Prof. Bryan Caplan

Econ 410


Week 5: Efficiency and Bargaining

I.                     Divergence Between Median and Mean Preferences

A.                 Politicians cater exclusively to the median voter when:

1.                  There is one voting dimension,

2.                  preferences are single-peaked,

3.                  and politicians have no uncertainty about voter preferences.

B.                 Question: Is this an efficient outcome? 

1.                  Recall that efficiency requires the maximization of total social surplus.

C.                Answer: In general, no.  The efficient outcome is for politicians to cater to the mean preference.

D.                Why?  Total surplus equals average surplus multiplied by the number of people.  If the number of voters is fixed, then, total surplus reaches its maximum when you maximize average surplus.

E.                 Special case: Median and mean preference are identical. 

F.                 Intuition: Under democracy, a vote is a vote; there is no incentive to care about the intensity of preferences. 

1.                  Alternate terminology: Voting asks only about ordinal preferences ("Do you prefer A to B?").  In contrast, markets let people express cardinal preferences ("What dollar values do you place on A and B?").

G.                Ex: If 51% of the population wants to impose $1000 harm to the 49% in order to benefit $1 each (a highly inefficient transfer), democracy gives the majority what it wants.

H.                 In contrast, in markets, intensities matter because people express their wants in number of dollars, not merely a for/against vote.

1.                  Imagine running a store democratically, when there are many more customers than employees.

I.                     Thus, there is a major inefficiency built into democracy: It treats all preferences equally, even when some are vastly more intense than others.  This is one way of thinking about the "tyranny of the majority" - a nearly indifferent majority may habitually vote to make the minority intensely miserable.

II.                   Log-Rolling, Bargaining, and the Coase Theorem

A.                 The Coase Theorem: When transactions costs are zero, people bargain to the efficient allocation regardless of initial endowments.

B.                 Classic example: Farmer/railroad case.

C.                My example: How I bought Murder at the Margin

D.                In politics, especially in legislatures, bargaining is often called "log-rolling," but a similar logic holds.

E.                 Main unusual feature of political bargaining: You don't need unanimous consent for a bargain!

F.                 Election rules create the "initial endowments," the status quo from which bargaining starts.

G.                The Mean Voter Theorem: with zero transactions costs, political bargaining implements the mean voter preference on any number of issues, even if preferences are not single-peaked.

III.                  Bargaining to Efficiency on a Single Dimension

A.                 The Coase Theorem implies that log-rolling can take care of the divergence between median and mean preferences.

B.                 Median voter has the power to pick the "initial endowment" from which bargaining begins.

C.                But it remains possible for the minority to "bribe" the majority to switch to a different policy.

D.                Ex: Rent control

E.                 Ex: Rights of religious minorities

IV.               Bargaining to Efficiency on Multiple Dimensions

A.                 The Coase Theorem similarly implies that log-rolling allows people to bargain to efficiency on multiple dimensions.

B.                 Even if median and mean preferences are identical for each issue, if a single election handles multiple issues, democracy need not yield the efficient result.

C.                But log-rolling across issues once again makes it possible to reach the efficient outcome.

V.                 Bargaining Around Intransitivity

A.                 Bargaining can even lead to the efficient outcome when the electorate is intransitive.

B.                 Why?  Social intransitivity ultimately stems from ignoring preference intensities.  There can be only one option that maximizes surplus.  But - without bargaining - voting is a poor method for reaching that point, because it only asks about ordinal preferences, not dollar values.

C.                Return to the school spending example:

1.                  Voter #1's surplus: {high - $1000, low - $400, medium - $0}

2.                  Voter #2's surplus: {medium - $500, high - $250, low - $0}

3.                  Voter #3's surplus: {low- $300, medium - $250, high - $200}

D.                Recall that under majority rule, high beats low, low beats medium, and medium beats high.

E.                 Summing total surplus for each option: {high - $1450, medium - $750, low - $700}.  High spending unambiguously generates more surplus even though pair wise voting on this issue is intransitive. 

F.                 Suppose you begin by voting on medium versus high.  Medium wins.  With bargaining, though, Voter #1 can "bribe" Voters #2 and #3 to increase spending, perhaps by agreeing to a tax on luxury cars to raise extra school revenue.

VI.               Pork Barrel Politics

A.                 While many praise the wonders of log-rolling, others are more skeptical. 

B.                 In particular, there are recurring criticisms of "pork barrel" spending, where all legislators swap votes to fund inefficient projects in their home districts.

1.                  Examples: Military bases, roads, museums, other infrastructure.

C.                The usual story is that all legislators have to participate in the scramble for "pork" because if representatives from one district/state hold back, the money just goes to other districts/states.

D.                Two alternative versions:

1.                  Politicians want to win popularity by loudly "doing something" for their constituents.

2.                  Politicians want to secretly pay off special interests without losing their popularity with voters.

E.                 Note: Rational ignorance cuts against the first and for the second.

F.                 On either of these account, the intuition is that restraining spending is a public good; the federal budget suffers from a "tragedy of the commons."

G.                Puzzle: Why bargain to inefficient outcomes when you could bargain to efficient ones? 

H.                 If you are trying to win popularity, wouldn't voters prefer a tax refund to inefficient programs?  If so, why not have the omnibus repeal bill, as with base closings?

I.                     If you're just trying to buy support from special interests, recall that rationally ignorant voters may be able to keep politicians in line with threats of severe punishment.

J.                  Conclusion for now: Pork barrel politics is intuitively plausible, but we will need to wait to get a solid account of it.

VII.              Supermajority Rules

A.                 Major political changes often require more than majority, or supermajority support.

1.                  Simple example: 2/3 vote.

2.                  More complex example: Amending the U.S. Constitution.  It requires 2/3 of both houses of Congress AND a majority vote in 3/4 of the 50 states.

B.                 Supermajority rules, like other voting rules, shift the "initial endowments" for political bargaining.

C.                Without bargaining, supermajority rules could easily lead to highly inefficient outcomes.

1.                  Question: When would supermajority rules without bargaining be efficiency enhancing?

2.                  Answer: When a minority has especially intense preferences.

D.                With bargaining, however, supermajority rules merely shift the distribution of political "wealth," putting a lot of power in the hands of those who want to block change.  This doesn't mean change won't happen, only that it may be necessary to "buy off" opponents.