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Non-Welfaristic Features of Kenneth Arrow’s Idea of Justice

Nao Saito

Tohoku Gakuin University*

March 8, 2017

Introduction

The aim of this paper is to clarify Kenneth Arrow’s idea of justice. Arrow is famous

for positing his general impossibility theorem (Arrow’s theorem) as a foundation of

social choice theory (which concerns voting systems). Theoretically, the aim of his

research is to prove the existence of a desirable way to aggregate individual preferences

as the criterion of individual welfare, in order to create one social preference as the

criterion of social welfare. To prove his theorem, Arrow applied consumer choice theory

to social choice theory by subsuming economic and political decision-making into one

category of general collective choice. Because the normative foundation of consumer

choice theory is welfarism, he was regarded as a welfarist when he first posited the

theorem.

However, he gradually differentiated between economic and political

decision-making through discussions with other scholars, such as Ian Little and John

Rawls. Arrow finally concluded that social choice theory can be useful to deduce a

standard of justice, which has non-welfaristic aspects, although market analysis cannot

be.

This paper clarifies this transformation of Arrow’s ideas and, hence, his idea of

justice.1 First, we show that economic and political decision-making are assumed to be

similar from the formal point of view in Arrow’s theorem. Second, we explain that

Arrow subsequently changed his position and attached importance to this difference. We

then show that he gradually realized that consequences of both economic and political

decisions are not always just. He specifically appreciated the difference between welfare

* Department of economics, email: naosaito@mail.tohoku-gakuin.ac.jp 1 Famous previous studies on the philosophical aspect of Arrow’s theorem include Mackay (1980), Riker (1982), Pildes and Anderson (1990), Amadae (2003), and Mackie (2003). However, these studies do not analyze the theoretical change in Arrow’s view of democracy, on which this paper focuses.

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and right, which is one option of political decision-making. Accordingly, he recognized

the significance of justice, which cannot merely be reduced to economic efficiency.

Finally, we argue that Arrow insisted that a criterion of justice can be deduced by an

impersonal collective decision process in the hypothetical original position. We

conclude that Arrow’s idea of justice includes non-welfaristic aspects, such as freedom,

equality, and right.

1. New welfare economics and Arrow’s theorem

Welfare economics, established by Pigou in 1920, is a field of economics that

searches for social welfare. In this field, new welfare economics established after

Robbins’s criticism against old welfare economics. In 1938, Abram Bergson

successfully formalized the economic welfare function that can deduce a criterion of

social welfare from a set of economic variables. His study was outstanding because now

welfare economists could formally analyze a criterion of social welfare. Bergson did not

clarify whose value judgment this function represents. By contrast, Arrow inquired into

the collective decision process that deduces a criterion of social welfare from a set of

individual preference orderings as a criterion of individual welfare.

Arrow’s theorem proves the impossibility of collective decision-making in a

democratic society using an axiomatic approach, which he introduced in 1951 in his

book, Social Choice and Individual Values (hereafter SCIV). In that book, individuals

can be assumed to have a binary relation across all possible alternatives. This binary

relation is ordinal and non-comparable among individuals. Individuals can also be

assumed to have an ordering, which satisfies the conditions of completeness and

transitivity. They then choose the top of their ordering over an opportunity set of

feasible alternatives at each time, acting to maximize their welfare in their decisions

(Arrow 1963). It is also assumed that an individual’s own preference is the criterion of

his/her individual welfare and that social preference is the criterion of social welfare.

Arrow analyzes whether there is a desirable collective decision process (i.e., social

welfare function) that derives one social preference from numerous and different

individual preferences.

Accordingly, his theorem questions whether the collective decision process can meet

four desirable conditions. The first is the condition of unrestricted domain, which

requires the collective decision process to accept any pattern of individual preference.

The second is the Pareto principle, which dictates that society should prefer what its

members prefer. The third is the condition of indifference to irrelevant alternatives,

which dictates that a decision on one opportunity set should be independent from

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external alternatives. The fourth is the condition of non-dictatorship, which directs that

no individual preference should become a social preference regardless of the others’

individual preferences (Arrow 1963, pp. 96-103). These four conditions of the collective

decision process are assumed to be axioms. Arrow tried to determine the existence of

the process by using this axiomatic approach, and proved that no collective decision

process satisfies these four conditions (Arrow 1963).

