Ethical Rules, Expected Values, and Large Numbers

Author(s): James M. Buchanan

Source: Ethics , Oct., 1965, Vol. 76, No. 1 (Oct., 1965), pp. 1-13
Published by: The University of Chicago Press

Stable URL: https://www.jstor.org/stable/2379366

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 ETHICS AN INTERNATIONAL JOURNAL OF
SOCIAL, POLITICAL, AND LEGAL PHILOSOPHY

Volume LXXVI OCTOBER 1965 Number i

ETHICAL RULES, EXPECTED VALUES, AND

LARGE NUMBERS1

JAMES M. BUCHANAN

I. INTRODUCTION culus concerning the ethical choices

W HAT influences an individual's made by "others" in the relevant group.

choice among ethical rules? I

Section III examines the importance of
group size for this probability calculus,
shall demonstrate that the
and simple examples are introduced to
size of the group within which he con-
show how the individual's decision can
sciously interacts is a critical determi-
nant. Individual choice behavior, even be modified solely by a change in num-

at this fundamental level of ethical

bers. The dilemma of the individual
who finds himself a member of a criti-
rules, may differ sharply between small
groups and large groups. This hypothe- cally large group is treated in some de-
tail. Section IV develops comparisons
sis is corroborated by well-known and
with individual choice behavior in eco-
commonly observed experience. To my
nomic theory, where the relevance of
knowledge, however, ethical theorists
have neglected the apparent importance
group size has been recognized even if
not sufficiently clarified. Finally, Sec-
of group size.2
In the remainder of this introductory tion V briefly explores some possible
implications of the critical size hypothe-
section I relate my discussion to the
sis for reforms in social institutions.
standard questions in ethical theory. In
To avoid preliminary misunderstand-
so doing I am guided solely by the ne-
cessities of the argument that I want to ing, let me state what this paper is not.
It is not an essay in "ethics," by which
develop. My lack of competence to dis-
cuss ethical theory per se will be fully I mean a discussion of what individuals

apparent. In Section II I discuss the should or should not do. Aside from
individual's choice among ethical rules this, as will be evident to informed read-
in terms of an ordering of potential so- ers, the paper is not designed to con-
cial states or situations. One particular tribute to Kantian criticism, either in
ordering will be advanced as plausible the traditional sense of discussing what
and its appropriateness will be de- Kant really meant or in the modern ver-
fended. The individual's choice among sion of discussing the generalization
ethical rules is shown to depend on this principle of argument. I shall be con-
ordering along with his probability cal- cerned exclusively with an individual's

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 2 ETHICS

choice among ethical rules and with the havior in subsequent actions? There are
possibilities of predicting this choice. two alternatives before him. He can
Any analysis of choice must involve adopt a rule, which we shall call "the
some consideration of the alternatives, moral law," or he can adopt a rule
and it is here that I accept, without ar- which, loosely, we shall call "the private
gument, the relevance of something akin maxim." By selecting the first, the in-
to the Kantian distinction between the dividual commits himself to act in sub-
moral law and the subjective or private sequent situations on the basis of some-
maximt. My concern is with a question thing like the generalization principle.
similar to one put by Beck: "it is a That is, he will not act in ways other
question of what are the conditions, in than those which allow his particular
a being like man, that make it possible action to be universalized, regardless of
for him to take an interest in the law the specific consequences. By selecting
and have the law as his incentive."3 I the second rule instead, he commits
am not directly interested in the indi- himself in advance to no particular
vidual's ability to make an appropriate principle of behavior. He retains full
distinction between that action dictated freedom to act on the basis of expedient
by the "moral law" and that dictated considerations in each particular in-
by the "private maxim," either univer- stance that arises. Note that, in terms
sally or in specific instances. I simply of observed or revealed behavior in par-
accept that the generalization or uni- ticular acts, there need be no difference
versality principle can be applied in a in the results of these two ethical rules.
sufficient number of cases to make my The person who rejects the moral law
argument, which is restricted to those as an ethical rule that effectively con-
cases, worth developing.4 The analysis strains his choices among acts may,
requires only that the individual be as- nonetheless, fully accept the behavior
sumed to confront a choice among ethi- dictated by this law in particular cir-
cal rules and that something loosely cumstances. For this reason, the choice
similar to the Kantian dichotomy de- that I am centrally concerned with
scribes the alternatives that he faces. should not be interpreted as one be-
In this setting I want to examine the tween "moral" and "immoral" rules.
possibilities of predicting this choice.
II. THE ORDERING OF SOCIAL STATES
Note that the choice to be analyzed is
that between separate rules for behav- As soon as the notion of generaliza-
ior, not that between separate acts in tion or universalization is introduced,
particular circumstances. Much of my individual behavior embodies social
discussion can be applied directly to the content. The choosing-acting party in-
latter choice, but, for reasons to be teracts with other parties, whose behav-
noted, there are advantages to limiting ior in turn becomes a part of the nec-
specific analyses to the choice between essary environment within which his
rules, which, once chosen, will serve to own choices take place. In this respect
predetermine acts within the limits im- much of the Kantian criticism seems to
plied. me to have been overly individualistic.
The individual is presumed to be fac- The individual's decision as to whether
ing the following question: What ethical he should adopt the moral law or the
rule shall I adopt as a guide to my be- expediency criterion as an ethical rule

