SECTION 12B HIGHLIGHTS
Assignment: Read about Theory of Voting in Section 12B of the text. Do pp. 676-678 RQ(2), BSC(9-11,15-18,22-24,29,30).
Vocabulary: Fairness Criteria, Arrow's Impossibility Theorem
Notes:
In section 12B of the text we consider closely the issue of fairness in
elections with more than two candidates. The methods ( plurality, top-two
runoff, sequential runoffs, Borda count, and pairwise comparison) discussed in
section 12A of the text will be evaluated with regard to four fairness
criterion. The four criterion are as follows:
Criterion 1: If a candidate receives the majority of first place
votes, that candidate should be the winner.
Criterion 2: If a candidate is favored over every other candidate in
pairwise races, then that candidate should be the winner.
Criterion 3: Suppose candidate X is declared the winner of an election, and
then a second election is held. If some voters rank X even higher in the
second election (without changing the order of the other candidates), then X
should also win the second election.
Criterion 4: Suppose candidate X is declared the winner of an election, and
then a second election is held. If voters do not change their
preferences, but one or more of the losing candidates drop out, then X should
also win the second election.
Of the five methods for voting discussed in section 12A of the text, none of the methods satisfy all four of these reasonable fairness criterion.
Arrow's Impossibility Theorem is a landmark application of mathematics to social theory. Arrow proved mathematically that is is impossible to find a voting system that will always satisfy all four fairness criteria.
Skills to be mastered:
1. State the four fairness criteria.
2. Identify the fairness criteria that may be violated by the various voting
methods.
3. State Arrow's Impossibility Theorem.