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ENTITLEMENT THEORY: PROSPECTS AND PROBLEMS

Comment on the Green Paper

Thomas Schwartz

University o f Texas at Aust in

Thoughtful and thought-provoking, Edward Green's "Equilibrium and Efficiency

Under Pure Ent i t lement Systems" is no tewor thy for its promise even more than its product ,

for the subject it pioneers even more than the result it reports. That subject is the deductive

theory of ent i t lement systems, inst i tut ions that regulate conduct and allocate social product

solely by assigning enforceable rights to individuals. Green's main result is what I like to

call a converse welfare theorem: under certain conditions, the equilibria of an ent i t lement

system include all the Pareto-efficient outcomes. This promises to be the first in a series

of theorems about ent i t lement systems, technically interesting because ent i t lement theory

is more abstract (it imputes less structure to reality) than or thodox general equilibrium and

welfare theory.

Basic Concepts of Entitlement Theory

Green couches his theory in terms of a set of social states (states, for short) , a

subset of attainable states, a number n of individuals (Messrs. 1, 2 . . . . . n, to name them),

and assignments to each individual, say Mr. i, of two binary relations on the set of states.

One is Mr. i's preference relation. The other represents Mr. i's rights. Green calls this relation

Mr. i's ascribed welfare and occasionally (in § IV) formulates it thus:

Mr. i is viewed as being bet ter off under state x than under

state y.

Such language is misleading. Here is the correct formulation :

Mr. i does not have the right to veto the change from state

y to state x.

The assignment of these relations to Messrs. 1 ,2 , ..., n is an ent i t lement system.

Green's solution concept for ent i t lement systems is tha t of a f inal state, which he

also calls an equilibrium :

Public Choice 39:213-219 (1982) 0048-5829/82/0391-0213 $01.05. © 1982 Martinus NijhoffPublishers, The Hague. Printed in the Netherlands.

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A f inal s ta te is a state from which every change that is preferred by anyone is opposed by someone who has the right to veto it.

Green's Theorem

An ent i t lement system is unbiased (the term .is Hurwicz's, I believe) if every Pareto -

e f f i c ien t s ta te is f inal (relative to tha t system). Green's converse welfare theorem says tha t

an ent i t lement system must be unbiased under certain conditions. These include some

geometric conditions on preferences and technology, plus three conditions on preferences

and rights :

LONE DISSENTER If exac t ly one individual opposes a

change, he has the right to veto it.

SURROGATES I f s o m e o n e opposes a change, s o m e o n e

has the right to veto it.

COHESIVENESS There is some conceivable (not necessarily

attainable) change that everyone has the right to veto.

Rights to Effect Changes

Every right in an ent i t lement system is the right to ve to a change. What about rights

to e f f e c t claanges? Has Green made no room for them? The problem is to define the right

to effect a change in the terms Green has provided.

A natural suggestion is tha t the right to effect a change is the right to veto the

reverse change :

Mr. i has the right to effect the change from x to y if, and

only if, Mr. i has the right to veto the change from y to x.

This does not work. Suppose (what surely is possible) tha t x and y are bo th Pareto-

efficient, that someone prefers x to y, and that someone prefers y to x. It follows, as you

will see in the final section, tha t someone who prefers x to y has the right to veto the change

from x to y, while someone who prefers y to x has the right to veto the change from y to x.

In this case the suggested definition has the absurd consequence tha t someone has the right

and desire to make a change that someone else has the right and desire to veto.

Another suggestion is that the right to effect a change is the absence of any right

to veto that change :

Mr. i has the right to effect the change from x to y if, and only if, no one has the right to veto that change.

This does not work either. Suppose Mr. 1 prefers x to y and no one prefers y to x;

the change from y to x, therefore, would be a Pareto improvement. Suppose Mr. 2, and he

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alone, has the right to veto the change from y to x, but because he does not prefer y to x

he waives this right, permit t ing the change to take place. Surely, then, Mr. 1 has every

right to effect the change from y to x. According to the suggested definition, however, Mr. 1

has no such fight, for Mr. 2 has the right (which he waived) to veto this change.