Arrow’s theorem perpetuated the research interests of new welfare economics,

especially that of Bergson. It is clear that Arrow wanted to identify the criterion of

social welfare in new welfare economics because he argues for a relationship between

his social welfare function and Abram Bergson’s economic welfare function (Arrow

1963, pp. 22-24; Bergson 1938). However, the scope of the theorem is not only new

welfare economics, but also political science, because it deals with general collective

decision making, such as voting, using an axiomatic approach (Samuelson 1967, p. 42).

2. The relationship between political and economic decision

2.1 Similarities between economic and political decision

Arrow notes that consumer or economic choice and political choice can be

generalized as a single category within a more general rational choice.2 In other words,

Arrow deals with the general collective decision process, not economic or political

decisions in particular. He does not insist that economic decision and political decision

are the same; instead, he extracts the common characteristics of these two (Arrow 1963,

p. 5). He realizes that there is no collective decision-making in the market, making

social preference ordering unnecessary. However, there are two common characteristics

of these two types of decisions.

First, one is assumed to be rational in that he/she has such a preference ordering in

both types of decision-making. In other words, Arrow considered that economic

decision and political decision have the same informational foundation of rationality.

A conception of welfare in a political decision is, however, different from that in an

economic decision. In the consumer choice theory, it is assumed that the rational

consumer creates his/her preference of goods to maximize his/her utility, which

increases as the amount of one’s consumption of economic goods increases. However,

Arrow excludes the assumption of the individual utility function to make individual

preference more general. It includes non-economic matters, such as an ethical judgment

2 The social choice theory was established to solve Arrow’s question and amend his negative conclusion. Moreover, his theorem influenced the foundation of the rational choice theory in political science.

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on the distributive sharing of goods in society (Arrow 1963, Arrow 1985).3 Moreover,

he accepts any individual preference ordering. For example, he mentions that he does

not distinguish between one’s preferences over foreign culture or over his/her personal

matters. This means that, for example, if one prefers not having any goods to having all

goods, such a preference is acceptable in his theory. 4 Consequently, individual

preference is regarded as the informational foundation of the general collective decision

process (Arrow 1963, pp. 11-17).

When regarding one’s welfare as an informational foundation, Arrow considers it to

be ordinal and not comparable with others’ welfare. Thus, he was regarded as a welfarist,

though he was not regarded as an economic welfarist.

Second, the consequences of collective choice are considered to comprise a value

judgment of social welfare. The reason for this is as follows. Arrow regarded one’s

preference ordering as an informational foundation. He mentioned that economists can

know one’s preference ordering by observing his/her real choice. According to the

Australian school, in particular, one’s real choice is related to estimation and judgment.

This assumes that what one chooses must be what he/she prefers and what he/she

prefers must be better than what he/she does not prefer (Arrow 1985, p. 141).5 Arrow’s

setting of the Pareto principle as one condition of collective decision-making leads

society to optimization of social welfare. Thus, Arrow considers that social preference

ordering can be the criteria of social welfare.

In short, Arrow focuses on common characteristics and does not take the difference

between economic decision and political decision seriously in the 1950s–1960s. He

applies utilitarian ideas of consumer choice theory to social choice theory, and regards

social ordering that values social states according to their consequences as a criterion of

social welfare. Because of these ideas, he was considered to advocate welfarism and

consequentialism.6

2.2 Different motivations of two types of decision-making

After publishing his theorem, Arrow gradually started attaching importance to the

difference between economic and political decisions. He states that some scholars

consider a state to be a system of individual rational agency whose actions can be 3 The former is called “value” and the latter is called “taste” (Arrow 1963). 4 This is a meaning of a condition of unrestricted domain, as explained previously. 5 This idea may be criticized because it combines fact and value. Arrow believed fact and value should be separated. He also admitted, though, that logical analysis makes this difference unclear (Arrow 1985, p. 141). 6 Arrow mentioned that he did not consider procedural aspects of social choice theory in SCIV (Arrow 1963).

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analyzed by an analogy to the price system. They believe that these two systems (i.e.,

state and price systems) contain the same individuals with the same motivation (Arrow

1970, p. 18).

