Voting and Democracy

What is Democracy?

• “Democracy is the worst form of government except for all those others that have been tried” – Winston Churchill

• What, exactly, is so great about democracy?

Democracy and its follies

• Not always stable

• Relatively new form of government

• Catch-all term, does it mean anything?

• Reduces economic growth

Sacred Cows

• What is so special about democracy?

• What is so special about majority rule (50%+1) in particular?

Choice of voting rule

• How to determine the “optimal majority?”

• Two costs to consider:

1. Decision making costs

2. External costs (tyranny of the majority)

There are two general rules … First, the more grave and important the questions discussed, the nearer should the opinion that is to prevail approach unanimity. Secondly, the more the matter in hand calls for speed, the smaller the prescribed difference in the numbers of votes may be allowed to become: where an instant decision has to be reached, a majority of one vote should be enough. The first of these two rules seems more in harmony with the laws, and the second with practical affairs. In any case, it is the combination of them that gives the best proportions for determining the majority necessary.--Jean Jacques Rousseau (The Social Contract)

Calculus of Consent

Expected Costs

0 N

With unanimity rule, any law that passes is necessarily Pareto optimal. As we require fewer people to agree with a law, the expected external cost rises

External Costs

With rule of one, there are no costs of getting a majority. As we require more people to agree with a law, the expected bargaining cost rises

Bargaining Costs

The optimal voting majority is the majority that minimizes the sum of the expected bargaining costs and expected external costs.

Expected total costs

OM# of individuals whose agreement is required for collective action

Multiple optimal majorities

• The optimal majority will vary depending on what type collective action we are talking about.

• So what is so special about 50%+1?

• Bargaining and external costs are probably discontinuous at 50%

Spatial Competition

• Hotelling (1929)

• Assume a town is composed of one street with 100 evenly-spaced, identical households

• Assume that two petrol stations are going to enter the city, and that residents will go to whichever station is closest to them

Spatial CompetitionWhere will the two petrol stations set up?If they set up like this, they would each get half the market, and nobody would be too far from the station, which is good

A B

But this is not an equilibrium—why not?

A

Either station can get more of the market by moving next to their competitor!

B, in turn, would want to move just to the left of A

B

This leapfrogging would continue until both were in the centre of town

BA

Which centre? Turns out the median is where they want to be

Spatial Competition

• What does this model explain?

• Why shopping centres develop

• Why fast food restaurants are often next door to each other

• Why political parties are often very similar!

Spatial Competition in Voting

• If:

• voter ideology can be arrayed along a single dimension, and

• Individuals have single-peaked preferences, then

• Median Voter Theorem--Politicians will seek to put the policies desired by the median voter into effect

Median Voter Theorem

• What does it mean for preferences to be single peaked?

• For any good, Individuals must:

1. Always prefer more of that good than less, or

2. Always prefer less of that good than more, or

3. Have a bliss point. A bliss point is an optimal quantity of a good such that as the actual quantity consumed deviates from that bliss point, the utility of the individual declines

Single Peaked Preferences-1 dimensional case

Utility

Quantity

Preferences are said to single peaked if:

An individual always prefers more of a good to less of that good, or

An individual always prefers less of a good to more of that good, or

An individual has a bliss point

Bliss Point

Q*

Median Voter Theorem

U

Q

Consider 5 individuals with different bliss points over the quantity of a public good:

Person 1-$10

Person 2-$20

Person 3-$90

Person 4-$100

Person 5-$150$10 $20 $90 $100 $150

The Median Voter Theorem says that $90 will be the amount of the public good provided if the decision is left to democracy—regardless of preference intensity, dispersion of bliss points, or efficiency. Is this equilibrium efficient?

It is only efficient if the median valuation is equal to the mean valuation. In this case, it is not. If the median voter valued the public good at $70, however, we’d get the efficient result

Median Voter Theorem

• Choosing public goods through voting and democracy does not by any means ensure the efficient quantity—need considerable luck for the mean voter to be the same as the median voter.

• Not only are you likely to get inefficient results, if we relax the assumptions of single-dimensionality or single-peakedness, voting becomes very unstable!

Multiple Peaked Preferences

• Sometimes single peaked preferences make little sense

• Options might be discrete

• All or nothing response is appropriate

All or Nothing

• Consider a country with 3 citizens and three options; all-out war (W), limited involvement (L), or no war (P).

• You might have Hawks (W>L>P), Doves (P>L>W), and All-or-Nothing types (W>P>L)

• How do we compare these three options with voting?

