When there are several candidates or alternatives in an election, and there is no clear winner with a majority, runoff elections are often used to determine the winner. Sometimes the order of the runoffs is determined by the number of votes received, while at other times it may be determined by some other method (even as simple as drawing straws).
Ten members of the city council are voting on three budget options, referred to as A, B, and C. The preferences of the council members are summarized as follows:
Four members prefer A to B, and B to C.
Three members prefer B to C, and C to A.
Three members prefer C to A, and A to B.
a. Which option is selected if the council first chooses between A and B, and then chooses between the winner and C? (Note: You should assume that if voters prefer A to B and B to C, then they would prefer A to C when selecting between those two choices. This principle is referred to as transitivity, and underlies all our work with preference schedules.)
b. Which option is selected if A and C are considered first, with the winner against B?
c. Which option is selected if B and C are considered first, with the winner against A?
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