Intro
Prefs & Voting
Electoral comp.
Voter Turnout
Agency
GIP
SIP
Political Economics
Dr. Marc Gronwald
Dr. Silke Uebelmesser
Ludwig-Maximilians University Munich
Summer term 2010
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Intro
Prefs & Voting
Electoral comp.
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Motivation
Total government spending as fraction of GDP in the late
1990s: Sweden: 60%; Continental Europe: 50%; Japan,
Switzerland, United States: 35%
Spending on the unemployed as fraction of total public
spending: ranges from 2% to 17% within the EU-15
Unemployment insurance replacement rate: ranges from
20% to 90% in the EU-15
Public debt as fraction of GDP: Norway: 40%; Italy and
Belgium: 120%
Inflation: UK: 8%; Germany: 3%
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Motivation
Growth of government took off in many industrial countries
in the mid 1930s as well as in the late 1960s
Slowdown after World War II and in the late 1980s
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Motivation
Economic policy varies greatly across time and place
But there are also common patterns
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Motivation
Why is policy the way it is?
What is policy ought to be?
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Keywords
Social Choice / Voting rules / Preferences
Median voter / Condorcet winner
Electoral competition / Motivation of politicians
Rational voters / Probabilistic voting
Rent seeking
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Intro
Prefs & Voting
Electoral comp.
Voter Turnout
Table of contents
1 Introduction(DR)
2 Preferences and voting (DR)
3 Voter turnout (DR)
4 Electoral competition (SÜ)
5 Agency problems (SÜ)
6 General-interest politics (SÜ)
7 Special-interest politics (DR)
8 Applications
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Textbook literature
Grossman, G.M. and E. Helpman (2001), Special Interest
Politics, Cambridge, Mass: MIT Press.
Mueller, D. (2003), Public Choice III, Cambridge University
Press, Cambridge.
Persson, T. and G. Tabellini (2000), Political Economics —
Explaining Economic Policy, MIT Press, Cambridge.
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2. Preferences and voting
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2.1 Voting rules
Consider 7 voters and 4 alternative policies (A, B, C, D). The
voters’ preferences over the alternatives are defined in the
following Table:
1st
.
.
4th
1
A
B
C
D
2
A
B
C
D
3
A
B
C
D
4
B
C
A
D
5
B
C
D
A
6
C
D
A
B
7
C
D
A
B
Table 1: Preferences I
⇒ How should we aggregate these individual preferences into
”social preferences“?
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2.1 Voting rules
At least 4 different voting rules can be distinguished:
Majority/Plurality rule: All alternatives are voted on
simultaneously. The alternative which receives the
maximum number of votes is selected in the political
process.
⇒ A:3; B:2; C:2 → A wins
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2.1 Voting rules
Pairwise voting without agenda setting (open agenda):
Multiple voting rounds - in each round voting takes place
over two alternatives (pairwise voting). The winning
alternative is opposed against another option. The winning
option in this round is opposed against another ”untested“
option and so on. The alternative which beats all other
alternatives in a pairwise vote is the winner (Condorcet
winner).
⇒ A vs B 5:2; A vs C 3:4; C vs D 7:0; C vs B 2:5; B vs D
5:2; B vs A 2:5
⇒ No Condorcet winner exists
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2.1 Voting rules
Pairwise voting with agenda setting (closed agenda):
The agenda setter determines the order of pairwise voting.
The alternative which survives the last round is the winner.
For instance,
⇒ A vs B 5:2; A vs C 3:4; C vs D 7:0; C wins
⇒ A vs C 3:4; C vs B 2: 5; B vs D 5:2; B wins
⇒ D vs C 0:7; C vs B 2: 5; B vs A 2:5; A wins
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2.1 Voting rules
Borda rule: All alternatives are voted on simultaneously.
