北大微观经济学课件(英文版)CH31_WELFARE.ppt

chapter thirty-one welfare *中级微观经济学 social choice udifferent economic states will be preferred by different individuals. uhow can individual preferences be “aggregated” into a social preference over all possible economic states? date中级微观经济学 aggregating preferences ux, y, z denote different economic states. u3 agents; bill, bertha and bob. uuse simple majority voting to decide a state? date中级微观经济学 aggregating preferences more preferred less preferred date中级微观经济学 aggregating preferences majority vote results x beats y date中级微观经济学 aggregating preferences majority vote results x beats y y beats z date中级微观经济学 aggregating preferences majority vote results x beats y y beats z z beats x date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! date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! date中级微观经济学 aggregating preferences date中级微观经济学 aggregating preferences rank-order vote results (low score wins). date中级微观经济学 aggregating preferences rank-order vote results (low score wins). x-score = 6 date中级微观经济学 aggregating preferences x-score = 6 y-score = 6 rank-order vote results (low score wins). date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). date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). date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). date中级微观经济学 manipulating preferences uas well, most voting schemes are manipulable. ui.e. one individual can cast an “untruthful” vote to improve the social outcome for himself. uagain consider rank-order voting. date中级微观经济学 manipulating preferences these are truthful preferences. date中级微观经济学 manipulating preferences these are truthful preferences. bob introduces a new alternative date中级微观经济学 manipulating preferences these are truthful preferences. bob introduces a new alternative date中级微观经济学 manipulating preferences these are truthful preferences. bob introduces a new alternative and then lies. date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 date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 date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 date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! date中级微观经济学 desirable voting rule properties u1. if all individuals preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. u2. if all individuals rank x before y then so should the voting rule. u3. social preference between x and y should depend on individuals preferences between x and y only. date中级微观经济学 desirable voting rule properties ukenneth arrows impossibility theorem: the only voting rule with all of properties 1, 2 and 3 is dictatorial. date中级微观经济学 desirable voting rule properties ukenneth arrows impossibility theorem: the only voting rule with all of properties 1, 2 and 3 is dictatorial. uimplication is that a nondictatorial voting rule requires giving up at least one of properties 1, 2 or 3. date中级微观经济学 social welfare functions u1. if all individuals preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. u2. if all individuals rank x before y then so should the voting rule. u3. social preference between x and y should depend on individuals preferences between x and y only. date中级微观经济学 social welfare functions u1. if all individuals preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. u2. if all individuals rank x before y then so should the voting rule. u3. social preference between x and y should depend on individuals preferences between x and y only. give up which one of these? date中级微观经济学 social welfare functions u1. if all individuals preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. u2. if all individuals rank x before y then so should the voting rule. u3. social preference between x and y should depend on individuals preferences between x and y only. give up which one of these? date中级微观经济学 social welfare functions u1. if all individuals preferences are complete, reflexive and transitive, then so should be the social preference created by the voting rule. u2. if all individuals rank x before y then so should the voting rule. there is a variety of voting procedures with both properties 1 and 2. date中级微观经济学 social welfare functions uui(x) is individual is utility from overall allocation x. date中级微观经济学 social welfare functions uui(x) is individual is utility from overall allocation x. uutilitarian: date中级微观经济学 social welfare functions uui(x) is individual is utility from overall allocation x. uutilitarian: uweighted-sum: date中级微观经济学 social welfare functions uui(x) is individual is utility from overall allocation x. uutilitarian: uweighted-sum: uminimax: date中级微观经济学 social welfare functions usuppose social welfare depends only on individuals own allocations, instead of overall allocations. ui.e. individual utilit