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 ETHICAL RULES, EXPECTED VALUES, AND LARGE NUMBERS 3

surely depends upon his own predic- state only in the individual's own choice
tions about the behavior of others and of an ethical rule. Here he adopts the
upon his evaluations of comparative rule of following his own private max-
states of society incorporating this be- ims in determining particular acts.
havior. The rules predicted to be chosen Clearly he will expect to experience, on
by others will be of importance in de- some occasions, differentially favorable
termining the descriptive characteristics consequences from this retained free-
of alternative social states or situations. dom.
We want to examine now the indi- 5. The generalized world.-This
vidual's evaluation of separate social state may, within limits, be called the
states or situations, and we can best do idealized Kantian world. The individual
so in terms of an ordering that he places who is making the ordering, along with
on alternative consequences or out- substantially all of his fellows, adopts
comes. These outcomes can be described the moral law as a general rule for be-
in terms of two sets of ethical rules, his havior. Mutual self-respect, honesty,
own and those of "others." Listed be- duty: these make for a highly desirable
low in ascending rank is an ordering of social interaction process.
six social states. 6. Expediency in a duty-bound world.
1. The worst possible world.-The -In this state the individual himself
individual himself adopts the moral retains the rule that allows him to act
law, but almost none of his fellows does from his own private maxims whereas
so. He should expect to be grossly ex- substantially everyone else in the group
ploited. This is clearly an undesirable follows some version of the moral law.
state of affairs for other than a masoch- Clearly, this state is the most desirable
ist. for the individual. He retains complete
2. Mondo cane.-This second state is freedom to follow the dictates of expe-
only slightly better than the first. Here diency in particular actions as his own
the individual predicts that almost none subjective attitudes may suggest, while
of his fellow citizens will follow the also enjoying a wider freedom to act, if
moral law as an ethical rule. However, he so chooses, strictly in terms of the
in this combination he, too, follows the categorical imperative.
criterion of expediency. He can, by fol- I suggest that the ordering presented
lowing the dominant behavior pattern, above is a reasonable one for most indi-
prevent differential exploitation. viduals. It may be objected that this or-
3. Commitment in a mixed world.- dering of social states itself reflects the
This is a state in which the individual evaluations of an immoral person be-
predicts that roughly one-half of his cause it does not impute to the adoption
fellows will follow some version of the of the moral law itself a positive com-
moral law and in which he also adopts ponent or value. An individual, it might
this law as an ethical rule. Along with be argued, "should," and if moral
the other committed persons in the "will," prefer a world in which he him-
group, he will expect to be forced, on self acts in accordance with the moral
occasion, to behave contrary to the dic- law because of some intrinsic worth of
tates of expediency. morality itself. I do not propose to quar-
4. Expediency in a partially commit- rel with those who might take this posi-
ted world.-This differs from the third tion, even were I equipped to do so. But

