Lesson 1 Assessment [50 minutes, 10 questions]: MATH 36, Spring 2024, WC

MATH 36, Spri… Quizzes Lesson 1 Assess…  Lesson 1 Assessment [50 minutes, 10 ques ! ons] Due Mar 15 at 11:59pm Points 10 Ques ! ons 10 Available a ! er Mar 11 at 12am Time Limit 50 Minutes A " empt History A " empt Time Score LATEST A " empt 1 23 minutes 8 out of 10  Correct answers are hidden. Score for this quiz: 8 out of 10 Submi " ed Mar 11 at 11:31am This a " empt took 23 minutes. 1 / 1 pts Ques ! on 1 Answer 1: Given the Preference Schedule: Number of Voters 5 11 6 3 5 7 5 2 6 1 Choice A A A A B B B C D 2 Choice B B C D A A D B B 3 Choice C D B B C D A A A 4 Choice D C D C D C C D C How many people voted in this elec # on? 50 st nd rd th 50 5 + 11 + 6 + 3 + 5 + 7 + 5 + 2 + 6 = 50 0 / 1 pts Ques ! on 2 Incorrect Incorrect A poll was conducted where of 840 voters were asked to "rank" the 4 candidates. The four candidates are: Gill, White, Ho ff , and Smith. The elec # on count will be based upon the plurality-with- elimina # on method. Follows is the preference schedule: Number of voters 315 245 140 105 35 1 Choice Gill Ho ff Ho ff Gill White 2 Choice White Gill White White Ho ff 3 Choice Smith Smith Gill Smith Smith 4 Choice Ho ff White Smith Ho ff Gill Who wins? st nd rd th Gill White Ho ff Smith A Tie breaker is needed. The total number of votes is 840, and to obtain a majority, a candidate would need 421 votes. The round 1 first choice totals are: Gill has 420 votes. White has 35 votes Ho ff has 385 votes Smith has no votes. Based upon the first choice row, Smith has no votes (and is eliminated), and then White has the fewest votes and is eliminated. The resul # ng schedule becomes: Number of voters 315 245 140 105 35 1 Choice Gill Ho ff Ho ff Gill Ho ff 2 Choice Ho ff Gill Gill Ho ff Gill Both Gill and Ho ff have exactly 420 votes. Neither candidate has a majority and a # e-breaker process will be required. st nd 1 / 1 pts Ques ! on 3 For the following preference schedule, who is the majority candidate ? Number of Voters 12 8 7 7 3 1 Choice A C D B C 2 Choice B B C D D 3 Choice C D B C B 4 Choice D A A A A st nd rd th Candidate A Candidate B Candidate C Candidate D There is NO majority candidate . A majority candidate is determined by 1 choice votes. Since there are 37 total votes, a candidate must have 19 first-choice votes to have be a majority candidate. In this case, NO candidate holds a majority of first choice votes. In this problem, candidate A could be called a plurality candidate since they have the most first-choice votes. st 1 / 1 pts Ques ! on 4 The Spanish Club is holding elec # ons for President and there are 3 candidates (James, Carlos and Jenny) running for that o ffi ce. There are 40 members of the club. What is the number of votes that a candidate must obtain in order to win by a majority? 20 21 40 25 40/2 = 20. Next integer greater than 50% is 21. 1 / 1 pts Ques ! on 5 In an elec # on with 5 candidates, what is the maximum number of columns that can appear in the preference schedule? 15 25 100 120 A classical mul # plica # on coun # ng problem. 5! = 5 x 4 x 3 x 2 x 1 = 120 1 / 1 pts Ques ! on 6 Using the plurality method, the winner of the elec # on and the correct number votes that they received is # of voters 5 6 2 3 1 Choice A C A B 2 Choice B A C C 3 Choice C B B A st nd rd A wins with 5 votes C wins with 6 votes A wins with 7 votes C wins with 8 votes For the plurality method, only first place (choice) votes are counted. The candidate with the most first place votes wins. 1 / 1 pts Ques ! on 7 Consider the Preference Schedule: Number of Voters 5 11 6 3 5 9 5 2 5 1 Choice A A A A B B B C D 2 Choice B B C D A A D B B 3 Choice C D B B C D A A A 4 Choice D C D C D C C D C Which candidate wins using the plurality method? st nd rd th A B C D Count First Place votes: A: 5 + 11 + 6 + 3 = 25 B: 5 + 9 + 5 = 19 C: 2 D: 5 Candidate A has most votes (but it is NOT a majority of votes) 1 / 1 pts Ques ! on 8 Consider the Preference Schedule: Number of Voters 5 11 6 3 5 9 5 2 5 1 Choice A A A A B B B C D 2 Choice B B C D A A D B B 3 Choice C D B B C D A A A 4 Choice D C D C D C C D C Which candidate wins using the plurality with elimina # on? st nd rd th A B C D Candidate C has the least number of 1st place votes and is eliminated. The "new" preference schedule becomes: Number of Voters 5 11 6 3 5 9 5 2 5 1 Choice A A A A B B B B D 2 Choice B B B D A A D A B 3 Choice D D D B D D A D A Clearly D has the least number of votes and is eliminated. Number of Voters 5 11 6 3 5 9 5 2 5 1 Choice A A A A B B B B B 2 Choice B B B B A A A A A We now have Candidate A with a total of 25 votes and B with a total of 26 votes. B wins. st nd rd st nd 1 / 1 pts Ques ! on 9 A group of people were asked to vote for their favorite person among the candidates Alice (A), Bob (B), Cassie (C) and Dave (D) and the results are shown in the preference schedule below. Using the plurality-with-elimina # on method, the winner is # of Voters 16 12 10 6 1 1 Choice A D C B C 2 Choice B C B D D 3 Choice C B D C B 4 Choice D A A A A st nd rd th Alice Bob Cassie Dave First note that a “majority” is the next greatest integer more than 50% of the total number of voters (45/2 = 22.5, thus 23 or more needed for majority). Round 1, A has 16, B has 6, C has 11, and D has 12. No majority. B is eliminated. Round 2, A has 16, C has 11, and D has 18. No majority. C is eliminated. Round 3, A has 16, D has 29. Dave has a majority and wins. 0 / 1 pts Ques ! on 10 Incorrect Incorrect Rank the "top two" candidates using the extended plurality-with- elimina # on method. Number of Voters 12 8 7 7 3 1 Choice A C D B C 2 Choice B B C D D 3 Choice C D B C B 4 Choice D A A A A st nd rd th Place 1st 2nd Candidate B C Place 1st 2nd Candidate B A Place 1st 2nd Candidate C A Place 1st 2nd Candidate A C Place 1st 2nd Candidate A B Extended ranking using the plurality with eilimina # on method, only the 1st Choice votes are tallied. Tally - 1st Round 1st 2nd 3rd-4th ! e Candidate A C D B 1st Choice votes 12 11 7 7 Since B and D " # e" for last place, both are eliminated. (Note the ques # on asked for rank 1 and 2 and we have two candidates le ! .) New preference table: Number of Voters 12 8 7 7 3 1 Choice A C C C C 2 Choice C A A A A Tally - 2nd Round 1st 2nd Candidate C A 1st Choice votes 25 12 st nd Quiz Score: 8 out of 10  Previous Next  Submission Details: Time: 23 minutes Current Score: 8 out of 10 Kept Score: 8 out of 10 1 2241 - 202324SP Home Syllabus Announcements Assignments Discussions Grades People Quizzes BigBlueBu " on Chat Tutor.com Media Gallery Collabora # ons Library Resources Account Dashboard Courses Groups Calendar Inbox History My Media No # ces Help