David A. AndersonPaul G. Blazer Professor

Centre College

Voting Solutions to the

Problem of Social Cost

Pigou (1920)

Tax / Subsidy = Marginal External Cost / Benefit

Best for market goods with MEC/MEB known to policymakers

Problems with compounding of tax + expected litigation cost + risk burden + ethical behavior

Approaches to Externalities

Coase (1960)

Private bargaining achieves efficiencyMost effective when transaction costs low

(e.g., few affected)Strategic bargaining can deter efficiencyUnderused

Approaches to Externalities

Hardin (1968)

Privatization leads to internalization and better care

Austrian Economists, e.g., Block (1998)Difficult to privatize air, flowing water

Approaches to Externalities

Buchanan and Tullock (1962)voting outcomes can be inefficient

van Mill (1996)“… majority rule is inherently irrational

and unstable in its outcomes.”

Walker et al. (2000)voting solutions lead to efficiency via

information signaling

Voting

The Kentucky Division of Water and the Kentucky Department of Health Services warn swimmers to avoid portions of the • upper Cumberland River, • the North Fork of the Kentucky River and

• the Licking River because they contain high levels of fecal coliform bacteria.

n homesc = cost per home of a septic systeme = damage from each home’s emissions

With uniformly distributed pollutant, each home’s share of own damage is e/n

Rational private response:purchase septic system if c < e/n

Socially efficient response:purchase septic system if c < e

If individuals are identical and fully informed, votes among any number of individuals on the abatement of a uniformly distributed pollutant will yield efficient policy decisions.

Proposition 1

Each home internalizes e/n of its own emissions damages and receives (n-1)e/n of the damage from other homes. The total damages felt by each home are thus

( 1)e en en n

Proposition 2

If individuals are fully informed but heterogeneous in terms of the size of the externality they create, votes among any number of individuals on the abatement of a uniformly distributed pollutant will yield efficient policy decisions.

Suppose there are two levels of emissions,

high (eh) and low (el),

and that x homes emit at the high level and n-x homes emit at the low level. Homes emitting eh internalize eh/n and receive

[(x-1)eh + (n-x)el]/n

of the damage from other homes. The total damage received by each high emitter is thus

( 1) ( ) ( )h h l h le x e n x e xe n x ee

n n n

For low emitters the analogous equation is

( ) ( 1) ( ) l h l h le x e n x e xe n x e

en n n

Each resident will vote for a septic system requirement if

c < ē, or equivalently, if the total cost of the requirement (nc) is less than the total emissions damages (nē).

If individuals are fully informed and create the same or different levels of a uniformly distributed pollutant, and if a standard amount of the damage created by each individual is completely external, a vote among affected parties will yield the efficient solution.

Proposition 3

Allow ε to represent the completely external damage created by each home. The damage received by each home is thus:

( 1) ( 1)1

e n e n en n n

From Proposition 2, each will internalize the average level of uniformly distributed pollution.

From the last equation, each will also internalize the full per-capita external component.

Thus, each will fully internalize the average level of both types of damage, and clean-up measures will receive the majority of votes if

c < ē + ε.

If individuals are fully informed and a standard level of emissions is completely external, a vote among affected parties will yield the efficient solution.

Corollary

This is a special case of Proposition 3 in which e = 0. The previous equation becomes

( 1)01

nn

and again the voting solution will be efficient.

$10 / glass

The check is split

Pigou: Tax each person $9 per drink

Pigou: Tax each person $9 per drink

Hardin: Privatize the decision by having everyone pay for their own drink

Pigou: Tax each person $9 per drink

Hardin: Privatize the decision by having everyone pay for their own drink

Coase: Each person offers others bribes of up to $1 per recipient not to buy another drink

Pigou: Tax each person $9 per drink

Hardin: Privatize the decision by having everyone pay for their own drink

Coase: Each person offers others bribes of up to $1 per recipient not to buy another drink

Voting Solution: Vote on whether to have another round