Condorcet Voting

• Evaluate all possible pairwise votes and look for a Condorcet Winner

• Condorcet Winner-An option that beats all other options in pairwise voting

• Condorcet Loser-An option that loses to all other options in pairwise voting

Condorcet Voting

• Back to our Hawks (W>L>P), Doves (P>L>W), and All-or-Nothing types (W>P>L)

• We have everybody vote on the 3 possible pairwise votes: W v. L, W v. P, and P v.L

• If we assume there are the same number of hawks as doves as all-or-nothing types…

• W v. L, W wins• W v. P, W wins• P v. L, L wins

Condorcet Voting

• W v. L, W wins

• W v. P, W wins

• P v. L, L wins

• W is our Condorcet winner

• P is our Condorcet loser

• We can construct a social preference ordering of W>L>P

Condorcet Voting

• What if our example had Doves (P>L>W), All-or-Nothing types (W>P>L), but instead of Hawks you have people who feel we need to do something, but would prefer being “reasonable” (L>W>P)

• W v. L, L wins• W v. P, W wins• P v. L, P wins• What is the social ordering? P>L>W>P…

Cycling

• This constellation of preferences yields what is called a voting cycle.

• How likely are cycles? Very

• More voters → increased likelihood of cycles

• Relax assumption of single dimensional policy space → cycles are almost certain!

The inevitability of cycles in 2-dimensions

A

B

C

Y

X

A, B, and C represent the bliss points in 2 dimensional policy space of voters A, B, and C

Let’s start by choosing the median point:

We can draw indifference circles around each bliss point that pass through the median:

Any point in these three areas…

Would beat the median point in a pairwise vote

The inevitability of cycles in 2-dimensions

A

B

C

Y

X

Let’s choose some point within one of the winsets.

In a vote between the orange and pink points, A prefers orange and B and C prefer pink. Let’s draw new indifference curves for the pink point.The pink point also has a winset. Let’s pick another point that would beat pink in a pairwise vote:

In a vote between the blue and pink points, A and B like blue and C prefers pink. Let’s draw new indifference curves for the blue point.

Now, compare the blue point with the orange point. A and C prefer the orange point to the blue point, while B prefers blue to orange. We can make this more obvious by getting rid of all of the extra indifference curves:

We have generated a cycle in 2 a two-dimensional policy space. It is almost impossible for a cycle NOT to exist!

The inevitability of cycles in 2-dimensions

• The likelihood of avoiding cycles in a 2-dimensional issue space is remote at best

• As the number of dimensions increases, cycles become more likely as well

• How likely—Arrow’s impossibility theorem! It is impossible to construct a rational social ordering

Back to voting

• As said before, there is no reason to suspect that voting on public goods will get you the efficient quantity or Pareto Optimal solutions

• Moreover, voting will often lead to Kaldor-Hicks inefficient results as well!

Consider an example

Individual Cost to Taxpayer

Benefit to Taxpayer

Net Benefit

Taxpayer 1 100 40 -60

Taxpayer 2 100 110 10

Taxpayer 3 100 140 40

Total 300 290 -10

Example, cont’d

• From a cost benefit standpoint, this project is inefficient.

• Still, however, it would garner a majority of votes.

Another Example

Individual Cost Benefit Net Benefit

1 100 140 40

2 100 90 -10

3 100 160 60

4 100 70 -30

5 100 80 -20

Total 500 540 +40

Example, cont’d

• From a cost benefit standpoint, this project is efficient.

• However, it would be voted down in a majority election.

• Both of these examples illustrate the fact that the nature of cost benefit analysis has changed—rather than can the winners compensate the losers, question is whether there are more winners than losers, irrespective of magnitude of win or loss!

Vote selling

• All of these problems would be solved if individuals were able to sell their votes.

• Ethical issues…

• Despite illegality of vote selling, vote trading does take place (and often!)

Coalitions and Logrolling

• Logrolling—two parties agree to vote for the preferred project of the other.

• Does logrolling improve efficiency? We know vote buying would, but what about vote trading?

Logrolling

Project Politician1 Politician2 Politician3 Net Benefit

A 120 -30 -40 50

B -20 80 -20 40

C -50 -20 130 70

Total 50 30 70

Logrolling

• Each of these policies is efficient.• A vote for policy A, B, or C on its own

would not win. • A coalition/logroll between politicians 1&2,

1&3, or 2&3 would be feasible, however, with the coalition between 1&2 the most likely.

• Why is a coalition between 1&2&3 infeasible?

Logrolling

Project Politician1 Politician2 Politician3

A&B 100 50 -60

A&C 70 -50 90

B&C -70 60 110

A&B&C 50 30 70

Logrolling

• In this case, vote trading has led to a Pareto improvement (although we are not at a Pareto efficient outcome).

• Vote selling would have led to an efficient outcome (all three projects getting funded)

• However, it is not always (typically?) the case that logrolling leads to Pareto improvements.

Logrolling

Project Politician1 Politician2 Politician3 Net Benefit

A 60 -30 -50 -20

B -40 70 -40 -10

C -50 -60 80 -30

Total -30 -20 -10

Logrolling

• Each of these policies is inefficient.

• A vote for policy A, B, or C on its own would not win.

• However, A coalition/logroll between politicians 1&2, 1&3, or 2&3 would be feasible, and again the coalition between 1&2 is the most likely.

Logrolling

Project Politician1 Politician2 Politician3

A&B 20 40 -90

A&C 10 -90 30

B&C -90 10 40

A&B&C -30 -20 -10

Logrolling

• Here, vote trading has led to a reduction in the general welfare of society.

