a. Suppose there are 24 social workers employed by the county. Use Hamilton's method to apportion the social workers to the towns based on the caseloads shown in Table 4-29.

b. Suppose there are 25 social workers employed by the county. Use Hamilton's method to apportion the social workers to the towns based on the caseloads shown in Table 4-29.

c. Compare your answers in (a) and (b). What is strange about the two apportionments?