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 4 ETHICS

the possible objection along these lines ing rank-1, 2, 30, 40, 500, 600-indi-
is not germane to my analysis, and it is cating wide differentials between the
precisely to cover myself in this respect world of moral law as an ethical rule
that I have concentrated on the choice and the world of expediency. The point
of ethical rules rather than on the to be emphasized is, however, the essen-
choice of acts. The individual may, for tial arbitrariness of the particular num-
reasons indicated, prefer to act in ac- bers assigned. It is in part to emphasize
cordance with the moral law, even this, as well as for simplicity, that the
though he does not choose to adopt this simple numerical listing will be used
law as his overriding ethical rule. If, here.
however, he places any value at all on We can summarize the individual's
a widened area of choice, he will tend to ordering that has been suggested in a
rank the states where he retains such simple 2-by-3 matrix (Table 1) in
which the rows indicate the alternative
TABLE 1 rules that he may choose while the col-
umns indicate the possible behavior pat-
"OTHERS" terns that he predicts for "others" in
the interacting group. It is evident that
INDIVIDUALS Almost About One- Almost there can be as many columns as de-
None Fol- Half Follow All Follow
low Moral Moral Law Moral Law
sired, depending on the detail with
Law as Rule as Rule as Rule which he might want to specify the in-
Follow private dividual's predictions about the choices
maxims as rule. 2 4 6 of rules by others.
Follow moral law
as rule .1 3 5 The information summarized in the
matrix is not sufficient to enable us to
predict how the individual will actually
choice, all other things being equal, choose between the two ethical rules
higher than the states where this choice that he confronts. There is no indica-
is explicitly narrowed. tion to this point as to his estimates of
The suggested ordering was presented the probabilities of the choice patterns
in a simple numerical listing, 1 through of "others." Until we introduce such es-
6. Some numerical scale will be helpful timates, expected values for his own
in discussing the individual's choice of choice alternatives cannot be derived.
rules, but this scale is wholly arbitrary We need to know what probability the
so long as the numbers stand in the individual assigns to each of the three
same order one to another. For simplic- possible behavior patterns of his fel-
ity only I shall use the numbers in the lows.
simple listing to indicate the relative Let us suppose that he assigns a prob-
evaluations that the individual might ability of 0.6 to the first pattern, 0.3 to
place on the several possible social the second, and 0.1 to the third. The
states. Alternatively, any number of matrix is rewritten in abbreviated form
zeros could be added to each number, as Table 2, with the predicted or as-
or, perhaps more realistically, there signed probabilities in parentheses.
may be multiples placed between each Given the values in the ordering, along
subset of two in the listing. In the latter with the probabilities as assigned in Ta-
case the ordering might run, in ascend- ble 2, we can compute expected values

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 ETHICAL RULES, EXPECTED VALUES, AND LARGE NUMBERS 5

for each alternative confronting the in- side door. I am, of course, tempted to
dividual who must decide. As the right- call "that which the individual maxi-
hand column indicates, the expected mizes in his choice behavior" something
value from following the moral law as a like "utility," and the approach here
rule is less than that from adopting the stems from the expected utility analy-
rule of expedient behavior. Under the sis that is familiar in modern econom-
conditions depicted, the individual can ics. It must be emphasized, however,
be predicted to reject the moral law as that the numerical scale does nothing
an ethical rule, and to adopt instead a other than provide a helpful tool for
rule that will allow him to act in each analyzing individual choice among ethi-
case on his own subjective maxims. cal rules, and any connection between
The expected values depend, of this scale and "utility" in any connota-
course, on the probabilities that the in- tion of "happiness" or "pleasure" can
dividual assigns to the various patterns be quite explicitly rejected. Individuals
of behavior for "others" than himself. choose what they choose, whether this
Careful examination of the numerical
TABLE 2
example reveals, however, that a change
in these probabilities will not modify the
"OTHERS
choice of a rule that is dictated. Sup-
pose, for illustration of this point, that INDIVIDUAL

the probabilities are changed from (0.6, None One-Half All Expected
Value
0.3, 0.1) to (0.0, 0.4, 0.6). Clearly, un-
Privatermaxim.. 2(0.6) 4(0.3) 6(0.1) 3
der this new situation the expected Moral law ..... 1(0.6) 3(0.3) 5(0.1) 2
value under either rule is increased; the
individual simply lives in a "better"
world. But note that, given the same be apples or ethical rules, and we can,
rank ordering and same valuations, the in both cases, discuss their choices in
expected value from adopting the moral terms of some ranking of "better" and
law as a rule, which is now 4.2, remains "worse") results. If we could not do so,
less than that expected from the alter- we should be unable to discuss choice at
native-rule choice, which becomes 5.2. all. This is the only function of intro-
Hence, we conclude that in this model, ducing the arbitrarily precise numeri-
regardless of the pattern of rule choice cal ordering of social states. If this were
that the individual predicts on the part the end of it, much of the matrix illus-
of his fellows, he will not be led to adopt tration would, of course, be almost
the moral law as a binding ethical rule wholly unnecessary baggage. As I shall
for his own behavior so long as his eval- demonstrate in the following section,
uation of comparative social states re- however, the construction does enable
mains that indicated in the matrix illus- significant conclusions to be reached.
trations.
III. THE RELEVANCE OF NUMBERS
Ethical theorists may object to the
usage of any numerical scale to indicate In a sense, the example presented
the evaluations that the individual above is deceptive because one assump-
places on social states, and because I tion that is essential for the results has
am an economist I may stand accused been deliberately left unmentioned. Re-
of introducing expected utility by the call that changes in the probabilities as-

