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Suppose that there exist three voters, each of whom is given three alternatives: A, B and C. There exist six possible strict preference orderings for these three alternatives: A>B>C, A>C>B, B>C>A, B>A>C, C>A>B, and C>B>A. The first voter has preferences A>B>C. The second voter has preferences B>C>A. Preferences of the third voter are unknown. How many of the six possible preference orderings, if selected by the third voter, would produce a voting cycle? (In a voting cycle, A defeats B, B defeats C, and C defeats A).
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