justice-constrained libertarian claims and pareto efficient collective decisions

W U L F G A E R T N E R

J U S T I C E - C O N S T R A I N E D L I B E R T A R I A N C L A I M S

A N D

P A R E T O E F F I C I E N T C O L L E C T I V E D E C I S I O N S *

ABSTRACT. This paper discusses justice-constrained libertarian claims that were proposed as a way to circumvent the impossibility of the Paretian liberal. Since most of the results are negative in character, we suggest an alternative route: A requirement on the structure of individual orderings should be combined with the idea that under particular circumstances individual decisiveness should be controlled by higher-order principles.

1. I N T R O D U C T I O N

The property of Pareto efficiency is a well cherished concept in economics. The question whether a certain economic allocation is Pareto efficient is always immediately raised after the question of the existence of that allocation (see [6] as an example). Alternative tax policies are analysed under the aspect as to what extent the various systems lead to a deviation from an optimal, i.e. Pareto efficient allocation [3]. Also in social choice theory the Pareto principle is a widely accepted condition requiring that if every member of society prefers alternative x to alternative y, let's say, so should society. Now, more than a decade ago, it was shown by Sen [14] that this minimal amount of efficiency in collective choice procedures can heavily collide with a fairly weak libertarian requirement also considered to be rather appealing in choice processes that guarantees a minimum of individual freedom to the members of society. This phenomenon has become known under the heading "The impossibility of the Paretian liberal". The following illustration which is due to Sen [15, 16] depicts the dilemma.

Consider a two-person society. A social decision is to be taken as to the employment of these two individuals. Imagine that there are four possible alternative states available to the two persons: (1/2, 0) person 1 gets a half-time employment while person 2 is without job (the first number in brackets indicates person l 's situation, the second number gives person 2's employment); (0, 1/2) the exact opposite of the first state; (1, 1/2) person 1 has a full-time employment while person 2 has a half-time job; (1/2, 1)

the exact opposite of the third alternative state. Now consider the following strict preferences of both individuals (they are arranged in perpen-

Erkenntnis 23 (1985) 1 17. 01654)106/85.10 ~f~) 1985 by D. Reidel Publishing Company

2 W U L F G A E R T N E R

dicular order with the more preferred alternative arranged above the less preferred one):

person 1 person 2

(1/2, O) (0, 1/2) (1, 1/2) (1/2, 1) (0, 1/2) (1/2, O) (1/2, 1) (1, 1/2)

Ceteris paribus, both persons obviously prefer more employment to less employment. Given the job situation of the other person, each individual should on libertarian grounds be free to decide autonomously hew much he (she) wants to work. Before entering into the world of precise definitions in section 2, we wish to state that the second and third alternative in each strict ordering represent the "'private sphere" of person 1 resp. person 2. The problem in our example now is that in some sense each individual attaches greater importance to the other being jobless than to his (her) own employment situation. Via the Pareto principle the two social states (1, 1/2) and (1/2, 1) are eliminated. The libertarian requirement that individuals should act as "local dictators" over their own private spheres furthermore knocks out the other two alternatives so that for our society there remains nothing to choose from. This is the dilemma.

One can, of course, argue that our result depends on the chosen orderings of the individuals. This is true, but are these preferences pathological? They are malevolent to some extent but this does not mean that they could never occur. Therefore, we should be able to grapple with situations such as the one depicted once we find both the Pareto rule and the decisiveness over private spheres attractive within collective choice mechanisms.

A lot of energy - coming both from economists and philosophers has been devoted to the task of circumventing the "liberal paradox" (see [15] and [8] for a review). In this paper, we wish to consider social systems in which the exercise of individual rights can be made contingent on the non-violation of some ethical criterion, a justice principle, for example.