However, Arrow criticizes this view, considering that the motivations of these two

systems differ. On the one hand, it is assumed that an individual acts according to

his/her own utility in economic decision-making. On the other hand, in political

decision-making, it is assumed that the individual acts according to social good or moral

obligation.

The reasons for this may be twofold. The former reason is the empirical reason that

the existing condition cannot be explained absent this assumption. The latter reason is

the normative reason that one should act according to moral obligation to improve

social welfare. The first empirical reason involves the scale of political decision. If an

individual considers only his/her utility, he/she does not vote for a large-scale political

decision because, in this situation, the expected utility of his/her vote is smaller than

his/her opportunity cost. However, many people actually vote in such a situation. It

naturally follows that they vote according to certain social obligations that are

irreducible to rationality.7

The second reason is that one need not consider the influence of one’s action in the

market, but must do so in political decisions. According to Arrow, one merit of the price

system is that the participant does not need to know much about the influence of his/her

action. He/she may only know his/her own needs, and need not be concerned about

social influence or the consequences of his/her action. This is because he/she pays a

price to the extent that he/she influences others, and does not need to be concerned

about his/her influence on others beyond that (Arrow 1974, p. 12). Moreover, individual

selfish action is recommended to maximize social utility. 8 Hence, it is assumed that an

individual does not need to act according to others’ interest.

However, the price system is not perfect and there are many social actions for

improving social welfare outside of the market. For example, the establishment of a

relationship of trust does not have a price and may be broken if one is not concerned

about others. If social members do not trust each other, transaction cost increases, which

is not good for social welfare. As this example suggests, one must consider his/her

influence on others when acting outside the market, including political decision,

7 It is worth noting that this position is not contradicted by Arrow’s theorem, according to which an individual will vote according to any conviction or values because of the condition of unrestricted domain. 8 This is the fundamental theorem of welfare economics that Arrow proved with Debreu in 1954 (Arrow and Debreu 1954).

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because one does not pay any money in exchange for action. In other words, he/she

must act according to his/her conscience and take his/her influence on others into

account when he/she makes a political decision.

In short, Arrow clarifies the difference between economic and political decision after

publishing his theorem. He became aware that an individual must choose politically

according to social ethics, and that his/her motivation to vote must be ethical.

Accordingly, he concludes that political decision, rather than economic decision, entails

social ethics. He observes that “the market is one system; the polity another. … Looking

at policy issues from the point of any one system is likely to lead to unsatisfactory

conclusions somewhere” (Arrow 1997, p. 765). Arrow gradually came to understand

and accept the diversity of social decision in the real world.

The next question is whether the consequences of these decisions are just.

Consequently, the next section analyzes the relationship between economic decision and

justice.

3. Theoretical change of Arrow’s idea of justice, or the ethical consequences of

social choice

3.1 Price system and justice

In the 1960s, it seems that Arrow did not clearly criticize the consequences of the

market as injustice. However, Arrow clearly stated in the 1970s that the distribution of

goods in a price system does not necessarily achieve distributive justice. This point

draws a clear distinction between Arrow and other new welfare economists, such as

Little and Bergson.

Arrow refers to the condition of Pareto efficiency that Little and Bergson support as

the idea of justice in the new welfare economics. According to Little and Bergson, if

everyone is better off in one situation than in another, the former situation is better than

the latter. If everyone comes to be better off by one distribution than another, society is

judged to be better off. Such a value judgment is both efficient and just. If this is true,

laissez-faire policy and the consequence of the free market are both efficient and just,

because they lead society to Pareto efficiency according to the fundamental theorem of

welfare economics. Little and Bergson regard the criteria of efficiency and justice as the

level of an individual’s satisfaction (Arrow 1983, p. 176).

However, Arrow opposes this idea. According to him, there are three drawbacks of

the price system. The first drawback is the imperfection of this system. As mentioned

above, something can be useful to social good but not have a price. For example, we

know that it is beneficial to establish a relationship of trust to deal with goods

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effectively in the market. If one cannot trust his/her business acquaintance, he/she must

investigate the products and bear numerous transaction costs. Similarly, honesty and

faithfulness are beneficial for business efficiency. Nevertheless, such qualities do not

have a price and cannot be purchased with money (Arrow 1974, p. 14). Therefore, we

should establish a legal system and social norm to promote such relationships of trust if

we want to promote social welfare.9

The second drawback is that competitive equilibrium satisfies Pareto efficiency but is

not necessarily desirable for social good (Arrow and Debreu 1954). To clarify this point,

it is necessary to consider Arrow’s criticism of Robert Nozick. Arrow interprets

Nozick’s entitlement theory to support that the distribution of goods in a market satisfies

distributive justice, and argues that such distribution overlooks the public utility of

private goods.

