1. Political Equilibrium
Public choice – one made through political interaction of many people according to established rules
Political equilibrium – an agreement on the level of production of one or more public goods, given the specified rule for making the collective choice and the distribution of tax shares among individuals
Tax shares – preannounced levies assigned to citizens; equal to a portion of the unit cost of a good proposed to be provided by government

2. Elections and Voting
Economic analysis assumes that people evaluate government goods in the same way as market goods and vote in favor of a proposal only if they will be made better off by its passage.
The most-preferred political outcome is the quantity of the government-supplied good corresponding to the point at which the person’s tax share is exactly equal to the marginal benefit of the good.
Lindahl Equilibrium

3. Elections and Voting

4. Elections and Voting Many citizens choose not to vote because:
The cost of time and effort to vote outweighs the perceived benefit.
Indifference
They may see little or no difference between the alternatives considered in the election.
Alternatives may be different, but equally (un)acceptable
Rational Ignorance
They believe that their votes do not make any difference.
Lack information about public issues because the marginal cost of obtaining the information exceeds the apparent marginal benefits of doing so

5. Calculus of Voting
Net Benefits = Gain from preferred policy * Probability of vote affecting outcome – Cost of voting
R = PB – C
Policy has characteristics of public good
Act of voting entails private cost

6. Determinants of Political Equilibrium
Public choice rule; the proportion of yes votes in relation to the number of votes required for approval of the issue
Average and marginal costs of the public good
Information available to voters on the cost and benefit associated with the issue
Distribution of tax shares among voters and the way in which extra taxes vary with extra output of the good provided
Distribution of benefits among voters

7. Political Equilibrium Under Majority Rule
An example:
Under simple majority rule, citizens must decide on the quantity of a pure public good to produce.
Given the average cost of producing the good, a tax-sharing scheme is announced whereby each person will pay the same tax per unit of the good.
If the good can be produced under conditions of constant costs and there are n individuals in the community, each individual will pay a tax equal to AC/n per unit of the public good.

8. Political Equilibrium Under Majority Rule
Marginal Benefit, Cost, and Tax
Security Guards per Week
∑MB
350
MC = AC E 1 2 3 4 5 6 7
MBF
MBG
MBM
MBA
MBB
MBC
MBH 50 t

9. The Median Voter Model
The median voter is the one whose most-preferred outcome is the median of the most preferred outcomes of all those voting.
The greater the dispersion of most-preferred outcomes from the median, the more likely there will be dissatisfaction with public choices under majority rule.
Political externalities occur when voters do not obtain their most-preferred outcomes, given their tax shares.
Political transactions costs measure the value of time, effort, and other resources expended to reach and enforce a collective agreement.

10. The Median Voter Theorem
The unique political equilibrium occurs at the optimal choice for the median voter.
Assumptions
Binary vote
Majority Rule
Single-peaked Preferences

11. Voter Rankings of Alternatives
Net Benefit for A
Single Peak Q
Net Benefit for A
Single Peak Q
Net Benefit for A
Multiple Peaks Q
Net Benefit for A
Single Peak Q

12. Security Guards per Week
Median Voter Result H G F M
Net Benefit C B A 1 2 3 4 5 6 7
Security Guards per Week

13. Implications of MVT
Candidates moderate their positions to attract more votes
Political Equilibrium: both candidates adopt median voter position
Only the median voter gets his most-preferred outcome.
Others get either too little or too much.

14. What if not all preferences single-peaked?
Town Council Rankings For Bond Fund
Voter
First Choice
Second Choice
Third Choice
Groucho
Police
Tourism
Bridge
Harpo
Chico

15. Voting Cycle Tourism vs Police Police vs Bridge Bridge vs Tourism
Winner = Police
Police vs Bridge
Winner = Bridge
Bridge vs Tourism
Winner = Tourism
Continuous cycle (no equilibrium)
or arbitrary winner depending on order

16. Pair-Wise Elections
Pair-wise elections are held between any two alternatives when three or more alternatives are possible.
Each loser can become a winner when paired with another alternative.
Depending on the order in which elections are held, any alternative can emerge as the winner under simple majority rule; this is called cycling.
no political equilibrium exists.
If all preferences single-peaked, median’s preference would always win

17. Agenda Manipulation If Chico gets to choose order
will select M1 vs M3, winner versus M2
Bridge
winner
outcome
Tourism
Police

18. Strategic Voting B T B T P P P T

19. Arrow’s Impossibility Theorem
Conditions for “collective rationality”:
All voters must have free choices among alternatives, and public choices cannot be made by any one individual. (non-dictatorship)
A unique political equilibrium must be attained no matter what the preferences of individuals comprising the electorate. (unrestricted domain)
If all voters change their rankings of a particular alternative, the public choice that emerges must not move in the opposite direction of their new preferences (monotonicity)

20. Arrow’s Impossibility Theorem
Conditions for “collective rationality” (continued):
Public choices and political equilibrium must not be influenced by the order in which alternatives are presented to voters. (transitivity)
Public choices must not be affected by the elimination or addition of an alternative. (independence of irrelevant alternatives)
Public choices should be transitive: If A is chosen over B and B is chosen over C, then A should be chosen over C. (rationality/completeness)

21. Collective Choice Rules
Minority rule runs the risk of imposing decisions that do not satisfy a majority of the community.
Decisions are made by a specific minority group: oligarchy
Decisions are made by one member of the community: monarchy
Majority rule may mean simple majority rule (agreement of 51%) or other majority standards (such as a two-thirds majority).