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 6 ETHICS

signed to different rule choices on the exceeds that for the alternative "follow
part of "others" do not change the private maxims." There is no change in
ranking of the expected values of the the individual's ordering of the social
two alternatives for the individual who states or even in his presumed numeri-
is trying to decide which rule to adopt cal evaluations.
for himself. But this is true only within The question is one of determining
the limits of the particular example, and the conditions under which an individu-
it should have been noted that the ref- al's rational calculus will lead him to as-
erence individual was assumed to as- sign probabilities of one sort or another.
sign the same probability distribution to When will he assign probabilities of the
"others," regardless of his own choice sort shown in Table 3 rather than those
of an ethical rule. In terms specifically of Table 2? The central hypothesis of
of the matrix of Table 2, the same prob- this paper is that the size of the inter-
ability distribution was assumed appli- acting group is one of the important de-
cable for each row. This assumption will terminants in this assignment. An indi-
be appropriate only in those situations vidual who consciously interacts with
only a small number of other persons in
TABLE 3
ethical relationships will tend to assign
probabilities similar to those illustrated
"OTHERS"
in Table 3, while the same individual, if
INDIVIDUAL he consciously interacts with a critically
None One-Half All Expected
Value
large number of other persons, will as-
sign probabilities similar to those of Ta-
Private maxim.. 2(0.6) 4(0.3) 6(0.1) 3
Moral law . 1(0.0) 3(0.4) 5(0.6) 4.2
ble 2. The precise numerical values are
not, of course, important here. The only
requirement is that there be some posi-
where the individual predicts that his tive relationship between the individu-
own choice of a rule in no way modifies al's own choice of an ethical rule and the
or influences the similar choices of choices that he predicts for others.
"others." The general validity of this hypothe-
Consider, now, a sharply different sis for the small-number model may be
setting in which only this one element is shown by reference to a simple, three-
modified. The probability distribution person example. There are three per-
in the first row of the matrix, which ap- sons in an isolated setting, say, a desert
plies when he rejects the moral law as a island, and each person faces the choice
rule, is assumed unchanged from that among ethical rules when considering
of Table 2. For the second row, which how to behave with his fellows. Clearly,
holds when he chooses to adopt the any one of the three will tend to recog-
moral law as a rule governing future nize that his own choice of a rule, and
acts, let us introduce a different proba- subsequent adherence to it, will to some
bility distribution, that which was pre- considerable extent influence the similar
viously used as the modification on our choices to be made and followed by the
illustration. The matrix will then look other two members. Since we may as-
as shown in Table 3. Note that in Table sume that each of the three prefers to
3 the expected value for the choice rep- live in a setting of mutual self-respect,
resented in "follow the moral law" now as shown by our ordering, the most like-