Although Mr. 2 had the right to veto the change from y to x, he did not oppose

the change. This suggests tha t someone 's right to effect a change is the absence of the right

to veto it by anyone who opposes it:

Mr. i has the right to effect the change from x to y if, and

only if, no one else bo th prefers x to y and has the right to

veto the change from x to y.

But even this is unsatisfactory. Suppose you damage my car, effecting a change from

a state x in which my car is undamaged to a s t a t e y in which it is damaged. You are properly

judged to be entirely responsible for the damage, and I successfully sue you for the cost of

repairs - two thousand dollars, say. Be,cause my claim is a just one, you must have wronged

me. That means you had no right to effect the change from x to y. According to the latest

suggested definition, then, someone who preferred x to y must have had the right to veto

the change from x to y. Who? Since the car was mine and no other harm was done by the

change from x to y, I alone was wronged by this change, so I alone had the right to veto

the change. But I did not prefer x to y : I preferred y to x. I happened to have valued two

thousand dollars more than an undamaged car. My preference was an unusual one, but a

possible one: I was glad you wronged me.

What blocked your right to effect the change from x to y (your right to damage

my car) was not my preference for x over y, but my failure to waive my right to veto the

change from x to y: I did not give you permission to damage my car. This suggests that the

right to effect a change is the absence of any unwaived right to veto tha t change:

Mr. i has the right to effect the change from x to y if, and

only if, everyone who has the right to veto that change has waived his veto right: he has permit ted Mr. i to effect the

change from x to y.

The problem is that there is no evident way to couch the idea of waiving a right (or per-

mit t ing a change) in the language of ent i t lement theory as Green has presented it.

Is Any Form of Government n o t a n Ent i t lement System?

Let us ignore the problem just discussed and assume that ent i t lement systems can

somehow include rights to effect changes of social state. Then every form of government

is an ent i t lement system, because the rights assigned by an ent i t lement system can include

all the powers and liberties of citizens and officials.

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Consider, in particular, absolute dictatorship and unrestricted majority rule -- two

simple, centralized forms of government. Absolute dictatorship by Mr. i is the ent i t lement

system that assigns to Mr. i the right to veto or effect any change of social state. Unre-

stricted majority rule is the ent i t lement system that assigns to each individual the right

to veto - or to effect - any change from any state in which a bare majority, of the n-1

other individuals have voted against -- or for - that change.

Besides libertarian utopias, then, ent i t lement systems include totali tarian forms of

government tha t directly allocate the entire social product. This shows that ent i t lement

theory is broader in scope than it seemed to be. It also shows that ent i t lement theory says

nothing about the peculiarities of the minimal, decentralized variety of government it was

designed to characterize. Green er~s when he says, "Ent i t lement theory describes a govern-

ment.., which does not intervene directly to move a society toward particular goals."

Ent i t lement theory describes no special sort of government.

Lone Dissenters and Busybody Extemalities

The Lone Dissenter condit ion is unreasonable. Green's Aunt Bertha from Altoona,

Pennsylvania did not want him to become an economist. She wanted him to become

something respectable, preferably a chiropractor like his late Uncle Ignatz. Although no one

else shared Bertha's preference, tha tvery fact securedher right, according to Lone Dissenter,

to veto Ed's becoming an economist. It is for tunate for economics that our society's pre-

vailing ent i t lement system did not satisfy Lone Dissenter.

Lone Dissenter licenses mischief more heinous than occasional meddling by the likes

of Aunt Bertha. Take any imagined atrocity describable as a fiend's veto of a social-state

change. By increasing the fiendishness of the atrocity to the point where no one else wants

i t commit ted (where the fiend alone opposes the change of social state), the fiend can,

according to Lone Dissenter, thereby secure the right to commit the atrocity. Thus, al-

though it does not let the Pope veto my use of contraceptives, Lone Dissenter might let

John Kenneth Galbralth veto Allan Meltzer's consumpt ion of food. It would let a lone

traitor veto acts of national defense, or a lone pyromaniac veto the sounding of a fire alarm.