The structure of the rest of the paper is as follows: Section 2 introduces some amount of notation and defines the basic concepts that will help to clarify our formal analysis. Section 3 examines justice-constrained libertarian claims which were suggested as a way to circumvent the impossi-

ON J U S T I C E - C O N S T R A I N E D LIBERTARIAN CLAIMS 3

bility of the Paretian liberal. Unfortunately, most of the results are negative in character. Therefore, in the final section 4, an alternative route is proposed. Within the framework of extended orderings, a requirement on individual preference orderings is combined with the idea that, at least in some situations, individual decisiveness should be "control led" by higher-order principles such as considerations of equity or fairness or equal treatment.

2. NOTATION, DEFINITIONS, AND BASIC CONCEPTS

Let N = {1, 2 . . . . . n} denote a finite set of individuals (n > 2) and let X = {x, y, z . . . . } denote the set of all conceivable social states. ~ stands for the family of all finite non-empty subsets of X, and each S e Y denotes a set of implementable social states. Ri is person i's subjective preference ordering on X and R -- (R~, R2 . . . . . R.) is called a subjective preference profile of society. We say that i e N weakly prefers a state x e X to another state y e X if and only if (x, y) e Ri. The strict preference relation corre-

sponding to Ri will be denoted by Pi: (x, y) ~ Pi ~-+ [(x, y) e Ri /', 0', X) q~ Ri]. The indifference relation will be denoted by Ii: (x , y ) e Ii *--+ [(x, y) e Ri A (y, X) e Ri]. A collective choice rule ( C C R ) is a function F which for each profile R generates a social choice C ( S ) = F ( R , S ) , where C ( S )

# 0 for any S e ~ is the set of socially chosen states from S. We now intrcduce a decomposition of each social state x e X into dif-

ferent components 2. Let Xo and X~ stand for the set of all impersonal features of the world and the set of all private features of person i e N respectively; the set of all social states is then given by X = Xo x (1-I Xi).

i eN

7(o and X~ are assumed to be finite with at least two elements each. Define

X~il = Xo • X1 • . . . • X i 1 • X i + t x . . . x X . f o r e a c h i a n d x = (Xo, x l . . . . . x , ) e X . I f xi ~ X i and z = (Zo, z l . . . . . z i - 1 , zi+ l . . . . . z , ) e X~il, then (x i ; z ) = (Zo, z l . . . . . z ~ - l , x i , z i + , . . . . . z . ) .

We assume that each individual i e N has a "private sphere" D~ con- sisting of at least one pair of personal alternatives over which he (she) is decisive "both ways" in the social choice process, i.e., (x, y) e D~ ,--+ 0', x) e D~ with x # y. Under the decomposition just introduced individual i's private sphere can be identified as

D , = { ( x , v ) ~ X • X l x ) . = y ) . A x , # V,}.


We call D = (D1, D2, ..., D.) a rights system; it is an assignment of ordered pairs of states to the members of society. According to Suzumura [18, p. 331], the rights system D = (Dx, D2 . . . . . D.) is coherent if and only if for every n-tuple of subjective orderings (R1, R2 . . . . . R.) there exists an order extension E of w (Di ~ R~). Coherent rights assignments prevent the Gib-

i~N

bard paradox [9, p. 392] from occurring. We should like to illustrate the property of coherence by means of the

following example which is a modification of our initial employment problem. This time, the feasible social alternatives are (1, 1), (1, 1/2), (1/2, 1) and (1/2, 1/2). We assume that person 1 has a preference for situations in which both individuals differ in the number of hours employed, while person 2 has a clear preference for states in which both individuals are employed an equal amount of time. The strict preferences of both individuals are:

person 1 person 2

(1, 1/2) (1, 1) (1/2, 1) (1/2, 1/2) (1, 1) (1/2, 1) (1/2, 1/2) (1, 1/2)

In our example, persons 1 and 2 are decisive both over the pair of outer states and the pair of inner states. The extension of w (D~ ~ R~) does

i~{1,2}

not constitute an ordering; there is a cycle instead. The rights assignment is said to be incoherent.

We next define Gibbard's [9] notion of unconditional preferences.

