(a) Is the social preference ordering de?ned in this way complete? Re?exive?? Transitive? (b) If everyone prefers ac to y, will the Borda count rank :10 as socially pre? ferred to 3/? Explain your answer (0) Suppose that there are two voters and three candidates, :10, y, and 2. Suppose that Voter 1 ranks the candidates, :10 ?rst, 2 second, and y third. Suppose that Voter 2 ranks the candidates, y ?rst, :10 second, and 2 third. What is the Borda count for ac?? For y?? For z?? Now suppose that it is discovered that candidate 2 once lifted a beagle by the ears. Voter 1, who has rather large ears himself, is appalled and changes his ranking to :10 ?rst, y second, 2 third. Voter 2, who picks up his own children by the ears, is favorably impressed and changes his ranking to y ?rst, 2 second, :10 third. Now what is the Borda count for :v?? For y?? For 2? (d) Does the social preference relation de?ned by the Borda count have the property that social preferences between :10 and y depend only on how people rank :10 versus y and not on how they rank other alter? natives? Explain
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