Each voter receives k+(k-1)+(k-2)+..+(k-k) points which
he/she can allocate to the alternatives. The most preferred
alternative gets k points, the next most preferred one k-1
points ... The winning alternative is the one with the
maximum number of points. For k=1 the Borda rule and
the Majority/Plurality rule coincide.
k=1⇒ A: 3; B: 2; C: 2 → A wins
k=2⇒ A: 6; B: 7; C: 6; D: 2 → B wins
k=3⇒ A: 12; B: 12; C: 13; D: 5 → C wins
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2.1 Voting rules
Punchline:
Even in this subset of possible political mechanisms the choice
of the aggregation rule is decisive for the political outcome: The
will of society is highly sensitive to the specifics of the political
process and is thereby ambiguous.
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2.1 Voting rules
What are ”desirable“ voting rules?
If voting rules lead to different outcomes how should society
decide among them? Frequently mentioned desirable
properties of voting rules comprise:
Anonymity: This is one of the fundamental principles of
democracy. The political outcome should not depend on
the identity of the voters - only individual preferences
should matter, i.e. a rich voter or a member e.g. of the
political elite/aristocracy matters as much as any other
voter. This principle rules out dictatorships.
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2.1 Voting rules
Neutrality: The voting rule should not introduce a bias in
favor of one option. All options should be treated alike.
Decisiveness: The voting rule must pick a winner.
Positive responsiveness: Increasing the vote for the
winning option should not lead to declare another option a
winner.
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2.1 Voting rules
With only two alternatives we have a powerful result:
Theorem (May’s Theorem)
With only two options the majority rule is the only voting rule
which satisfies the requirements of anonymity, neutrality,
decisiveness and positive responsiveness.
Proof: See Mueller, 2003, p. 135.
What happens if there are more than two alternatives?
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2.1 Voting rules
In the remaining part of this chapter, we study preference
aggregation by pure majority rule which we define by means of
the following assumptions:
A1 Direct democracy. Voters do not elect political agents (as
in a representative democracy) but rather decide on policy
issues themselves.
A2 Sincere voting. Every citizen votes for the alternative that
delivers the highest level of utility according to his/her
preferences. In other words, there is no strategic voting.
A3 Open agenda. Voters decide among pairs of policy options
such that the winner of one round is posed against a
further alternative in the next round. The set of policies
among one has to decide includes all feasible options.
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2.2 Preferences: One-dimensional voting
Example 2.1: Consider pairwise voting without an agenda
setter. The preferences of three voters over three alternatives
are as described in Table 2:
1st
.
3rd
1
A
B
C
2
B
C
A
3
C
A
B
Table 2: Preferences II
A vs. B: 2:1; A vs. C: 1:2; C vs. B: 1:2; B vs A: 1:2 and so on.
Voting is cyclical.
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2.2 Preferences: One-dimensional voting
Fig 2.1
1
A
2
3
B
C
Figure 1: Preferences II
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2.2 Preferences: One-dimensional voting
Voting cycles are closely linked to the concept of transitivity:
Definition (Transitivity)
If A is weakly preferred to B and B is weakly preferred to C,
then A must be weakly preferred to C, i.e. if A B and B C,
then A C.
Discuss transitivity in example 2.1.
We will derive in the following sections sufficient conditions
for the existence of a well-defined majority winner in
elections. In particular, we will introduce the
single-peakedness and the single-crossing condition,
respectively.
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Median voter theorem with single-peakedness
The concept of transitivity (and thus the existence of voting
cycles) is related to the notion of single-peakedness.
Definition (Single-peakedness)
Let qi∗ denote voter i’s most preferred alternative. Then, if
q 00 ≤ q 0 ≤ qi∗ or q 00 ≥ q 0 ≥ qi∗ , it follows that ui (q 00 ) ≤ ui (q 0 ).
Are preferences in example 2.1 and the introductory
example single-peaked?
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MedianFig.voter
theorem with single-peakedness
2.2
1,2,3
6,7
4
5
A
B
C
Figure 2: Preferences I
D
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Median voter theorem with single-peakedness
A condition for voting cycles not to arise is that individual
preferences are single-peaked. More explicitly,
Theorem (Median voter theorem (single-peakedness
version))
If there is an odd number of voters, individual preferences are
singled-peaked and the policy space is one-dimensional, then
the median of the distribution of the voters’ most preferred
alternatives wins in a pairwise vote. This policy alternative is
referred to as the Condorcet winner. The voter whose most
preferred alternative is the median of the distribution is called
the median voter.
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