1. Voting and Apportionment

2. The spirit club at Lakeview High School is voting for President, Vice President, and Treasurer. Their Choices are Ken Walters (KW), Jocelyn Suthers (JS), and Amelia Crest (AC). The preference table follows. How many members of the spirit club voted? A) 25B) 20C) 8D) 21 # of Votes8543 FirstKWJSAC SecondJSKW JS ThirdAC JSKW

3. The spirit club at Lakeview High School is voting for President, Vice President, and Treasurer. Their Choices are Ken Walters (KW), Jocelyn Suthers (JS), and Amelia Crest (AC). The preference table follows. Does any choice have a majority of votes? A) KWB) JSC) ACD) No # of Votes8543 FirstKWJSAC SecondJSKW JS ThirdAC JSKW

4. The spirit club at Lakeview High School is voting for President, Vice President, and Treasurer. Their Choices are Ken Walters (KW), Jocelyn Suthers (JS), and Amelia Crest (AC). The preference table follows. Determine the winner using the plurality method A) KWB) JSC) AC # of Votes8543 FirstKWJSAC SecondJSKW JS ThirdAC JSKW

5. The spirit club at Lakeview High School is voting for President, Vice President, and Treasurer. Their Choices are Ken Walters (KW), Jocelyn Suthers (JS), and Amelia Crest (AC). The preference table follows. Determine the winner using the Borda count method A) KWB) JSC) AC # of Votes8543 FirstKWJSAC SecondJSKW JS ThirdAC JSKW

6. The spirit club at Lakeview High School is voting for President, Vice President, and Treasurer. Their Choices are Ken Walters (KW), Jocelyn Suthers (JS), and Amelia Crest (AC). The preference table follows. Determine the winner using the plurality with elimination method A) KWB) JSC) AC # of Votes8543 FirstKWJSAC SecondJSKW JS ThirdAC JSKW

7. The spirit club at Lakeview High School is voting for President, Vice President, and Treasurer. Their Choices are Ken Walters (KW), Jocelyn Suthers (JS), and Amelia Crest (AC). The preference table follows. Determine the winner using the pairwise comparison method A) KWB) JSC) AC # of Votes8543 FirstKWJSAC SecondJSKW JS ThirdAC JSKW

8. The spirit club is also given the responsibility of picking the new school color. The choices are Navy Blue (N), Maroon (M), and Gold (G). The results of the election are given in the following preference table. Which color wins this election if the plurality method is used? A) MB) GC) N # of Votes5636 FirstNNMG SecondMGNM ThirdGMGN

9. The spirit club is also given the responsibility of picking the new school color. The choices are Navy Blue (N), Maroon (M), and Gold (G). The results of the election are given in the following preference table. Which color wins this election if the Borda count method is used? A) MB) GC) N # of Votes5636 FirstNNMG SecondMGNM ThirdGMGN

10. The spirit club is also given the responsibility of picking the new school color. The choices are Navy Blue (N), Maroon (M), and Gold (G). The results of the election are given in the following preference table. Which color wins this election if the plurality with elimination method is used? A) MB) GC) N # of Votes5636 FirstNNMG SecondMGNM ThirdGMGN

11. The spirit club is also given the responsibility of picking the new school color. The choices are Navy Blue (N), Maroon (M), and Gold (G). The results of the election are given in the following preference table. Which color wins this election if the pairwise comparison method is used? A) MB) GC) N # of Votes5636 FirstNNMG SecondMGNM ThirdGMGN

12. Which voting method(s) – plurality, Borda count, plurality with elimination, or pairwise comparison – violate the head- to-head criterion using the following election data? A)Plurality and Borda count B)Plurality, Borda Count, and Plurality w/Elimination C)All methods D)None # of Votes2032245041 FirstABCAD SecondDCACB ThirdBADBA FourthCDBDC

13. The board of a local country club is voting for the date of their golf tournament. The choices for the date are June 14 (14), June 21 (21), or June 28 (28). The 21 board members rank their choices according to the following preference table. Using the data provided, does the Borda count method violate the majority criterion? A)Yes B)No # of Votes3756 First14212821 Second28 1428 Third21142114

14. A country has four states and 50 seats in the legislature. The population of each state is shown below. A)5, 13, 13, 19 B)6, 11, 13, 20 C)5, 12, 13, 20 D)6, 12, 13, 20 StateABCDTotal Population101325422731400410,290 Determine each state’s apportionment using Hamilton’s method.

15. A country has four states and 50 seats in the legislature. The population of each state is shown below. A)5, 13, 13, 19 B)6, 11, 13, 20 C)5, 12, 13, 20 D)6, 12, 13, 20 StateABCDTotal Population101325422731400410,290 Determine each state’s apportionment using Jefferson’s method.