The goals of this problem set were to test your knowledge, and “stretch” some of the material discussed in class. Everyone did an excellent job! Now you guys are the masters and I am the apprentice! Keep up the good work!
Problem Set One True or False
1) Whenever you have only two voters or stakeholders then they are both pivotal.
Answer: False
Explanation:
Counter Example 1: Neither voter is pivotal.
Counter Example 2: Both voters are pivotal. Here we have a tie as to which policy will win. However, excluding either stakeholder leads to a definite policy winner. Thus each voter changes the decision from an “ambiguous outcome” to a clear-cut winner.
I think Carl did a good job of fleshing this out. Carl said that either they are both pivotal or they are both not pivotal.
Counter Example 4:
In this case, Timothy is “pivotal” and Ronaldo is not.
The purpose of this problem was to show the tricky nature of making generalizations. One of the keys to the demand revelation is experimenting with different scenarios and possibilities. “What if” thinking is essential to the procedure.
2) The VCG measures the intensity of the voter’s preferences.
Answer: True
Explanation:
Stakeholder |
Policy 1 |
Policy 2 |
Timothy |
30 |
0 |
Ronaldo |
30 |
-5 |
Stakeholder |
Policy 1 |
Policy 2 |
Timothy |
30 |
15 |
Ronaldo |
15 |
30 |
Stakeholder |
Policy 1 |
Policy 2 |
Timothy |
15 |
30 |
Ronaldo |
30 |
5 |
The VCG is not a “majority rules” voting procedure. The winning policy is the one with the most total net benefits; not the one with the most support. Indeed, examine the following scenario:
Here policy 1 wins, even though the majority of people oppose it. The intensity of the preferences determines who wins; not the quantity (number of voters). One downside would be income inequality; a few wealthy people could out-vote a majority of poor people. I will address this issue later, in greater detail.
3) The VCG can always be used to completely solve the free rider.
False
No. It can solve it completely, but certainly not always. In these cases it can still lessen the free rider problem, and lead to more efficient outcomes.
4) When you have large numbers of voters the Clarke tax increases!
False
Carl pointed out that given certain assumptions, the Clarke tax can actually increase as you add more and more stakeholders. Eventually, however you approach an upper limit after which the Clarke tax decreases. However, it is technically possible to have a large number of voters (it all depends upon what you call “large number”) and increasing Clarke taxes!
Stakeholder |
Policy 1 |
Policy 2 |
A |
$1000 |
|
B |
|
$5 |
C |
|
$5 |
D |
|
$5 |