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 ETHICAL RULES, EXPECTED VALUES, AND LARGE NUMBERS 7

ly outcome will surely be one where potentially honest man who finds him-
each and every person adopts, and fol- self among thieves. In a group of criti-
lows, something that is akin to the cally large size, the individual will tend
Kantian categorical imperative.5 His to adopt the rule of following the ex-
standard for behavior will be some ver- pediency criterion even if he thinks that
sion of the generalization principle. all of his fellow citizens are saints, pro-
This result will tend to emerge in a vided only that the suggested ordering
small group quite independently of the holds. Numerically, this is clearly shown
individual's particular evaluations of in the illustrations, but repetition of the
the several possible social states so long point seems warranted. The conditions
as the suggested rank order holds. The of individual choice are such that there
differences in evaluation between the will be a rationally based rejection of
idealized Kantian world and that peo- the rule, "follow the moral law," quite
pled by subjective maximizers may be independently of predictions as to the
great or small. The critical requirement ethical rules that may be chosen by oth-
is located only in the diagonally ers in the interacting group.
weighted probability assignments of the If the analysis is applicable for any
matrix. The upper-right-hand squares one individual in the critically large
must tend toward zero in expected value group, it must, of course, be applicable
because of the unlikely event of the in- to all. Because of this interdependence,
dicated combinations of rules emerging each member (and hence all members)
in the social interaction process. In will find himself in a genuine dilemma.
small groups, the individual simply can- He may value the social state depicted
not expect uniquely to enjoy a widened by the combinations on the right-hand
range of choice. side of the matrix much higher than
The small-group model can be con- those on the left. But despite this, he
trasted with that which includes a large will find that he ends up, necessarily, in
number of persons, and for which the the upper-left-hand square. Rationally,
matrix illustration of Table 2 applies. he cannot adopt the moral law as a prin-
Here the individual considers his own ciple for his own behavior. Neither can
choice of an ethical rule to exert no in- his fellows. Therefore, the predictable
fluence on the choices of rules made by consequences of ethical choices are
others. In effect, the choices of others those characteristic of a world where all
here are treated as a part of the natural persons reject the moral law as a con-
environment, so to speak, and not de- trolling rule, and, instead, follow their
pendent on the individual's own deci- own private maxims. Each and every
sion. In this limiting case, the individual person may, of course, consider that he
must make probability assignments that would be "better off," in terms of his
are described in their critical character- own evaluation, in a different world
istics by Table 2. An interchange be- where the moral law is widely accepted
tween the rows in the matrix will not as an overriding ethical rule. But, pri-
change the probability distribution of vately and voluntarily, there is simply
the choices of rules by others. no means through which the single in-
It is perhaps worth emphasizing that dividual can choose to make this alter-
my argument is not the relatively famil- native state of the world more nearly
iar one that presents the plight of the realizable.6

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 8 ETHICS

The dilemma is a real one, and it is the rule of moral law in his small-group
similar to, although not identical with, interactions, there is some increase in
that which is commonly discussed in group size that will cause him to mod-
game theory as "the prisoners' dilem- ify his ethical rule and become a private
ma." In the latter, each of two prisoners maximizer.
is led to confess by the conditions of the When stated in this fashion, the nu-
situation in which he is placed, despite merous corroborations of the hypothesis
the fact that both prisoners would be in in everyday experience are familiar.
a more desired position should they Volunteer fire departments arise in vil-
both refrain from confessing. The dif- lages, not in metropolitan centers.
ference between the prisoners' dilemma Crime rates increase consistently with
and the large-group ethical dilemma dis- city size. Africans behave differently in
cussed here lies in the fact that, as or- tribal culture than in urban-industrial-
dinarily presented, the former remains ized settings. There is honor among
a small-group phenomenon. The results thieves. The Mafia has its own stand-
emerge because of the absence of com- ards. Time-tested honor systems in uni-
munication between the prisoners and versities and colleges collapse when en-
because of their mutual distrust. The rolments exceed critical size limits.
large-number dilemma is a more serious Litter is more likely to be found on
one because no additional communica- main-traveled routes than on residential
tion or repetition of choices can effec- streets. Even the old adage, "Never
tively modify the results. trust a stranger," reflects a recognition
There is nothing in the analysis that of this elemental truth, along with, of
suggests the actual size that a particu- course, additional ethical predictions.
lar group must attain before the indi- Successful politicians organize "grass-
vidual choice calculus undergoes the rel- roots" support at the precinct level.
atively dramatic change that has been Only some of these examples are ex-
noted. It seems evident that the divid- plicitly ethical, but the phenomenon is
ing line between the critically small and not limited to the choice of ethical rules
the critically large group will vary with or acts. The large-number dilemma per-
many circumstances, and no attempt vades many areas of social interaction.
will be made here to list these. Similar-
IV. FREE RIDERS AND PERFECT
ly, it is also clear that the individual dif-
COMPETITION
ferences will make for important differ-
ences in ethical choices. Under identical The proposition that this paper ex-
external circumstances, some members tends to ethical theory has been widely
of a group of a given size will tend to recognized in economics, although even
choose rules as if they are interacting in here the vital distinction between indi-
a critically small setting, while other vidual choice behavior in small-group
members may choose rules as if the and in large-group situations has not al-
group is critically large. The hypothe- ways been fully appreciated. Two sepa-
sis does not require that these distinc- rate applications will be summarized
tions be made. All that is necessary for here. The first of these, commonly
the hypothesis to hold is that, for any called "the free-rider problem" is a di-
given individual who may be observed rect analogue to the ethical theory ex-
to follow what may loosely be called tension, and my work on this problem

