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).
The school board is considering three options for a new career-counseling program. The preferences of the board members are summarized as follows:
Two members prefer A to B, and B to C.
Five members prefer A to C, and C to B.
Four members prefer B to A, and A to C.
Four members prefer C to B, and B to A.
a. Which option is selected if the council first chooses between A and B, and then chooses between the winner and C?
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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