22. Unanimous Consent Allows only Pareto-efficient changes to be approved
Will block those changes that involve redistribution of either property rights to ownership or wealth, or income
Could result in high transactions costs
May encourage strategic behavior on the part of voters
Concern for minority rights has led to discussion of “relative unanimity,” such as a seven-eighths majority

23. Back to Patty and Selma MSB=16, MSC=18 Include Marge with MPB=0
Equal tax share yields MPCi=9
Unanimous defeat on referendum
Include Marge with MPB=0
Equal tax share yields MPCi=6
MR pass
Will also pass if MPC=18 for Marge, MPC=0 for Patty, Selma

24. Compensation Principle
Unanimity requires everyone to agree so full compensation for all
Majority rule requires only majority to agree so full compensation only for majority
Risk aversion changes this conclusion
Because individual consent not required if enough others do consent, may be willing to accept less than full compensation to ensure some compensation
Equilibrium yields almost no compensation to most of the majority with large gain to minority within that majority

25. Costs of Voting Rule
costs EC
EC+TC TC
100 M*
% needed to pass

26. Plurality Rule
A commonly use collective decision-making rule when at least three alternatives are on the ballot
Disadvantage of simple majority rule in this case is that when more than two alternatives are on the agenda, no single one may receive a simple majority
May result in high transactions costs, runoff elections
Often allows a minority to decide
Can result in cycling

27. Point-Count Voting
Each voter is assigned a set number of points they may allocate in any way they wish among the possible alternatives
Affords opportunity for greater revelation of preferences
May protect the rights of minority voters with strong feelings on particular issues
Increases possibility to strategic behavior

28. Instant Runoff Voting
A scheme that makes it more likely that a winning candidate receives a simple majority rather than a plurality
Voters rank candidates according to their first, second, third choices, and so on.
If no candidate receives a simple majority based on first choice votes, the one with the fewest first place votes is eliminated.
A recount is taken for the remaining candidates.
Ballots are retabulated with votes registered based on ranking for the remaining candidates.
If no candidate has a majority, repeat steps 2-4 until majority winner emerges

29. Voting Rules Example Suppose 6 Grouchos, 5 Harpos and 3 Chicos
Pure MR – no winner (status quo bias)
Pairwise – cycle (no winner)
MR runoff – Bridge wins (because Tourism eliminated)
Instant Runoff is same as MR runoff if 3 alternatives
Taking top two is same as eliminating bottom
Plurality – Police wins
First
Second
Third
G = 6
Police
Tourism
Bridge
H = 5
C = 3

30. Representative Democracy
Benefits
Lowers transaction costs (fewer decision makers)
Specialization (eliminates rational ignorance on policy but not for elections)
Costs
Incomplete information (difficult to determine what constituency wants)
Principal agent problems (shirking)

31. Political Parties
Political parties are individuals with similar ideas on the role of government and other issues who group together
Act as brokers to encourage vote trading among voters
Characterized by economists as vote maximizers, because they tend to put together political programs and tax-sharing arrangements designed to maximize the votes that they receive

32. The Median Voter and Political Parties
Assuming each voter has a single-peaked net benefit function, Q* will emerge as the political equilibrium, because the net benefits will be higher than for any alternative quantity of goods and services, given tax shares.

33. The Median Voter and Political Parties
Number of Voters
Output of Government (Voter ideal points) Q *
R=D =I D R D

34. Logrolling
When intensities of preference differ on issues, groups may trade votes for those issues of great interest to them; this is called logrolling.
Incentives exist when an asymmetry of gains on the issues is involved.
Implicit logrolling occurs when political interests succeed in pairing two or more issues of strong interest to divergent groups on the same ballot or the same bill.

35. Security Guards and Fireworks Displays
Logrolling Example
Marginal Benefit,
Cost, and Tax
Fireworks Displays
Marginal Benefit,
Cost, and Tax
300 MC
300 MC
MBC
MBB
MBA
250 1
MBA
MBB
MBC
250 1
100 t
100 t
Security Guards
Marginal Benefit,
Cost, and Tax
Security Guards and Fireworks Displays
600
MC = MSC
250 1
500
∑MB
MBC
MBA
MBB
200 t

36. Logrolling Implications
Logrolling allows two policies which would fail individually to pass jointly
Logrolling can either decrease or increase efficiency because MR may fail to pass to efficient policies or pass inefficient policies

37. Special-Interest Groups
Special-interest groups are organizations that seek to increase government expenditures that benefit their constituents.
Differ from political parties in that their leaders do not run for political office
Exist to promote policies favorable to workers, regions, minorities, environmental preservation, and taxpayers in general
Successful special-interest groups are likely to be small relative to the portion of the population that pays taxes to support their subsidies
As a result, will be most successful where there are concentrated benefits to their group and diffuse costs which can be spread out to others

38. Bureaucracy and Public Output
A bureaucracy is developed to implement public choices made through political institutions.
Influences the delivery of services and the efficiency with which services can be produced
Bureaucrats do not directly own the inputs they use for production, and any financial gains for efficiency are rare

39. Issues Associated with Bureaucracies
Bureaucrats often have monopolistic power.
Bureaucrats often have specialized information not available elsewhere.
Difficult to manage bureau activities because of high transactions costs
Bureaucrats can seek to convince governing authorities that their output needs to be increased.
Can increase the amounts of input necessary to produce any given amount of output by using inefficient production techniques

40. Bureaucratic and Efficiency
Output per Year
Cost (Dollars)
Benefit and
TSB
TSC
MSC
MSB QB * Q E
TSB' B Q’

41. Bureaucratic and Efficiency
Budget size
Net Benefits X
X-e Q0 Q M Q *