Please turn in your homework at the start of class. Please staple or use a paperclip if you use multiple sheets. You may collaborate with (but not copy from!) others. But (a) please try them by yourself first, and
\n(b) acknowledge anyone you work with.<\/p>\n
1. Suppose there are only two people: person 1 prefers x to z and z to y (xP1zP1y), and
\nperson 2 prefers y to x and x to z (yP2xP2z). Suppose that our CCR ranks y above
\nx (yPx) for this profile of individual preferences. Suppose also that our CCR always
\ndelivers a transitive weak social preference relation R, and satisfies the Strong Pareto
\nprinciple (defined by Sen on p. 101) and Independence of Irrelevant Alternatives.
\nShow that our CCR must always rank y above z whenever person 2 prefers y above z,
\nno matter what person 1 prefers.
\n2. Our proof of Arrow\u2019s theorem in class (based on Sen\u2019s pp. 286\u2013289) appealed to two
\nlemmas: the Spread of Decisiveness and the Contraction of Decisive Sets. Suppose
\nwe relax the assumption of completeness for social preference. Would the Spread of
\nDecisiveness still hold? Would Contraction of Decisive Sets still hold? Explain why
\nor why not.
\n3. Would the Method of Majority Decision qualify as a SWF if restricted to cases where
\nthere are two individuals and three alternatives? Prove your answer.
\n4. Suppose that individuals are allowed to have incomplete preferences. Say that x is
\npseudo-Pareto-superior to y if and only if someone prefers x to y (for some i, xPiy)
\nand no one prefers y to x (for all i, \u00acyPix). Show that, when individuals can have
\nincomplete preferences, pseudo-Pareto-superiority is not a transitive relation.
\n5. Give an example in which the Pareto-extension rule violates Positive Responsiveness.<\/p>\n","protected":false},"excerpt":{"rendered":"
Please turn in your homework at the start of class. Please staple or use a paperclip if you use multiple sheets. You may collaborate with (but not copy from!) others. But (a) please try them by yourself first, and (b) acknowledge anyone you work with. 1. Suppose there are only two people: person 1 prefers […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-11486","post","type-post","status-publish","format-standard","hentry","category-economics"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/11486","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=11486"}],"version-history":[{"count":2,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/11486\/revisions"}],"predecessor-version":[{"id":11489,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/11486\/revisions\/11489"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=11486"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=11486"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=11486"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}