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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?
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Chapter 17 Solutions
EBK NATURE OF MATHEMATICS
- An American study published in a recent year claimed to find evidence of voting by nanditizens. The conclusion was based largely on a survey several years prior in which approadmately 38,000 registered voters were asked both whether they voted and whether they were diens. A total of 309 of those surveyed reported being noncitizens, total of 48 of people also voted. Complete parts (a) through (d) balow a. Based on the survey, what percentage of noncitizens claim to have voted? (Round to the nearest whole number as needed.) b. One difficulty with any survey is response amor, in which, for emple, people accidentally check the wrong bax Suppose that the response error rate for this survey was only 0.1%, meaning that 99.9% of those surveyed answere question Incorrectly? people (Round to the nearest whole number as needed.) c. Assume that the result from part (b) represents citizens who accidentally said they were nondiizens when they were citizens, and that all these people voted. If all…arrow_forwardA professional organization for lion tamers does an approval election for their president. The X below indicates approval. Percentage of Voters 15 3 16 28 31 7 Graves X X X Tuttle X X X Jones X X A) Which person wins the approval election? (Show vote totals) In any Approval election, what effect does a voter who approves of all the candidates have on the outcome of the election? B)arrow_forward
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