• Again, vote selling would have led to an efficient outcome (none of the projects going forward).

• Is logrolling used for efficient or inefficient projects? Or is all logrolling just Pork-Barrel politics?

Representative Democracy

• Thus far, we have been talking mostly about direct democracy, but most decisions are made via representative democracy.

• Biggest benefit of direct democracy is that there is no principal-agent dilemma between voters and representative.

• Biggest costs are costliness of always voting and rational ignorance (or even rational irrationality)

Back to the Median Voter Model

• If:

• voter ideology can be arrayed along a single dimension, and

• Individuals have single-peaked preferences, then

• Median Voter Theorem--Politicians will seek to put the policies desired by the median voter into effect

Duverget’s Law

• What would happen if we attempted to add a third candidate to our model?

• The third candidate would get “squeezed out”

• Duverget’s Law: In a majoritarian political system, there is a tendency for party structure to be a two party system.

Convergence

• Why don’t we see full convergence toward the median?

• Asymmetric information—candidates may not know the median

• Campaign contributions—candidates may want to move away from the median to get contributions

• Ideology• Cohesion—voters may be less likely to vote for a

politician who is known to ‘waffle’

“Flavours” of Democracy

• Plurality Rule

• Majority Rule (with and without runoffs)

• Proportional Representation

• Borda Count

• Transferable-Vote

• Point Voting

• Approval Voting

“Flavours” of Democracy

• What do they all have in common?

• All methods of voting lead to inefficient outcomes (especially the most common ones!)

• Each is unlikely to pick a Condorcet winner if one exists.

• Each is susceptible to strategic or sophisticated voting

Condorcet Efficiency

Utilitarian Efficiency

Efficiency and voting

• No voting rule leads to efficient results• Why? Voting is, in effect, like doing CBA

without taking into effect magnitudes of gains and losses.

• There is no reason to assume that policies selected by voting will be efficient, especially in large societies with many options/candidates!

• So how are we to get efficient results?

Bureaucracy

Bureaucracy

• Once collective decisions have been made, the implementation of these decisions is left to government bureaucracy.

• Somebody needs to administer policies related to taxation spending.

• Problem: Principal-Agent Dilemma!

• Problem: Rents!

Principal-Agent Problems and Bureaucracy

• Agents—Bureaucrats, civil servants, government officials, individuals who have a career in the government bureaucracy.

• Principals—voters or their representatives

• P-A problems arise due to information asymmetry between Principal and Agent

Rents

• Most government agencies act as monopolists, which generate monopolistic rents

• Private monopolists receive these rents as profits

• Governments (or non-profit agencies) can not receive these as profits—where do they go?

• Typically, these rents are “dissipated” away through increased costs—Government run projects are far less efficient than prive projects

Efficiency—the Australian Experience

• Davies (1971, 1974, 1977)—Australia’s private airlines are 12-100% more efficient than its’ public airlines

• Davies (1981)—Australia private banks are more productive and profitable than public banks

• Davies and Brucato (1987)—Private banks hold riskier assets and are more profitable than public banks.

Efficiency—the International Experience

• Massive body of literature, about half looking at the US.

• In nearly all cases in this literature, bureaucratic decision-making is far more inefficient than private decision making.

• Why is this?

The folly of bureaucracy

• What prevents bureaucrats from being as efficient as private firms?

• Budget-maximization behaviour and rent seeking

• Creating demand for their own output• Information asymmetry between bureau and

sponsors• Difficulty in measuring output and substitution

into visible activities• Biased “expert” advice

Budget-Maximization Behaviour and Rent Seeking

• If bureaucrats are self interested, what do they want (what is in their utility function?)

• Power, prestige, income, stuff like that.

• All of these things will be positively related to the size of their budget

• While private firms have incentives to cost minimize, bureaucracies have incentives to cost maximize!

Creating Demand for their Own Output

• One way of budget maximizing is to create demand!

• Militaries might “manufacture” enemies, for example

Information asymmetry

• Bureaucrats know what their costs are, but sponsors do not!

• Sometimes it is even illegal to distribute these “confidential” or “top secret” costs.

Difficulty in measuring output and substitution into visible activities

• What is the output of a military?

• Many of the goods that governments produce are unobservable and very difficult to measure.

• These bureaucracies may try to do fewer of the unobservable things (that people want) and do more unobservable things (that nobody cares about).

“Experts”

• Bureaus often hire external experts to do cost-benefit analysis

• Will they hire somebody who is critical of their projects?

• Will experts, who want future employment, be critical?

Where do bureaucrats come from?

• Often political appointments—positions are favours granted, not positions earned based on expertise etc.

• Bureaucratic advancement often a function of currying favour with elected officials—does this lead to efficient results?

Bureaucracies and Public Goods

• All of these add up to two basic principles:

1. Bureaucracies tend to oversupply public goods

2. Bureaucracies tend to supply public goods at inefficiently high cost