Unconditional Preferences (UP): Individual i has unconditional preferences with respect to his (her) sphere of rights D~ if and only if for all (x, y) ~ D,

if (x, y) ~ Pi, then ((x/; z), (Yi; z)) ~ Pi for all z ~ X~,.

We now introduce Gaertner and Kriiger's [7] concept of self-supporting preferences.

ON J U S T I C E - C O N S T R A I N E D LIBERTARIAN CLAIMS 5

Self-Supporting Preferences (SSP): Individual i has self-supporting preferences with respect to his (her) sphere of rights Di if and only if for all pairs (xi, Yi) �9 Xi x Xi with xi 4 = yl, if ((xi; z), (Yi; z')) �9 P~ for some z, : ' �9 X),, then ((xi; z), (Yi; z')) ~ Ri for all z, z' �9 X)i(.

Consider the following three conditions on a social choice procedure.

Condition U (unrestricted domain). The domain of C C R comprises all logically possible profiles of individual orderings on X.

Condition P (weak Pareto principle). For all x, y �9 X, (x, y) �9 ~ . Pi --~ [A"

�9 S --* 3' ql C(S)] for all S �9 ~ .

Condition L (Sen's libertarian claim). For each i �9 N, there exists at least one pair (x, y) �9 Di such that

(X, y) �9 Di c5 Pi ~ [x �9 S --, y ~ C(S)] for all S �9 5T.

Sen's famous "impossibility of the Paretian liberal" is enshrined in the following theorem [14].

THEOREM l (Sen). There does not exist a CCR satisfying conditions U, P, and L. 3

Taking conditions U and P and modifying condition L in the sense that individuals have to manifest unconditional preferences in order to be socially decisive leads to another impossibility result (Gibbard [9, p. 395]).

Conditions U and P together with a modification of condition L in the sense that individuals have to manifest self-supporting preferences in order to become socially decisive, however, yields a possibility result (Gaertner and Krfiger [7]).

We finally introduce the so-called extended sympathy approach (see e.g. Arrow [1, pp. 114 115; 2]. We assume that a certain type of interpersonal comparisons is possible, viz. statements of the form "individual i in state x is at least as well off as individualj in state y" can be made. In this way, individual extended orderings Ri are defined over the Cartesian product of states and individuals, X x N. Let Ri �9 Y (X x N) be individual i's extended ordering where Y (X x N) denotes the set of all logically possible extended


orderings. For all x, y �9 X and all j, k �9 N, ((x, j), (y, k)) � 9 means that according to individual i's interpersonal welfare judgments personj in state x is at least as well off as person k in state y. The problem now is to find a CCR which for each S �9 5 p and for each profile of individual extended orderings generates a non-empty social choice C(S). We denote the set of all logically possible profiles of individual extended orderings by (9. Given any profile (R,,/72 . . . . . /~,) e (9, we remind the reader that (R, , RE . . . . . R,) is the corresponding subjective profile (clearly ((x, i), (y, i)) �9 Ri can be stated equivalently as (x, y) �9 R~, for all i �9 N). An axiom due to Sen [14, p. 156] will turn out to be crucial in the analysis of the subsequent section.

AXIOM ID (identity). A profile (R1,/72 . . . . R,) satisfies the identity axiom if and only if for all x, y �9 X,

A i �9 N: [((x, i), (y, i)) �9 ~ A j �9 N: ((x, i), 0', i)) �9 R j].

The identity axiom ensures that there exists no discrepancy between individual i's view about his (her) own welfare in states x and y and everybody else's view about i's welfare in states x and y. We denote the admis- sible set of profiles under the identity axiom by (9m. Clearly we have (9~o

(9.

We should now redefine the property of unconditional preferences and the property of self-supporting preferences within the extended ordering framework. We shall, however, do it explicitly only for the concept of unconditionality. The redefinition for self-supporting preferences is completely analogous.

Unconditional Preferences: Individual i has unconditional preferences with respect to his (her) sphere Di if and only if for all (x, y) E Di, if ((x, i), (y, i)) e Pi, then ((xi, z; i), (Yi, z; i)) �9 Pi for all z �9 Xll ~.