Do not fault Green for using Lone Dissenter to prove unbiasedness. For besides

being one of a sufficient set of condit ions for unbiasedness, Lone Dissenter is a necessary

condit ion -- a fact made all the more interesting by the condit ion 's unreasonableness.

Unbiasedness and Discrimination

According to Green, an unbiased ent i t lement system is nondiscriminatory. Since

every Pareto-efficient state is final - even if it levels or reverses all inequalities found in the

initial state - the system itself does not favor rich or poor, well-born or low-born, or any

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other group. It prevents "any group in the population from benefit t ing systematically at

the expense of others": it "does not discriminate systematically on the basis of persons'

intrinsic characteristics."

If this seems too good to be true, that is because it is. Green has evidently assumed

that any final state of an ent i t lement system could be the actual outcome of the system,

the state that prevails in the end, hence that every Pareto-efficient state could be the actual

outcome if the system is unbiased. He is wrong. Every final state can be secured once it is

reached. Not every final state can be reached from the initial state.

Figure 1 depicts a two-person society in which A is the initial state and BE the

Pareto frontier. Because every p o i n t on CD Pareto dominates A, every such point can be

reached from A by unopposed individual action. Some points on BC or DE also might be

reachable from A, since ent i t lement systems do not necessarily proscribe actions that

impose external costs. But there is no reason to expect all the points onBC orDE to be reach-

able from A, and it is quite possible that none of them is. So we may suppose that some

points on BC or DE cannot be reached from A. But this means that not every Pareto-efficient

state, hence not every final state, can be the actual outcome.

Let us further suppose (as we may) that no point on BC or DE can be reached from

A. Then the inequality of initial endowments is reflected in the set of reachable points on

the Pareto frontier: the system is biased in Mr. 2's favor; it discriminates against Mr. 1.

Ent i t lement systems can be even more discriminatory than this argument suggests.

Built-in biases can be reflected not only in the reachable set (the set of states reachable

from the initial state) but even in the equilibrium set (the.set of final states) and the Pareto

set ( the set of Pareto-efficient states). Suppose an ent i t lement system favors one group by

letting its members appropriate almost the whole social product wi thout fear of veto by the

remaining group. Let x be any state in which the disfavored group enjoys most of the social

product. Unless it is identical or close to the initial state, x probably cannot be reached from

the initial state. But even if it can be reached, it is n o t f i n a h the favored group certainly pre-

fers some change from x that the disfavored group cannot veto. It follows by Green's theorem

that x is not Pareto efficient: some state must be preferred to x by someone and dispre-

ferred by no one.

Green took the coincidence of the Pareto and equilibrium sets as proof that the

equilibrium set comprises a broader range of distributional alternatives than expected. It

equally proves tha t the Pareto set comprises a narrower range.

Significance of the Theorem

What, then, does the converse welfare theorem show? Four things, at least:

Thing 1. As Arrow and Hahn contend, converse welfare theorems are not welfare

theorems at all; they are existence theorems. They show that equilibria exist, indeed abound.

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FIGURE 1

Mr. 2 's u t i l i t y

IB C

E

Mr. 1 's u t i l i t y

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Thing 2. The theorem helps to show that the initially attractive idea of a final

state is not a reasonable solution concept for ent i t lement systems : ent i t lement systems have

too many final states, not all of them reachable.

Thing 3. Because biases in an ent i t lement system can be reflected in the equilibrium

set (as well as the reachable set), Green's theorem shows that the Pareto set, too, can reflect

biases and so comprise a narrower range of distributional alternatives than one might have

expected.

Thing 4. Assuming Green's conditions, the theorem tells us that there is'a complete

coincidence of preferences and rights, at least within the Pareto set, in this sense:

If x and y are Pareto-efficient states and someone prefers

x to y, then someone who prefers x t o y has the right to veto

the change from x to y.

Proof: By the theorem, since y is Pareto-efficient, it is final. Thus, since someone prefers

x to y, someone must prefer y to x . But x, too, is final. So someone must prefer x to y and

have the right to veto the change from x t o y .