72 Chapter 2 preferences over some set of alternatives. For that society, majority rule violates at least one of transitivity, unanimity, or IIA. (c) Consider some arbitrary aggregation procedure that is not dictatorship. There exists a real society in the world (i.e., an actual country, city, or what have you) in which that aggregation procedure violates at least one of transitivity, unanimity, or IIA. (d) Consider some arbitrary aggregation procedure that is not dictatorship. You can imagine a society (i.e., a collection of individuals with preferences over alternatives), though it may not actually exist in the world, such that the aggregation procedure violates at least one of transitivity, unanimity, or IIA. Consider a society made up of three peopleDan (D), Erin (E), and Fred (F). The society must choose between three immigration policiesClosed Borders (C), Open Borders (0), and Regulated Immigration (R). Suppose preferences are as follows: R>DC>-DO C>ER>EO O>-FR>-FC. (a) Write down an ideological ordering on the alternative such that this issue is described by that ideology. (b) What is the preferred policy of the median voter under that ideology? (c) Use this fact to make an argument for why pursuing that policy might be considered serving the public interest in this setting. (d) Make an argument for why you might nonetheless reject the idea that this policy is clearly in the public interest or explain why you think there is no such argument. Imagine a society made up of two kinds of peoplethe Xs and the Ys. There are an equal number of Xs and Ys. The society is considering three policy actions: a, b, and 6. Each individual in the society cares only about his or her personal wealth. . Under action a, all members of society have wealth 10. 0 Under action b, the Xs each have wealth 11 and the Ys each have wealth 12. 0 Under action c, the X 5 each have wealth 15 and the Ys each have wealth 9. (a) Dene a policy as an action and a budget balanced transfer scheme. All budget balanced transfer schemes are feasible. People have quasi-linear preferences. Which policies are Pareto efcient? (b) Call the transfer scheme where no one gets any transfer to. Which of the following is true: i. (a, to) Pareto dominates (b, to). ii. (1'), to) Pareto dominates (a, to). iii. Neither of these two policies Pareto dominates the other. (c) Identify a normative framework that would be in favor of the move from (b, to) to (C, to) and explain why. (d) Identify a normative framework that would be opposed to the move from (b, to) to (c, to) and explain why. Explain why moving from a Pareto inefcient to a Pareto efcient policy need not be an unambiguously good policy decision. Give a policy example that you think illustrates your point. I argued that allowing for utility transfers and quasi-linear preferences \"built a bridge\" between Pareto efciency and Pareto improvementsthat is, made