The reader should note that in order to fulfil the requirement of unconditional preferences (the same applies to self-supporting preferences) a particular individual only has to manifest this property with respect to his (her) own positions under alternative social states. Considering the moti- vations underlying both concepts this requirement should be natural.

We also abstain from redefining condition P in the extended ordering framework. However, we shall redefine condition U.

ON J U S T I C E - C O N S T R A I N E D L I B E R T A R I A N CLAIMS 7

Condition UD. The domain of CCR comprises all elements from the set C.

Condition UDI (unrestricted domain under identity axiom). The domain of CCR comprises all elements from the set C~o.

3. J U S T I C E - C O N S T R A I N E D L I B E R T A R I A N R I G H T S

Kelly [10], Suzumura [18, 19] and Wriglesworth [20, 21] are the most prom- inent among those who have proposed to find a way out of the liberal paradox via restricting the exercise of libertarian rights by claims of equality or justice. The motivation for this approach is illustrated by the following quotation from Berlin [4, p. 55].

The extent of a man's or a people's liberty to choose to live as they desire must be weighed against the claims of many other values, of which equality, or justice, or happiness, or security, or public order are perhaps the most obvious examples. For this reason it cannot be unlimited . . . . Respect for the principles of justice, or shame at gross inequality of treatment, is as basic in man as the desire for liberty.

A rule by means of which ethical judgments are made will be called a principle of justice. Let q stand for a principle of justice. For each extended ordering/~i over X • N, q(Ri) denotes a binary relation on X such that x �9 X is considered to be at least as just as y �9 X if and only if (x, y) �9 q(/~). We require q(/]i) always to satisfy the transitivity property. Some of the justice principles we consider also satisfy the property of completeness; Suppes' criterion, however, with which we shall begin is not complete. The asymmetric part of q(/~) will be denoted by Q(R~).

Let Tu denote the set of all permutations on N. Suppes' [17] grading principle of justice QS(~i) says that for any individual extended ordering /~ and any x, y �9 X,

(x, y) ~ QS (R,i) ~ 3 p E TN:

[{A j e N: ((x, j), 0', P (/'))) ~/~} A {3 j ~ N: ((x, j), 0", P (]))) �9 Pi}].

According to this criterion, interpersonal permutations of individual positions are ethically irrelevant; no individual has any particular claim for a

8 WULF GAERTNER

particular (economic or social) position. Suzumura [19, p. 144] calls this property impartiality.

By now very well known is Rawls' "maximin" relation of justice [13] which is both complete and transitive. While we omit its definition here, we wish to explicitly define the lexicographic extension [14] of Rawls' maximin justice relation.

Let k(x), r(x) be the k-th resp. r-th worst off individuals in state x. The "leximin" justice relation Q~eX (/~) says that for any R~ and any x, y ~ X,

(X, y) e Qlex (/~i) +-~ [{3k e N(1 _< k _ n): ((x, k(x)), (y, k(y))) Pi} A {A r < k: ((x, r(x)), (y, r(y))) ~ I/}].

The leximin relation of justice also defines an ordering. We now assume that there exists one justice principle for each individual

in society (not necessarily identical for everyone). To summarize, we have for each profile of individual extended orderings (R1,/~2 . . . . . /],) the subjective profile (R1, R2 . . . . . Rn) and the ethical profile (q(/~l), q(/~2) . . . . . q(/?,)).

The idea that at least in some situations the exercise of libertarian rights should be restricted by claims of justice obviously means the following: If it is the case that the preference of a particular individual over some pair of alternatives from his (her) private sphere is opposed by the justice principle of one or several or all members of society, then this individual should no longer be socially decisive over that pair of private alternatives.

Let us turn this argument around and demand that if a particular preference of this individual over some pair of private alternatives is supported by the justice relation of every member of society, then the individual should be socially decisive over that pair of alternatives. This consequence seems natural.

