University of OregonDepartment of EconomicsEconomics 340: Issues in Public EconomicsFall 2016Instruc
University of OregonDepartment of EconomicsEconomics 340: Issues in Public EconomicsFall 2016Instructor: Nathan BiemillerProblem Set 3Due Thursday, December 1, in class20 pointsNote: for this problem set, remember that in a Borda count system, each individual ranks alloptions, and points are awarded as follows: the last-place option receives one point, second-tolast receives two points, and so on up to the best option, which receives a number of pointsequal to the number of possible options. The points are summed over all the individuals, andthe option with the most points wins.1. Majority voting (3 points)Suppose there are three voters: Michael, Bugs, and Lola. They need to decide whetherto have low (L), medium (M), or high (H) levels of spending on public art installations.Suppose that their preferences orderings are as follows: Rank123 MichaelMLH BugsLMH LolaHML Which level of public art spending wins if the election is H vs. L? L vs. M? M vs. H?Does pairwise majority voting lead to a stable collective decision-making rule in this case? 1 2. Voting cycles (5 points)The preferences of three voters, Mike, Henry, and Owen, over alternatives A, B, and C,can be described as follows: Mike: A B CHenry: B C AOwen: C A B a) Suppose that one proposal will be selected from the three using pairwise majorityvoting. Voters will choose between two alternatives, and then choose between thewinner of the first round and the third alternative.i) If you control the order of the proposals and prefer outcome A, how should youorder the proposals on the agenda? ii) If you control the order of the proposals and prefer outcome B, how should youorder the proposals on the agenda? iii) If you control the order of the proposals and prefer outcome C, how should youorder the proposals on the agenda? b) Demonstrate that the social preferences implied by pairwise majority voting fromthis example violate transitivity. c) Plot the three policy choices A, B, and C alphabetically and plot each voter’s preference over the policies. Demonstrate that two of the voters have single-peakedpreferences and one has double-peaked preferences. Which voter has double-peakedpreferences? 2 3. Plurality and rank-order voting (4 points)Suppose the preferences over three policy options of 100 voters can be summarized by thetable below:Number of voters:1st choice2nd choice3rd choice 25ABC 26 2A BC AB C 8BCA 4CAB 35CBA a) If the voters choose a single proposal using the plurality method, which proposal isselected?b) If the voters choose a single proposal using a Borda count, which proposal is selected?c) If the winner changed, explain why. Argue why each method might be perceived asmore fair. 4. Independence of irrelevant alternatives (4 points)Suppose we have three voters whose preferences over policy options A,B,C,D,E are:1: A 1 B 1 C 1 D 1 E2: B 2 C 2 D 2 A 2 E3: C 3 D 3 E 3 A 3 Ba) Using a Borda count, how does the social preference rank A relative to B?b) How could you change one voter’s preferences over A and C (without changing thatvoter’s preferences over A and B) so that the social preference over A and B willswitch?c) Explain how this violates the independence of irrelevant alternatives. 3 5. Inefficiency of the median voter (4 points)Show that with uniform benefits and proportional taxation, then the outcome of majority voting (as determined by the median voter theorem) is inefficient when medianincome is less than mean income (so the income distribution is right-skewed). Dothis by comparing the median voter’s decision condition to the condition that leadsto socially beneficial outcomes. 4