3.17. Consider the social choice function that selects as a winner the candidate (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.
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3.17. Consider the social choice function that selects as a winner the
candidate (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.
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Solved in 2 steps
- 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.When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .Suppose there are only five people in a society and each favors one of the five highway construction options in Table 16.2 (include no highway construction as one of the options). Explain which of these highway options will be selected using a majority paired-choice vote. Will this option be the optimal size of the project from an economic perspective?
- Suppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2. In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid. a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…There are three bidders participating in a first-price auction for a painting. Each bidder has a private, independent value vi for such a painting that is drawn uniformly from [0,1] Assume that each bidder i has a linear bidding function bi=avi, where a>0. What is the bidding strategy of bidder i , namely bi in the Bayesian equilibrium?In this version of the ultimatum game experiment, one participant is given £100, and is told to offer to split that amount with another participant. The second player can either refuse to accept the division, in which case the participant receiving the £100 has to give it back, or can accept the division, in which case, the player receiving the money splits the £100 as proposed. For the participant who has to accept or reject the offer A) The best strategy is to accept any offer which meets the social norm for fairness. B) The best strategy is to threaten to turn down any transfer of less than £100 to ensure that the person receiving the money makes a fair offer. C) There is a dominant strategy to accept any offer because gaining some money is better than gaining no money D) There is a dominant strategy to turn down any offer other than £50 because an unequal split would be unfair.
- 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.Explain the differce between oral auctions and second-price auctionsWho detected the endowment effect first? Tell us about the design of the experiment and its main conclusions.
- Consider the charity auction. In many charity auctions, altruistic celebrities auction objects with special value for their fans to raise funds for charity. Madonna, for example, held an auction to sell clothing worn during her career and raised about 3.2 million dollars. In the charity auction the winner of the lot is the highest bidder. The difference with the standard auction is that all bidders are required to pay an amount equal to what they bid. Suppose there are two bidders and assume bidders have valuations randomly drawn from the interval [2, 4] according to the uniform distribution. 1. Derive the equilibrium bidding function. Hint: After getting the differential equation given by the FOC, propose a non-linear bidding function b(v) = α + βv2 as solution. Your task is to find α and β. 2. Derive the revenue of the seller in the charity auction. 3. Would the seller obtain higher profits if she organized a first-price sealed bid auction instead? A. Yes, higher revenue B. No, lower…Which statements are true or false? S1: Multiple equilibria is a condition in which more than one equilibriumexists. S2: These equilibria sometimes may be ranked, in the sense that oneis preferred over another, but the unaided market will not move theeconomy to the preferred outcome.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…