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 ETHICAL RULES, EXPECTED VALUES, AND LARGE NUMBERS 9

provided the specific stimulus for this zens, contributes a share in the common
paper. The second application is, in one cost than he is in a situation where no
sense, the inverse analogue. This is the one contributes anything. Yet each per-
whole notion of "perfect competition," son may refuse, rationally, to contribute
a notion that has been basic to economic to this cost on an individualistic and
theory for almost a century. voluntary basis. The equilibrium posi-
The free-rider problem arises in the tion is evidently non-optimal, and this
theory of public finance, or, more prop- may be recognized by all participants;
erly, in the theory of public-goods sup- but unless the rules are somehow
ply. This analysis attempts to derive an changed the large-number dilemma
explanation for the supply of public holds. This result emerges, of course,
goods, as contrasted with private goods, only when the size of the group is criti-
from the choice behavior of individuals. cally large. Only in such large groups
The question is: Why is political or gov- will the individual consider his own ac-
ernmental organization required at all? tion to exert substantially no effect on
Why does the market or exchange proc- the actions of others.8
ess "fail," in some meaningful sense, The very usage of the term "free
when goods and services exist that must rider," however, suggests that the sig-
necessarily be shared in common by nificance of the large-group dilemma
large numbers of persons? An examina- may not have been fully appreciated.
tion of the conditions for equilibrium This term suggests some deliberate ef-
attained under private or independent fort on the part of the choosing indi-
trading adjustment reveals that the re- vidual to secure benefits at the expense
sults are clearly non-optimal. If so, what of his fellows. In the only situation
is there to prevent further pressures de- where the problem really emerges, how-
signed to remove the remaining mutual ever, the choosing individual enjoys no
gains from trade? The answer to these sensation oaf "riding free," of "letting
questions is found in the tendency of George do it." There is no personal in-
each person who is a potential benefi- teraction present at all. The individual
ciary from the commonly shared public is simply reacting to an environment in
good to choose, rationally, to remain a which he finds himself, to "nature," so
"free rider." If the potential benefits are to speak, not in any way against his fel-
genuinely non-divisible among separate low citizens.
persons, each one will find it to his own Once the large-number dilemma is
private advantage to refrain from mak- understood, the failure of the market
ing voluntary contributions toward the process to produce optimal results when
costs of provision. This remains true de- public goods are present is explained.
spite the possibility that the total bene- Further, as the argument has been de-
fits to be derived from supplying the veloped, an explanation is provided for
good, over all persons, may greatly ex- the tendency of individuals to turn to
ceed the total costs. And this may apply changes in the rules, specifically to the
for each and every member of the group introduction of political-governmental
simultaneously without changing the re- processes as substitutes for market proc-
sults. Each person may consider that he esses. Such changes in the institutions or
would be better off in a situation where rules can, of course, impose upon all
he, along with each of his fellow citi- members of the group common stand-

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 10 ETHICS

ards of conduct. From the analysis de- Broadly speaking, the direction of de-
veloped along these lines it becomes sired change in the first examples is to-
conceptually possible to demonstrate ward reducing group size, or at least
why, under certain circumstances, indi- modifying the rules so that something
viduals will, on purely rational grounds, similar to small-group results emerges.
agree to allow themselves to be coerced. In the organization of markets, how-
The similarities between this analysis ever, explicit attempts are made to place
of individual choice behavior in contrib- buyers and sellers in the large-number
uting to the cost of public goods and dilemma. The economic system works
that applied to the choice of an ethical efficiently only to the extent that the
rule are obvious. The second application large-number dilemma prevails over
of essentially the same proposition has wide areas, and institutional reforms are
an even longer history in economic the- aimed directly at extending group size.
ory, although its similarity is perhaps Legal restrictions are imposed on at-
less evident due to its inverse relevance. tempts to consolidate, and enforcible
This concerns the behavior of the indi- rules over whole groups are forbidden.
vidual or the firm under conditions of The essential difference between the
perfect competition. This state of affairs ethical-choice-public-goods models and
is, in fact, normally defined strictly by the perfect-competition models stems
the presence of the large-number dilem- from the fact that in the first instances
ma. Perfect competition is said to exist the groups are presumed inclusive of all
when a single buyer or single seller ex- members in the interacting social group.
erts so small an influence on the total In market process, by contrast, only the
market demand or supply of a product particular sellers of one product, as a
that he acts as if his own behavior exerts subgroup, find themselves in the large-
no influence on the price that is estab- number dilemma. And any change in
lished in the market. Each seller and the rules that will provide them with
each buyer is a price-taker. relief will automatically result in their
Among the sellers of a single com- exploitation of still other groups in the
modity, as a group, each single unit larger social system. Broader considera-
finds itself in a position precisely anal- tions involving the "social" constitution
ogous to that of the "free rider." Each for the whole system may dictate that
of the sellers would prefer to be in a institutions of the economy be organized
position where all sellers restrict supply so as to foster deliberately the placing
(with the net result being an increase of single buyers and sellers in the large-
in market price), but no single unit act- number dilemma. This is simply another
ing alone will find it profitable to restrict means of stating that the public at large
production. Given the situation, each may rationally choose to enforce the
must simply react to the external en- rules for perfect competition to the ex-
vironment. tent that this is possible.
The large-number dilemma in this Frank Knight often stresses that "in
competitive context is different from perfect competition there is no compe-
that confronted in the ethical-choice or tition." This statement summarizes the
in the public-goods examples. Its ap- essence of the large-number dilemma.
plicability is the inverse of these other The single seller in a perfectly com-
instances of the same proposition. petitive market, the single individual

