Voters arrive at a social ranking of alternatives by consulting a "holy book": the social ranking is the ranking found in this book. Which of the Arrow's axioms defining an attractive preference aggregation method is violated by this method? (a) Non-dictatorship (b) Independence of irrelevant alternatives (c) The Pareto principle (d) Unrestricted domain
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- 3.17. Consider the social choice function that selects as a winner thecandidate (or candidates) with the most second-place votes.(a) Show that this method violates monotonicity.(b) Show that this method violates the Pareto criterion.(c) Show that this method is anonymous and neutral.The Condorcet paradox illustrates Arrow’simpossibility theorem by showing that pairwisemajority votinga. is inconsistent with the principle of unanimity.b. leads to social preferences that are not transitive.c. violates the independence of irrelevantalternatives.d. makes one person in effect a dictator.Who detected the endowment effect first? Tell us about the design of the experiment and its main conclusions.
- Consider the following two sets of individuals and their group preference rankings, aggregated using the same voting rule. 1: individual preferences: x>y>z>w, y>z>w>x, and z>w>x>y group preferences: x>Gy, z>Gx, w>Gx, y>Gw, y>Gz and z>Gw 2:individual preferences: y>z>x>w, y>w>x>z, and y>w>z>x group preferences: y>Gx, y>Gw, z>Gy, x>Gw, z>Gx, and z>Gw Question: Which of Arrow's conditions (P, D, I, or Transitivity) is violated by their group preferences? (hint: checking I requires comparing the outcomes in the two different groups to find a violation).Suppose that friends Jennifer, Stephanie, and Megan cannot agree on how much to spend for a bouquet of flowers to send to a person who allowed them to use her beach house for the weekend. Jennifer wants to buy a moderately priced bouquet, Stephanie wants to buy an expensive bouquet, and Megan wants to buy a very expensive bouquet. Assuming no paradox of voting, majority voting will result in the decision to buy Multiple Choice an inexpensive bouquet. a very expensive bouquet. a moderately priced bouquet. an expensive bouquet. BTrue or False 31.The decline in the percentage of the federal government’s budget devoted to national defense is evidence of the lack of new demand for U.S. military activity. a.True b.False 32.In 2000, total United States spending on national defense was less than five percent of GDP. a.True b.False 33.The first priority of national defense spending is the defense of economic interests abroad. a.True b.False 34.Determining the optimal level of military expenditures is easy because the preferences of the median voter a reflected in the vote for president a.True b.False 35.If two nations are equally armed it is highly likely that neither will initiate a conflict. a.True b.False 36.The optimal sharing group for national defense is the size of a nation. a.True b.False 37.Spending so much on arms that the economy of an adversary collapses is called market warfare. a.True b.False 38.Dictatorships, whether stable or…
- Which of the following is true? a. Arrow’s Impossibility Theorem states that There is no voting method that will satisfy a reasonable set of fairness criteria when there are three or candidates. b. Gibbard-Satterthwaite's theorem states that there is a voting method is completely resistant to strategic voting. c. None of the given choices d. May's Theorem states that the majority method will always have a winner.Consider the following voting game. There are three players, 1, 2 and 3. And there are three alternatives: A, B and C. Players vote simultaneously for an alternative. Abstaining is not allowed. Thus, the strategy space for each player is {A, B, C}. The alternative with the most votes wins. If no alternative receives a majority, then alternative A is selected. Denote ui(d) the utility obtained by player i if alternave d {A, B, C} is selected. The payoff functions are, u1 (A) = u2 (B) = u3 (C) = 2 u1 (B) = u2 (C) = u3 (A) = 1 u1 (C) = u2 (A) = u3 (B) = 0 a. Let us denote by (i, j, k) a profile of pure strategies where player 1’s strategy is (to vote for) i, player 2’s strategy is j and player 3’s strategy is k. Show that the pure strategy profiles (A,A,A) and (A,B,A) are both Nash equilibria. b. Is (A,A,B) a Nash equilibrium? Comment.Arrow's impossibility theorem states that under certain assumptions about preferences, no voting system exists that satisfies all of the following properties: • Unanimity • Transitivity • Independence of irrelevant alternatives • No dictators
- Consider three individuals with the following preferences: Suppose the following dynamic voting protocol is in effect: first, there is a vote between a and b; then the winner goes against c; and the winner of this contest will be implemented. Focus on SPE where voters do not use “weakly dominated” strategies at any stage. (a) Show that these preferences are single peaked, but sincere voting is not equilibrium behavior. (b) Characterize the SPE of this game under strategic voting by all players. (c) Consider a generalization in which the society H consists of H individuals and there are finite number of policies, R = {p1, p2,...,pM}. For simplicity, suppose that H is an odd number. Voting takes M − 1 stages. In the first stage, there is a vote between p1 and p2. In the second stage, there is a vote between the winner of the first stage and p3, until we have a final vote against pM. The winner of the final vote is the policy choice of the society. Prove that if…Answer it correctly please. I ll rate accordingly with multiple votes. Explain why the options are correct or incorrect.Question 2 Demonstrate, by way of example, and explain fully, taking noting of the underlying assumptions, how you would derive Hicksian and Marshallian demand functions. What are the differences between these? Question 3 In the Walrasian world, Pareto optimal allocations are crucial in establishing an equilibrium outcome with respect to welfare. Give an exposition of the two Welfare Theorems, demonstrating also that they are Pareto efficient