5. Sparta and Thebes are at war. The Athenians must decide between three options A Remain independent S Ally with Sparta T Ally with Thebes Three equally-sized factions have different preferences over these options, given by 1 A > S > T (Peace-lovers) 2 S > T > A (The fighters) 3 T > A > S (Anti-Spartans) The Athenians decide on political matters through pairwise majority voting.. a) Does majority voting provide a Condorcet winner? The outcome will be decided by a two-round election. . Two options will be voted against in the first round. . The winner faces the third option in the second, round. . The winner of the second round will be implemented. The statesman Pericles will decide how the rounds are organized. Pericles belongs to faction 3 and wants to ally with Thebes. b) If Athenians vote sincerely, what option will Pericles put in the second round? C ) If Athenians vote strategically, and know each others' preferenceswhat option will Pericles put in the second round