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 ETHICAL RULES, EXPECTED VALUES, AND LARGE NUMBERS 11

who considers his own voluntary contri- mists in the position where they now
bution to a commonly shared public ask the proper questions. With this has
good, the single individual who tries to surely come a more comprehensive un-
decide on an ethical rule in a large derstanding of political as well as eco-
group: in each case rational choice dic- nomic processes. Such an understanding
tates that he make the best of the en- can yield suggestions for reforms that
vironmental situation that he confronts. may not be initially apparent. Public
He can, by the nature of the conditions finance theorists have, by and large, ac-
that he finds himself in, experience no cepted the classification between "pri-
sense of personal influence on the be- vate goods," which may be efficiently
havior of others directly or indirectly. supplied through market institutions,
and "public goods," which cannot be so
V. IMPLICATIONS
supplied, as being determined by forces
The large-number hypothesis in the not subject to social control. Closer ex-
theory of public goods supplies a possi- amination reveals, however, that this
ble logical explanation for the emer- important dividing line may itself be
gence of political-government institu- variable. To the extent that it is, under
tions as replacements for market-ex- certain circumstances it may be possible
change institutions in the provision of to secure both the greater freedom of
goods and services that exhibit the req- choice that market organization allows
uisite "publicness." Before specific re- and the potential enhancement of effi-
forms can be suggested, however, addi- ciency that modified rules can introduce.
tional questions must be answered. Careful analysis of the structure of legal
First, what value do individuals place and property rights may reveal pros-
on the voluntaristic elements of market pects for converting apparent cases of
processes, elements that must necessari- "free-rider" behavior into situations
ly be sacrificed, at least to some degree, where individual behavior can produce
under political organization? What is substantially optimal results.
the appropriate trading ratio between This paper is not the place to develop
freedom of individual choice and eco- this particular line of argument; my
nomic efficiency? Even if this question purpose here is to contribute something
were provisionally answered, another to the analysis oaf ethical choice. The
and equally difficult one would arise. brief review of the implications of simi-
How can the analyst, as an external ob- lar theorizing about the public-goods
server, distinguish or classify those problem is specifically helpful only to
goods and services that exhibit "public- the extent that the analogy with ethical
ness"? Merely to raise these questions choice is relevant. If the sweep of his-
indicates that the pure theory of public tory is considered to make inevitable
goods remains in its infancy; the theo- and irrevocable the interaction of larger
rist remains a long way from that posi- and larger numbers of persons in an
tion which would allow him to provide ethical context, the analysis must imply
normative advice to statesmen concern- that a smaller and smaller proportion
ing the specifics of institutional reform. of individuals will come to base their
This may seem a pessimistic estimate own actions on some version of the gen-
of the current state of theory, but mod- eralization or universalization principle.
ern developments have placed econo- The scope for an individualistic, volun-

