Question

In: Statistics and Probability

18. In the election shown below under the Borda Count method, explain why voters in the...

18. In the election shown below under the Borda Count method, explain why voters in the second
column might be inclined to vote insincerely. How could it affect the outcome of the election?
Number of voters 20 18
1st choice A B
2nd choice B A
3rd choice C C

Solutions

Expert Solution

PART-I

Suppose there are two “major-party” candidates (A and B), and one “minor-party candidate” (C).

C’s supporters can now honestly rank C first, rather than having to worry about “wasting their vote”.

But B supporters may decide, “A is the strongest threat to B, so I should rank A last whether or not I prefer A over C” This is called “burying”

PART-II

receiving a majority of the first-place votes WILL NOT guarantee a victory under the Borda Count method

  1. If a voting method does not satisfy the Majority Criterion, then it cannot satisfy the Condorcet Criterion. I Reason: If Candidate Q receives a majority of the first-place votes, then Q would beat any other candidate head-to-head, so Q is a Condorcet candidate.
  2. If a voting method satisfies the Condorcet Criterion, then it also satisfies the Majority Criterion. I On the other hand, it is possible for a voting method to satisfy the Majority Criterion, but not the Condorcet Criterion.

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