Math of Voting: Voting Paradoxes
Suppose three people rank the ice cream flavors C, S, and V (chocolate, strawberry, and vanilla) in the following way:
Chet: S > C > V
Omari: C > V > S
Taj: V > S > C
Only one flavor can be bought for a party, so they're going up for a series of runoff votes. That is, two of the flavors will be pitted against each other in a vote, and the winner will face the remaining flavor in a final vote.
For example, if C faces V in a vote, Chet and Omari prefer C to V so that C will win. Then C faces off against S in a vote; since Chet and Taj prefer S to C, S wins the final vote.
If the runoffs can happen in any order, is there a way for chocolate (C) to win the final vote?
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1 solution
First, S should face off against V.
Since Omari and Taj both prefer V to S, V wins.
Now, V faces off against C.
Since Chet and Omari both prefer C to V, C wins.