Let's see whether quadratic voting can avoid the paradox of voting that arose in Table 5.3 when using 1p1v in a series of paired-choice majority votes. To reexamine this situation using quadratic voting, the table below presents the maximum willingness to pay of Garcia, Johnson, and Lee for each of the three public goods. Notice that each person's numbers for willingness to pay match her or his ordering of preferences (1st choice, 2nd choice, 3rd choice) presented in Table 5.3. Thus, Garcia is willing to spend more on her first choice of national defense ($400) than on her second choice a road ($100) or her third choice of a weather warning system ($0). TABLE 5.3 Paradox of Voting Preferences Public Good Garcia Johnson Lee National defense 1st choice 3d choice 2d choice Road 2d choice 1st choice 3d choice Weather warning system 3d choice 2d choice 1st choice Election Voting Outcomes: Winner 1. National defense vs. road National defense (preferred by Garcia and Lee) 2. Road vs. weather warning system Road (preferred by Garcia and Johnson) 3. National defense vs. weather warning system Weather warning system (preferred by Johnson and Lee) Individual Voter Willingness to pay for the Listed Public Projects Public Good Garcia Johnson Lee National defense $400 $50 $150 Road 100 300 100 Weather warning system 0 150 250 a. Assume that voting will be done using a quadratic voting system and that Garcia, Johnson, and Lee are each given $500 that can only be spent on purchasing votes (i.e., any unspent money has to be returned). How many votes will Garcia purchase to support national defense? How many for the road? Place those values into the appropriate blanks in the table below and then do the same for the blanks for Johnson and Lee. Assume there are no additional costs beyond the cost of purchasing votes and that votes must be purchased in whole numbers. Instructions: Enter your answers as a whole number. Number of votes Purchased by Each Voter for the Listed Public Projects Public Good Garcia Johnson Lee National defense 12 Road 17 Weather warning system 0 Let's see whether quadratic voting can avoid the paradox of voting that arose in Table 5.3 when using 1p1v in a series of paired-choice majority votes. To reexamine this situation using quadratic voting, the table below presents the maximum willingness to pay of Garcia, Johnson, and Lee for each of the three public goods. Notice that each person's numbers for willingness to pay match her or his ordering of preferences (1st choice, 2nd choice, 3rd choice) presented in Table 5.3. Thus, Garcia is willing to spend more on her first choice of national defense ($400) than on her second choice a road ($100) or her third choice of a weather warning system ($0). TABLE 5.3 Paradox of Voting Preferences Public Good Garcia Johnson Lee National defense 1st choice 3d choice 2d choice Road 2d choice 1st choice 3d choice Weather warning system 3d choice 2d choice 1st choice Election Voting Outcomes: Winner 1. National defense vs. road National defense (preferred by Garcia and Lee) 2. Road vs. weather warning system Road (preferred by Garcia and Johnson) 3. National defense vs. weather warning system Weather warning system (preferred by Johnson and Lee) Individual Voter Willingness to pay for the Listed Public Projects Public Good Garcia Johnson Lee National defense $400 $50 $150 Road 100 300 100 Weather warning system 0 150 250 a. Assume that voting will be done using a quadratic voting system and that Garcia, Johnson, and Lee are each given $500 that can only be spent on purchasing votes (i.e., any unspent money has to be returned). How many votes will Garcia purchase to support national defense? How many for the road? Place those values into the appropriate blanks in the table below and then do the same for the blanks for Johnson and Lee. Assume there are no additional costs beyond the cost of purchasing votes and that votes must be purchased in whole numbers. Instructions: Enter your answers as a whole number. Number of votes Purchased by Each Voter for the Listed Public Projects Public Good Garcia Johnson Lee National defense 12 Road 17 Weather warning system 0
