Concept explainers
Consider an election with four candidates with the following results:
a. Is there a winner using the pairwise comparison method?
b. Is there a winner using the tournament method?
c. Do either of these methods violate any conditions of Arrow's impossibility theorem?
Want to see the full answer?
Check out a sample textbook solutionChapter 17 Solutions
Nature of Mathematics (MindTap Course List)
- Consider an election with three candidates with the results: (CBA) 2 (ACB) 6 (BAC) 5 (BCA) 2 Is there a majority winner? If not, who is the plurality winner? Answer No, B; Yes, A; No, A; No, C; or Yes, B. Who wins the election using the Borda count method? Answer B; A; C and B tie; C; or A and B tie. Who wins if they first eliminate the one with the most last-place votes and then have a runoff between the other two? Answer B; A; C and B tie; C; or A and B tie. Could the two voters with preference (BCA) change the outcome of the election in previous question if they voted insincerely and pretended to have the preference (BAC)? Answer yes or no.arrow_forwardThe Republic of Amador is composed of five states, A, B, C, D, and E. According to the country's constitution, the Congress will have 200 seats, divided among the five states according to their respective populations. State C D E Population |(in thousands) 1112 1118 1320 1515 4935 Use Adam's method with d = 50.6 to apportion the %3D 200 congressional seats for state A and E. Seats for state A = Seats for state E =arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education