Consider, however, the following situation of a two-person society (this example can easily be generalized to any number of individuals) where strict individual preferences are again arranged in perpendicular order: 4

person 1 person 2

(Xl, Y2, Z; 2) (xl, Yz, z; l) (xl, x2, z; 1) (Yl, Yz, z; 2) (Yl, Yz, z; 2) (xl, xz, z; 1)

ON JUSTICE-CONSTRAINED LIBERTARIAN CLAIMS 9

(Yl, xz, z; !) (Yl, x2, z; 2) (X1, Y2, Z; 1) (Xl, Y2, Z; 2) (xl, x2, z; 2) (xl, x2, z; 2)

(Yl, Y2, Z; l) (Yl, Y2, Z; l) (y~, X2, Z; 2) (Yl, X2, Z; 1)

It is easily seen that this is a case where the preferences of both individuals over all their respective private pairs are supported by everybody's justice principle (take Suppes' relation or the leximin justice relation). Just as an example, we have

((X1, X2, Z; 1), 0'1, X2, Z; 1)) ~ P1 and A i t {1, 2}:

((xl, x2, z), (Yl, x2, z)) e Qlex (/~i). Furthermore, both individuals manifest unconditional preferences.

According to the idea brought forward in the last paragraph both persons should be able to exercise their rights. This appears to be legitimate. Unfortunately, however, decisiveness over private pairs together with the weak Pareto principle precipitate the non-existence of a CCR in this case

the choice set is empty. Let's express this fact more formally by means of the following jus-

tice-constrained libertarian claim.

Condition JCL (1) (justice-constrained libertarian claim (1)). For every profile of individual extended orderings, every S ~ 5 ~, every x, y ~ X and every i ~ N, if (x, y) ~ Di c~ Pi and i has unconditional preferences and furthermore (x, y) e ~ Q(R~), then [x ~ S -~ v r C(S)].

jEN

Our result is

THEOREM 2. Assume that each individual i has chosen either the Suppes justice relation or the leximin justice relation as his (her) ethical criterion. There exists no CCR which satisfies condition UD, condition P and condition JCL (1).

Proqf. By the example above. Both individuals can exercise all their rights over their private pairs since their preferences are supported by everybody's justice principle. The individuals' decisiveness together with the Pareto condition eliminate all alternatives from the choice set.


There is a real dilemma. In our opinion this result is quite devastating for an approach that promised to resolve the liberal paradox via the ap- plication of justice principles. We should like to repeat: It seems quite appealing that individual preferences which are supported unanimously by ethical criteria should be socially recognized.

What can be done? Roughly speaking, there are two ways out of the impasse both of which, however, make rather strong additional require- ments. The first route introduces the identity axiom which we already defined in section 2; the other route requires that the Pareto principle be consistent with everybody's justice relation, too.

Consider the following justice-constrained libertarian claim which was formulated by Suzumura [19].

Condition JCL (2). For every profile of individual extended orderings, every S e 5P every x, y e X and every i e N, if (x, y) ~ Di ~ Pi and (y, x) r ~ Q(/~j), then [x e S ~ y r C(S)].

jeN

This condition requires that person i's rights-exercising be blocked when- ever at least one member of society it can be anyone - judges y to be more just than x.

Suzumura obtained the following possibility result.S

T H E O R E M 3 (Suzumura). Assume that the rights-assignment D = (D1, DE, .... D,) is coherent. Then there exists a CCR which satisfies condition UDI, condition P and condition JCL (2). 6

Unfortunately, condition JCL (2) is an extremely weak libertarian claim; the "ethical opposition" of only one person is sufficient to annul the rights- exercising of a particular individual. What is even worse is that once we drop the fulfilment of the identity axiom we are led back to an impossibility result (see Theorem 4.4 in [19]). 7

The identity axiom clearly implies a domain restriction. One may never- theless raise the question whether under this axiom it is possible to obtain a result that is stronger (more appealing) than Theorem 3. The following justice-constrained libertarian claim is in our view much more acceptable than the previous one.

