Question

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 of a road ($100) or her third choice of a weather warning system ($0).

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

b. Across all three voters, how many votes are there in favor of national defense? The road? The weather warning system?

     Votes for national defense:

     Votes for road:

     Votes for weather warning system:

c. If a paired-choice vote is taken of national defense versus the road, which one wins?

      (Click to select)  National defense  Road  Indeterminate

d. If a paired-choice vote is taken of the road versus the weather warning system, which one wins?

      (Click to select)  Indeterminate  Weather warning system  Road

e. If a paired-choice vote is taken of national defense versus the weather warning system, which one wins?

      (Click to select)  Indeterminate  Weather warning system  National defense

Answer 1

Answers-

a- Garcia purchase 32 votes for support of National Defence and Garcia purchase 5 votes for support for roads.

Number of Votes Purchased By Each Voter For The LIsted Public Projects-

Public Good Garcia Johnson Lee

National Defence 32 4 12   

Road 5 17 5

Weather Warning System 0 6 10

b-Across all the three voter , the votes are as follows -

Votes for national defense: 48 votes

     Votes for road: 27 votes

     Votes for weather warning system: 16 votes

c- The National Defence wins in the paired-choice vote is taken of national defense versus the road by margin of 21 votes.

d- The Road wins in paired-choice vote is taken of the road versus the weather warning system .

e-The National Defence wins in paired-choice vote is taken of national defense versus the weather warning system.