7. This exercise describes Condorcet's Voting Paradox (Sections 18.3.2 and 19.3.1). Horace, Boris, and Maurice vote...

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7. This exercise describes Condorcet's Voting Paradox (Sections 18.3.2 and 19.3.1). Horace, Boris, and Maurice vote honestly on who should be admitted to their club: Alice, Bob, or Nobody. Their preferences are 12 A <1B <1N B 2 N 2 A N 3 A 3 B. Who wins a vote between Alice and Bob? Who wins between Bob and No- body? Who wins between Nobody and Alice? If we think of the voting as determining a social preference , show that this preference is intransitive, and so democratic societies are collectively irrational in some situations. 7. This exercise describes Condorcet's Voting Paradox (Sections 18.3.2 and 19.3.1). Horace, Boris, and Maurice vote honestly on who should be admitted to their club: Alice, Bob, or Nobody. Their preferences are 12 A <1B <1N B 2 N 2 A N 3 A 3 B. Who wins a vote between Alice and Bob? Who wins between Bob and No- body? Who wins between Nobody and Alice? If we think of the voting as determining a social preference , show that this preference is intransitive, and so democratic societies are collectively irrational in some situations.