Suppose that there are three equal-size groups of voters in a community trying to select the amount of school spending per pupil. The options are to spend either $3,000, $7,500, or $12,000 per pupil. The lowest level would allow only a bare‑bones academic curriculum, the middle level would permit more varied academic courses and some transportation service, and the highest level would allow bus transportation for all students and extracurricular activities in addition to academics. The positions of the three voting groups are shown in this table:

Thus, Group Group II includes the middle-of-the-roaders, and Group III represents the “all-or-nothing” viewpoint.

(a) Plot the positions of the three groups on a diagram with level of preference on the vertical axis and level of expenditure on the horizontal axis. Connect the plots for each group with lines. Are the preferences of these groups single peaked?

(b) What level of spending will be selected by majority voting?

(c) Can you think of any ways for this community to select a level of school spending and avoid the problem of majority voting?

Transcribed Image Text:

Group Most preferred Second choice Least preferred I $3,000 $7,500 $12,000 II 7,500 12,000 3,000 III 12,000 3,000 7,500