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, 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 Preferences,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,Aggregating 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-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-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 selected!,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-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 alternative,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 = 8,2018/10/16,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 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 Properties,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.,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 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 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.,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 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.,