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 12 ETHICS

taristic enforced common standards

ethics must, of behav-
gressively narrowed through time. As ior? The theorist can provide no an-
individuals, increasingly, find them- swers here, and analysis suggests only
selves caught in the large-number di- that the price paid for freedom in-
lemma with respect to ethical choices, a creases with the size of the relevant in-
possible logical explanation is provided teracting group.
for resort to political-governmental As in the public-goods case, avenues
processes which can, effectively, change of reform other than collectivization
the rules and impose standards of con- should be explored. Must the effective
duct common to all individuals. In this size of interacting groups become ever
respect, the analysis yields helpful in- larger, in the context of ethical choice?
sights concerning the "legislation of What are the possible means of factor-
morals" in terms of straightforward ing down complex social interaction sys-
predictions if not of propriety. Common tems into small-group patterns? Imagi-
standards of conduct imposed and en- native and exciting modifications in tra-
forced by authority of the collectivity ditional property-right arrangements are
can, in the limiting case, result in "im- currently emerging to "internalize the
provement" for all members of the com- externalities" in private market proc-
munity by their own standards. The esses for certain types of interactions.9
limiting case is precisely that, however, Can an analogous change in institutions
and the overwhelming probability would be predicted to emerge in the realm of
be that collectively enforced standards ethics? Perhaps those whose profession-
of conduct would be those desired for al competence and interest lies primarily
"others" by "some." Here, as in the in ethics should begin to re-examine the
public-goods case, the question that biblical admonition to "love thy neigh-
must be asked is: What is the appro- bor," with the last word italicized. In
priate trading ratio between the greater the large-number group, who is my
freedom of choice allowed the individual "neighbor"? The lawyer's question was
under a voluntaristic ethics and the evaded, not answered, in Jesus' para-
greater social "efficiency" that might bolic response.
possibly emerge under legislated and UNIVERSITY OF VIRGINIA

NOTES

1. I am indebted to my colleague, Gordon Tul- Basis of Ethics" (Ethics, LXXII [July, 1962], 288-
lock, for several helpful conversations during the 98).
preparation of this paper. 5. In the extreme, the analysis may be extended
2. M. G. Singer's argument comes close at one to the one-person group. Here the behavioral rule
point to incorporating size as such, but in a con- chosen or the action taken will necessarily be the
text different from that of this paper (see his Gen- one-person analogue to the generalization principle.
eralization in Ethics [New York: Alfred A. Knopf, It is essentially on these grounds that the Aris-
Inc., 1961], p. 137). totelian defense of private property is based.
3. Lewis White Beck, A Commentary on Kant's 6. The large-number dilemma is apparently fa-
Critique of Practical Reason (Chicago: University miliar to ethical theorists through numerous exam-
of Chicago Press, 1960), p. 219. ples, but the relevance of large numbers per se
4. My reading of the literature is admittedly has not been appreciated. For examples of situa-
spotty. But within these limits I find my own posi- tions in which the dilemma appears see Singer, op.
tion to be reasonably close to that stated by Warner cit., pp. 69-70, 86-87.
Wick in his review paper, "Generalization and the 7. In an interesting recent study of individual

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 ETHICAL RULES, EXPECTED VALUES, AND LARGE NUMBERS 13

voting behavior in American municipalities, James 387-89; and his "Diagrammatic Exposition of a
Q. Wilson and Edward C. Banfield have noted Theory of Public Expenditure," ibid., XXXVII
significant differences in patterns of choice among (November, 1955), 350-56; and R. A. Musgrave,
different ethnic groupings. They attribute these dif- The Theory of Public Finance (New York: Mc-
ferences in part to the divergent "public conscious- Graw-Hill Book Co., 1959).
ness" of these groups (see their "Public-Regarding- The discussion in this paper owes much to a
ness as a Value Premise in Voting Behavior," still-unpublished paper by Otto A. Davis and
American Political Science Review, LVIII [Decem- Andrew Whinston: "Some Foundations of Public
ber, 1964], 876-87). Expenditure Theory" (Carnegie Institute of Tech-
8. The first explicit recognition of the problem nology) (Mimeographed). Also many of the as-
here is found in Knut Wicksell's classic work,
pects of the problem, especially in relation to large
Finanztheoretische Untersuchungen (Jena: Gustav
organizations, have been discussed by Mancur Ol-
Fischer, 1896). Relevant portions of this work are
son. In an early draft to which I have had access,
published in translation as "A New Principle of
Olson's work is entitled "The General Theory of
Just Taxation," in Classics in the Theory of Public
Public Goods" (U.S. Air Force Academy, March,
Finance, ed. R. A. Musgrave and A. T. Peacock
(London: Macmillan & Co., 1958), pp. 72-118. 1963) (Mimeographed) (forthcoming under a
The classic modern treatments of the theory of slightly different title from Harvard University
public goods all recognize the existence of the free- Press).
rider problem. See Paul A. Samuelson, "The Pure 9. Cf. Spencer MacCallum, "The Social Nature
Theory of Public Expenditure," Review of Eco- of Ownership," Modern Age, IX (Winter, 1964-
nomnics and Statistics, XXXVI (November, 1954), 65), 49-61.

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