ON J U S T I C E - C O N S T R A I N E D LIBERTARIAN CLAIMS l l

Condition JCL (3). For every profile of individual extended orderings, every S e ~ , every x, y e X and every i e N, if (x, y) e Di r~ Pi and 0', x) (~ ~ Q(~j), then Ix ~ S ~ y r C(S)].

j~N/(i}

Under this condition person i's rights-exercising will be withheld if all the other members of society unanimously believe that y is more just than x. Berlin [4, p. 55] might have thought of a societal control like the one in JCL (3) when he said that a man's liberty "cannot be unlimited". Unfor- tunately, however, there does not exist a CCR satisfying condition UDI, condition P and condition JCL (3) (see Theorem 4.5 in [19]; for an example of this inconsistency see [8, p. 302]).

The other route was proposed quite recently by Wriglesworth [21]. In- stead of requiring condition UDI it is demanded that both the libertarian condition and the Pareto condition be consistent with the justice relation of every member of society. Wriglesworth's libertarian claim JCL (4) is condition JCL (1) above without the requirement of unconditional preferences.

Condition Ps (justice-constrained weak Pareto). For every profile of individual extended orderings, every S ~ 5 ~ and every x, y ~ X, if ((x, i), (y, i))

i~Nc~ Pi and (x, y) ~ i~ Q(Ri), then [x ~ S -~ ~v r C(S)].

The following result now holds.

THEOREM 4 (Wriglesworth). There exists a CCR which satisfies condition UD, condition Ps and condition JCL (4). 8"o

The following situation of a two-person society is such that all individual rights are exercised according to JCL(4) and also the Pareto preference gets through untouched:

person 1 person 2

0'1, y2, z; 2) (Xl, x2, z; 1) (Xl, y2, 2; 2) (Xl, y2, z; 1) (xl, x2, z; 1) (Yl, y2, z; 2) (xl, yz, z; 1) (xl, y2, z; 2) (Yl, x2, z; 1) (xl, x2, z; 2) (Yl, y , , z; 1) (yl, x2, z; 1)

12

(xl, x2, z; 2) (Yl, x2, z; 2)

W U L F G A E R T N E R

(Yl, Y2, 7,, l )

(Yl, xz , z; 2)

4. AN A L T E R N A T I V E ROUTE

In the last section we have seen that a few positive results are thickly surrounded by impossibility theorems. The idea that individual decisions over private pairs of alternatives should be subjected to justice considerations cannot be dismissed as totally unacceptable. In the social choice processes we have been considering individuals (can) act as local dictators and this should not proceed in a completely uncontrolled way. The problem with the approach of the last section, however, is that (a) the libertarian claim JCL (2) is extremely weak, too weak in our view, and (b) this claim is only successful when it is combined with a domain restriction, the identity axiom. Domain restrictions cannot be justified easily, much less still in liberal societies.

Wriglesworth's approach via the Pareto principle avoids domain restrictions but it seems a bit strange. To keep a strict eye on a local dictator may be understandable, but why do the same with society where everybody has given expression to the same direction of preference? 1~

The proponents of the justice-constrained approach quoted a passage from Berlin [4] in order to motivate their resolution schemes. Let us pause a moment and remember the examples that were used to illustrate the liberal paradox. Among others, there was Sen's [14] issue of who should read a certain novel by D. H. Lawrence. Then there was the "belly or back" question, Gibbard's [9] Angelina-Edwin marriage problem and the issue of the colour of bedroom walls. All these situations and many more which were used in past discussions are very private ones with only minor repercussions on society as a whole. Therefore, at least for these issues, the approach to constrain libertarian claims by justice principles appears a bit like breaking butterflies on the wheel.

