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1、2018/10/16,中级微观经济学,Chapter Thirty-One,Welfare,2018/10/16,中级微观经济学,Social Choice,Different economic states will be preferred by different individuals. How can individual preferences be “aggregated” into a social preference over all possible economic states?,2018/10/16,中级微观经济学,Aggregating Preferences,x
2、, y, z denote different economic states. 3 agents; Bill, Bertha and Bob. Use simple majority voting to decide a state?,2018/10/16,中级微观经济学,Aggregating Preferences,More preferred,Less preferred,2018/10/16,中级微观经济学,Aggregating Preferences,Majority Vote Results,x beats y,2018/10/16,中级微观经济学,Aggregating Pr
3、eferences,Majority Vote Results,x beats y y beats z,2018/10/16,中级微观经济学,Aggregating Preferences,Majority Vote Results,x beats y y beats z z beats x,2018/10/16,中级微观经济学,Aggregating Preferences,Majority Vote Results,x beats y y beats z z beats x,No socially best alternative!,2018/10/16,中级微观经济学,Aggregati
4、ng Preferences,Majority Vote Results,x beats y y beats z z beats x,Majority voting does not always aggregate transitive individual preferences into a transitive social preference.,No socially best alternative!,2018/10/16,中级微观经济学,Aggregating Preferences,2018/10/16,中级微观经济学,Aggregating Preferences,Rank
5、-order vote results (low score wins).,2018/10/16,中级微观经济学,Aggregating Preferences,Rank-order vote results (low score wins).,x-score = 6,2018/10/16,中级微观经济学,Aggregating Preferences,x-score = 6 y-score = 6,Rank-order vote results (low score wins).,2018/10/16,中级微观经济学,Aggregating Preferences,x-score = 6 y
6、-score = 6 z-score = 6,Rank-order vote results (low score wins).,2018/10/16,中级微观经济学,Aggregating Preferences,x-score = 6 y-score = 6 z-score = 6,No state is selected!,Rank-order vote results (low score wins).,2018/10/16,中级微观经济学,Aggregating Preferences,x-score = 6 y-score = 6 z-score = 6,No state is s
7、elected!,Rank-order voting is indecisive in this case.,Rank-order vote results (low score wins).,2018/10/16,中级微观经济学,Manipulating Preferences,As well, most voting schemes are manipulable. I.e. one individual can cast an “untruthful” vote to improve the social outcome for himself. Again consider rank-
8、order voting.,2018/10/16,中级微观经济学,Manipulating Preferences,These are truthful preferences.,2018/10/16,中级微观经济学,Manipulating Preferences,These are truthful preferences. Bob introduces a new alternative,2018/10/16,中级微观经济学,Manipulating Preferences,These are truthful preferences. Bob introduces a new alte
9、rnative,2018/10/16,中级微观经济学,Manipulating Preferences,These are truthful preferences. Bob introduces a new alternative and then lies.,2018/10/16,中级微观经济学,Manipulating Preferences,These are truthful preferences. Bob introduces a new alternative and then lies.,Rank-order vote results.,x-score = 8,2018/10
10、/16,中级微观经济学,Manipulating Preferences,These are truthful preferences. Bob introduces a new alternative and then lies.,Rank-order vote results.,x-score = 8 y-score = 7,2018/10/16,中级微观经济学,Manipulating Preferences,These are truthful preferences. Bob introduces a new alternative and then lies.,Rank-order
11、 vote results.,x-score = 8 y-score = 7 z-score = 6,2018/10/16,中级微观经济学,Manipulating Preferences,These are truthful preferences. Bob introduces a new alternative and then lies.,Rank-order vote results.,x-score = 8 y-score = 7 z-score = 6 -score = 9,z wins!,2018/10/16,中级微观经济学,Desirable Voting Rule Prop
12、erties,1. If all individuals preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals preferences bet
13、ween x and y only.,2018/10/16,中级微观经济学,Desirable Voting Rule Properties,Kenneth Arrows Impossibility Theorem: The only voting rule with all of properties 1, 2 and 3 is dictatorial.,2018/10/16,中级微观经济学,Desirable Voting Rule Properties,Kenneth Arrows Impossibility Theorem: The only voting rule with all
14、of properties 1, 2 and 3 is dictatorial. Implication is that a nondictatorial voting rule requires giving up at least one of properties 1, 2 or 3.,2018/10/16,中级微观经济学,Social Welfare Functions,1. If all individuals preferences are complete, reflexive and transitive, then so should be the social prefer
15、ence created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals preferences between x and y only.,2018/10/16,中级微观经济学,Social Welfare Functions,1. If all individuals preferences are complete, refle
16、xive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals preferences between x and y only.,Give up which one of these?,2018/10/16,中级
17、微观经济学,Social Welfare Functions,1. If all individuals preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. 2. If all individuals rank x before y then so should the voting rule. 3. Social preference between x and y should depend on individuals preferences between x and y only.,
