The school Board has decided to completely re-build one of its educational facilities in our District. (Ranum H.S., Westminster H.S., C.E.P., A.C.E.) The new facility will be a state of the art facility. It will include a gymnasium (with a pool, weight room, basketball court and tennis courts), a chorus room (with recording capabilities), a new computer lab, computers in every classroom, student lounge areas, cafeterias and snack bars - THE WORKS!!!
The board decided to let all of the students in each of the school being considered vote on the site. The results of the voters' rank-ordered choices are as follows:
| LOCATION PREFERENCE | VOTES |
|---|---|
| Ranum, Westminster, CEP, ACE | 1,000 |
| Westminster, Ranum, CEP, ACE | 900 |
| ACE, CEP, Ranum, Westminster | 100 |
| CEP, Westminster, Ranum, ACE | 320 |
1(a) Based on these results, where should the facility be built?
(Please justify your reasoning and consider the methods we used in class You may want to consider the number of people in each school.)
(b) Use Arrow's Criteria to examine the fairness of the results of this survey and the method you used to arrive at your decision (You may want to make assumptions about the people participating in this survey).
(c) Based on the results of this survey, speculate on what the results of a similar survey would be is the survey employed an approval voting structure (assume that the same people participate in this approval voting).
(2) If the election were restricted to the principals of the schools in the District, how would you design a fair voting system? How would you decide how much weight each principal's vote should get as it relates to the student population. (In your examination of the fairness of your system, be sure to address winning coalitions, power, dictators, and dummies).