Without denying the importance of the justice-constrained approach in some instances we propose that the liberal paradox be resolved by some "standard" resolution scheme be it Sen [15] and Suzumura's [18] proposal to constrain the Pareto principle, or Gibbard's [9] theory of alien- ating rights, possibly in its "mixed libertarian claim" variant [11], or Gaertner and Kriiger's [7] route of self-supporting preferences and add

ON J U S T I C E - C O N S T R A I N E D L I B E R T A R I A N C L A I M S 13

a justice constraint in the sense of JCL (3). In the last part of the paper we wish to sketch the latter direction, i.e. using the concept of self-supporting preferences in the extended ordering framework.

In [7] we presented a description much richer than we have done in the present paper of how a social state can be decomposed. Each social state is a list of personal and collective features of the world. The collective features can be split into two subsets: Each element of subset a denotes a collection of "basic collective features" such as the political constitution or the economic policy or the social security system; each element of subset b is to be interpreted as representing a collection of "all the other" collective features, some of which (may) depend, others will not depend, on the decisions that the individuals take with respect to their private spheres. "Under normal circumstances" the basic collective features will be unaf- fected by the private decisions of the members of society.

We then required that only for those individuals who reveal self-supporting preferences the personal spheres Di should be converted into socially protected spheres. It is now important to note that our definition of Di in [7, p. 22] was a bit different from the one given in the present paper. Within the framework of that richer structure we allowed a person still to be decisive within his (her) sphere when there were concomitant changes in "all the other" collective features. We wrote (p. 23) that to weaken the right by admitting no changes at all in subset b would mean to open the possibility of weighing public utility against iindividual rights in each particular case, which would completely undermine, indeed virtually destroy the right. For one should expect at least some influence sometimes only very weak of every individual decision on public affairs (the right of conscientious objection against military service, for example, diminishes the number of conscripts).

Individual rights do have a price. What should, however, be done if this price becomes too high for society? This could occur, for example, by a coincidence of many individual decisions. Compare throwing one's rub- bish into the back-yard in a thinly populated (agricultural) socieLy with doing the same in one of the overpopulated metropolitan areas. We argued that changes in subset b should be tolerated as long as they do not change or at least do not impair the functioning of the basic collective features.1 When this occurs we now propose that this problem should be dealt with by introducing a justice-constrained claim like JCL (3) that keeps the social


decisiveness of individuals within bounds. The introduction of justice-constrained claims should be viewed as the adequate counter-measure against public damage, preferably applied to all members of society alike. With some justification claims like JCL (3) may be viewed as intermediate steps until eventually new laws are formulated and enforced within a decision process of higher order.

It has been argued that the property of self-supporting preferences im- poses rather heavy restrictions on individuals' preferences. It has, for example, been criticized that property SSP is being required with respect to the total set X. This may indeed be a bit too strict; one could demand that SSP only holds with respect to S, the set of implementable social states 12. Much more seriously do we take the objection that SSP is a condition acceptable to self-centred people but unacceptable to people with altruistic preferences. We should like to draw the reader's attention to the fact that within the extended sympathy approach property SSP is only required with respect to the particular individual's own positions. Outside of his (her) own positions the individual can have any ranking of social alternatives. He (she) can exercise extended sympathy on a large scale if he (she) so wishes without running the risk of losing social decisiveness over the own private sphere.

Consider the following justice-constrained libertarian claim.

Condition JCL (5). For every profile of individual extended orderings, every S e 5g, every x, 3' s X and every i e N, if (x, y) ~ Di c~ ei and i manifests self-supporting preferences and furthermore (y, x) r c~ Q(~j),

jeN/{i}

then [x e S --, y r C(S)].

T H E O R E M 5. There exists a CCR which satisfies condition UD, condition P and condition JCL (5).

Proof. The proof follows exactly the one of Theorem 1 in [7], now formulated in the extended ordering framework. As it is rather lengthy, we will omit it here.

