Ch31 - Chapter Thirty-One Welfare Social Choice Different...

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Chapter Thirty-One Welfare
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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?
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Aggregating Preferences x , y , z denote different economic states. 3 agents; Bill, Bertha and Bob. Use simple majority voting to decide a state?
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Aggregating Preferences Bill Bertha Bob x y z y z x z x y More preferred Less preferred
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Aggregating Preferences Bill Bertha Bob x y z y z x z x y Majority Vote Results x beats y
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Aggregating Preferences Bill Bertha Bob x y z y z x z x y Majority Vote Results x beats y y beats z
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Aggregating Preferences Bill Bertha Bob x y z y z x z x y Majority Vote Results x beats y y beats z z beats x
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Aggregating Preferences Bill Bertha Bob x y z y z x z x y Majority Vote Results x beats y y beats z z beats x No socially best alternative!
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Aggregating Preferences Bill Bertha Bob x y z y z x z x y 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!
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Aggregating Preferences Bill Bertha Bob x(1) y(1) z(1) y(2) z(2) x(2) z(3) x(3) y(3)
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Aggregating Preferences Bill Bertha Bob x(1) y(1) z(1) y(2) z(2) x(2) z(3) x(3) y(3) Rank-order vote results (low score wins).
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Aggregating Preferences Bill Bertha Bob x(1) y(1) z(1) y(2) z(2) x(2) z(3) x(3) y(3) Rank-order vote results (low score wins). x-score = 6
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Aggregating Preferences Bill Bertha Bob x(1) y(1) z(1) y(2) z(2) x(2) z(3) x(3) y(3) x-score = 6 y-score = 6 Rank-order vote results (low score wins).
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Aggregating Preferences Bill Bertha Bob x(1) y(1) z(1) y(2) z(2) x(2) z(3) x(3) y(3) x-score = 6 y-score = 6 z-score = 6 Rank-order vote results (low score wins).
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Aggregating Preferences Bill Bertha Bob x(1) y(1) z(1) y(2) z(2) x(2) z(3) x(3) y(3) x-score = 6 y-score = 6 z-score = 6 No state is selected! Rank-order vote results (low score wins).
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Aggregating Preferences Bill Bertha Bob x(1) y(1) z(1) y(2) z(2) x(2) z(3) x(3) y(3) 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).
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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.
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Manipulating Preferences Bill Bertha Bob x(1) y(1) z(1) y(2) z(2) x(2) z(3) x(3) y(3) These are truthful preferences.
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Bill Bertha Bob x(1) y(1) z(1) y(2) z(2) x(2) z(3) x(3) y(3) These are truthful preferences. Bob introduces a
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Ch31 - Chapter Thirty-One Welfare Social Choice Different...

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