Public choice

1
Public choice

• Alexander W. Cappelen
• Econ 4620
• 091003

2
Collective decision-making

• Public production and financing is a possible
  solution to important market failures.
• But in the absence of a market - how can we solve
  the tasks that the market traditionally solves?
• How do we decide what to produce and how much?
• How do we ensure an efficient resource
  allocation?
• How do we distribute costs of production?
• The market resolves this questions by using the
  information in the price system. Collective
  decisions must rely on other types of information.

3
Collective decision-making

• Different voting procedures are different ways to
  aggregate individual preferences
• The most common voting procedure is simple
  majority voting
• Qualified majority
• Rank-order voting is an alternative
• Two problems with collective decision making
• Preference revelation
• Preference aggregation
• People disagree about the optimal level of public
  expenditures
• Differences in preferences
• Differences in income
• Differences in price/tax-cost

4
Different preferences
Private goods
Bs indifference curve
As indifference curve
Common budget restrictions
Public goods
5
Different income
Private goods
As budget- restriction
A og Bs indifference curve
Bs budget- restriction
Public goods
6
Different tax-cost
Private goods
As budget - restriction
A og Bs indifference curve
Bs budget- restriction
Public goods
7
Utility as a function of public goods
8
The median voter

• Who will decide if there exist a majority
  equilibrium?
• The median voter (the median voter theorem)
• The number of people who prefers a higher level
  of public goods than the median voter is equal to
  the number of people who prefers a lower level.
• The median voter can thus always secure a
  majority for her preferred level.
• Does the median voter choose an efficient level
  of public goods?
• Is the median voters tax price equal to the
  average cost of public goods provision?
• Is the income of the median voter equal to the
  average income?

9
Implications for the party structure

• In a two-party system, where both parties want to
  maximize their votes, both parties position will
  be close to the median voters preferred level
  (Hotellings rule).
• why?
• Presupposes that
• There is only two parties
• Parties are only concerned with maximizing votes
• Voters have single-peaked preferences

10
The voting paradox

• Majority voting does not always give a stable
  equilibrium.
• Condorcet
• We can illustrate the problem in a simple model
• Three voters I, II, III
• Three alternatives A, B, C
• Preferences
• I A gt B gt C
• II B gt C gt A
• III C gt A gt B

11
Majority voting

• We do not have a stable equilibrium in this
  situation. We have three possibilities
• A against B A wins
• A against C C wins
• B against C B wins
• All three alternatives can win.
• There does not exist any consistent social
  preference ordering and therefore no social
  welfare function.
• We either get a cycle or, if we have a sequence
  of votes, the order in which the votes take place
  will determine the outcome.

12
Arrows impossibility theorem

• Does there exist any political mechanism that
  avoids this problem?
• Arrow formulates five minimal conditions that all
  political mechanism should satisfy.
• Pareto-efficiency
• Transitivity
• Nondictatorial choice
• Independence of irrelevant alternatives
• Unrestricted domain

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Arrow cont.

• There does not exist any mechanism that satisfy
  these requirements (Arrows impossibility
  theorem)
• Rank order does not satisfy independence of
  irrelevant alternatives.
• What is the main problem?
• Voting procedures do not give us enough
  information.
• In particular we do not get information about the
  strength of peoples preferences.
• What about the social welfare functions?
• Do they satisfy Arrows five requirements?

14
Is this important?

• An example illustrates the practical importance
  of Arrows insight.
• The decision about a new airport in Oslo in 1992.
• Three alternatives Fornebu (F), Gardermoen (G)
  and Hobøl (H).
• Studies of the preferences in the different
  political parties have shown that we probably
  would have got the following results
• H is preferred to G (101 64)
• G is preferred to F (101 64)
• F is preferred to H (105 60)
• The chosen sequence of votes resulted in G, but
  all the alternatives could have won.

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When is there an equilibrium

• Arrows impossibility theorem tells us that there
  is no mechanism that always satisfies the five
  requirements.
• However, majority voting satisfies these
  requirements in some situations
• For certain types of preferences when the
  preferences are single-peaked.

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Different preferences
Single-peaked preferences
Single-peaked preferences
Double-peaked preferences
17
When do we have single-peaked and double-peaked
preferences?

• Preferences for single peaked preferences is
  generally single-peaked.
• Preferences are generally not single-peaked if
• We vote over combinations of public goods.
• We vote over public goods for which there is a
  private alternative.
• We vote over issues of redistribution.

18
Alternative systems for determining public goods
supply

• Majority voting does not ensure an efficient
  supply of public goods.
• A public goods that is only valued by a minority
  will not be supplied at all
• Goods that everyone value equally will typically
  be oversupplied since the median voter does not
  pay the average cost of production.
• Does there exist an alternative solution?
• Lindahl equilibrium

19
Lindahl equilibrium

• The Lindahl equilibrium is found at the
  intersection between the collective demand cure
  and the supply curve.
• Lindahls solution involves that everyone pays a
  tax (price) equal to her marginal willingness to
  pay (in the equilibrium).
• The obvious problem is that people do not have
  any incentives to reveal their true willingness
  to pay.

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Lindahl cont.
Tax price
Tax price
Public expenditures
Public expenditures
Tax price
Public expenditures
21
Politics and economics

• We have studied an idealized version of
  democratic decision making.
• Everyone do not vote
• Is it rational?
• Do people know their own best?
• Lobby organizations have substantial influence
• What motivates politicians?