We should like to point out that Theorem 5 holds without any "control" at all by other people's ethical preferences, but dropping this aspect in our theorem would be contrary to our intention outlined above. Concerning the extent of societal control we have now achieved quite a bit of flexibility,


ranging from (y, x) r c~ Q(~j) as in JCL (5) above to (y, x) r vo q(/~j), j~N/{i} j~N/{i}

which is an extremely weak libertarian claim. In the example at the end of section 3, both individuals manifest self-

supporting preferences. Therefore, due to Theorem 5, a CCR exists. How- ever, the example is such that a CCR also exists according to Theorem 3 and, naturally, Theorem 4.~3

On the basis of Theorem 5 we can now do without the identity axiom, we can forget about the extremely weak claim JCL (2), and we can dispense with the justice-constrained Pareto principle Pj. The price we are paying is, of course, requirement SSP.

As our last example consider the following situation which is simply a reshuffle of the positions in the example just discussed:

person 1 person 2

0'1, x2, z; 2) 0'1, Y2, z; 1) (x> Y2, z; 2) (Yl, Y2, 7.; 2) (x~, xz, :; 1) (xl, x2, z; 1) (v,, Y2, z; 2) (xl, Y2, z; 2) (xt, Y2, z; l) 0'1, x2, z; 2) QI,' 1, X2, Z; 1) (Xl, X2, Z; 2)

(1'1, 3'2, z; 1) O'L, x2, z; 1) (xl, x2, z;2) (xl, y > z ; 1)

Both individuals still satisfy property SSP; the axiom of identity, however, is no longer fulfilled. Therefore, Suzumura's Theorem 3 is no help at all. According to Wriglesworth's Theorem 4, the social decisiveness of both individuals over all their private pairs of alternatives is annulled and in addition the weak Pareto preference is axed. 14 Consequently, in this example, C(S) is equal to the set S of social states if conditions JCL (4) and Pj are applied. Referring to our Theorem 5, the choice set is C(S) = {(x, y), (.v, y)}. Due to JCL (5), person 2 objects to the decisiveness of person 1 over the pair (xl, Y2, z), 0"1, Y2, z); person 1 objects to person 2 being decisive over the pair (Yl, Y2, z), (Yl, x2, z). All the other rights are exercised, and Pareto gets off unscathed.


NOTES

* Helpful suggestions from an anonymous referee of this journal are gratefully acknowl- edged.

A contrary position is held by Nozick [12] who argued that "rights do not determine a social ordering but instead set the constraints within which a social choice is to be made" (p. 166). We do not share this view as we consider the structure and exercise of individuals' rights as integral parts of social choice (see also Sen [15, p. 230]). Furthermore, we analyse the exercise of rights within a framework of preference maximization; this approach has recently been questioned by Chapman [5]. 2 This decomposition goes back to Gibbard [9]. 3 One should mention that Sen formulated his result without using Gibbard's framework of decomposed social states. 4 The component z refers to all impersonal features of the world. s See also section VII in [20]. 6 Actually, the theorem is still true when we require the strong Pareto rule which we did not define in this paper.

Our example above can serve as an illustration of this result. s In Wriglesworth's approach it would be superfluous to assume that the assignment of rights be coherent. The coherence aspect is taken into account in the simultaneous functioning of conditions Pj and JCL (4). 9 Would a combination of conditions Pj and JCL (3) be successful? Unfortunately, the answer is "no" (see again the example in [8, p. 302]). 1o What is a bit frightening in this proposal is that a single "ethical dissenter" is sufficient to neutralize a unanimous strict preference relationship. 1 ~ In our example the general state of health of a community could be at stake. 12 This would have some consequences as to the fulfilment of certain consistency conditions and the fulfilment of Arrow's [1] condition of the independence of irrelevant alternatives. An evaluation of these implications, however, is beyond the scope of the present paper.

3 Use, for example, the leximin justice relation as the common ethical relationship. ~4 See footnote 13.

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Manuscript submitted 6 August 1983 Final version received 20 December I983

Department of Economics, Postfach 44 69, University of Osnabr/ick, D-4500 Osnabr/ick, West Germany

justice-constrained libertarian claims and pareto efficient collective decisions

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