An election is held among four candidates (A, B, C, and D). Using a voting method we will call X, the winner of the election is candidate A. However, candidate D has more than 50% of the possible votes. Based on this information, we can say that voting method X violates the O Condorcet criterion O monotonicity criterion. O independence of irrelevant alternatives criterion. O majority criterion.

An election is held among four candidates (A, B, C, and D). Using a voting method we will call X, the winner of the election is candidate A. However, candidate D has more than 50% of the possible votes. Based on this information, we can say that voting method X violates the O Condorcet criterion O monotonicity criterion. O independence of irrelevant alternatives criterion. O majority criterion.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

An election is held among four candidates (A, B, C, and D). Using a voting
method we will call X, the winner of
the election is candidate A. However, candidate D has more than 50% of the
possible votes. Based on this
information, we can say that voting method X violates the
O Condorcet criterion
O monotonicity criterion.
O independence of irrelevant alternatives criterion.
O majority criterion.

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Give an example that illustrates why top-two IRV violates the Condorcet criterion. A. A candidate that beats all other candidates head-to-head but is not one of the top two candidates is eliminated in the first round of top-two IRV, but wins under the Condorcet criterion. B. A candidate that has the most first-place votes and last-place votes is eliminated in the first round of top-two IRV, but wins under the Condorcet criterion. C. A candidate that has the most first-place votes, but is not one of the top two candidates is eliminated in the first round of top-two IRV, but wins under the Condorcet criterion. D. A candidate that beats all other candidates head-to-head and is one of the top two candidates is eliminated in the first round of top-two IRV, but wins under the Condorcet criterion.
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Suppose 101 people vote in an election between 4 candidates using a modified Borda count. In this modified count, last place votes count as 1 point, 3rd place votes count as 2 points, and 2nd place votes count as 3 points. If we make 1st place votes worth enough points, we can force this election to satisfy the majority criterion. What is the smallest number of points that we could assign to 1st place votes in order to guarantee that the majority criterion is satisfied?
28. An exit poll of 300 persons showed that candidate A received 53 % of the vote in a given precinct. If you were the pollster, would you call the election for candidate A based on these results?
Answer the following questions for the voter profile shown to the right. Number of Voters Ranking 17 a >b>c> d >e (a) Which alternative is a majority candidate? (b) Which alternative is the Borda method winner? (c) Does the Borda method violate the majority criterion for the voter profile? 4 b>c>d>e > a 3 c>d>b> e>a 4 d>b>c> a >e 3. e >c>d> a > b (a) Which alternative is a majority candidate? e a There is no majority candidate. (b) Which alternative is the Borda method winner? e a b. O There is no Bordamethod winner. (c) Does the Borda method violate the majority criterion for the voter profile? Yes No O Time Remaining: 01:53:38 Next E O O O @ O 0 o
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