Nozick’s entitlement theory is as follows. An individual has the right of self-property.

It follows that he/she has the right of property that he/she produces by his/her labor and

talent. An individual can exchange this property by trade that meets the following three

principles. The first is the principle of justice in transfer, meaning that an owner can

exchange property with others. The second is the principle of justice in acquisition,

stating that one can acquire any good if no one else owns it. The third is the principle of

rectification: one can get back goods lost by illegal means. Individuals are entitled to

goods acquired through one of these three principles (Nozick 1974, Ch. 7).

Arrow points out that “Nozick’s criteria are very much like the welfare economics

theorem” (Arrow 1983, p. 177), because both consider that equilibrium of perfect

competition in the market is desirable. It is true that Arrow admits that Nozick does not

assume perfect competition. In his words, “Pareto optimality is not implied Nozick’s

voluntary, just transfers” (Arrow 1983, p. 177). However, according to Nozick’s idea,

only redistribution that improves one’s satisfaction can be accepted, because rational

agency would voluntarily accept only such a redistribution of goods. This idea is similar

to competitive equilibrium being desirable (Arrow 1983, p. 188). Therefore, it achieves

just distribution for both Nozick and the welfare economists.

Conversely, Arrow refuses this claim. Nozick assumes that one can freely use his/her

own property; however, from the viewpoint of social welfare, it is sometimes better to

use such property commonly and socially than privately. According to Arrow, private

usage of precious individual goods is not a optimal usage, because these goods become

more valuable by being used in the social system. Thus, redistribution is beneficial for

9 This is not a criticism of the fundamental theorem of welfare economics, but rather explains an assumption of that theorem.

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maximizing social welfare (Arrow 1983, p. 188).

In short, Nozick regards one’s talent as his/her own property, and goods acquired by

one’s own talent are his/her property. Arrow rejects this idea and considers one’s talent

and goods to be more valuable if they are used socially for others than if used privately.

For him, the redistribution of goods is recommended. It must be noted that Arrow

opposes Rawls’s idea that one’s property constitutes common goods and insists that it

belongs to the individual. However, he considers that individuals have a social

obligation to contribute to maximizing social welfare by using the property they obtain

through their talents. Arrow does not clarify whether one has a moral or legal obligation.

In other words, he does not clarify whether it is desirable to voluntarily make a

contribution as a matter of moral duty, or be obliged to pay taxes to rectify an imbalance.

Nonetheless, it is clear that Arrow does not regard market consequences for their own

benefit (Arrow 1983, pp. 185-7).10

The third drawback is that the price system does not provide for fair distribution of

income. Even if one accepts Pareto efficiency as a desirable distributive criterion of

goods, many social states satisfy it. One should use other criteria of distributive justice

to compare these social states (Arrow 1974, p. 11). Although Pareto efficiency is one

desirable criterion, it is not the only one.

Moreover, Arrow considers that some situations that satisfy Pareto efficiency are not

socially desirable if the method of distribution of individual goods is very unfair.

According to Arrow, Pareto efficiency sometimes contradicts other very reasonable

value judgments, such as a decrease in the gap between rich and poor. There can be a

Pareto efficient situation in which few rich and many poor people coexist. Arrow insists

that Pareto improvement does not become social improvement if the distribution of

income becomes unbalanced (Arrow 1983, p. 35). For Arrow, one role of distributive

justice is the correction of an imbalance. In short, a market consequence can be unjust.

Arrow clearly notices the difference between economic and political decision, and

notes that the consequences of economic decision do not necessarily fulfill the

requirement of distributive justice. According to Arrow, something beyond the market is

required to achieve efficiency, social welfare, and distributive justice (Arrow 1974, p.

17). In other words, the price system cannot be the final ruler of social life (Arrow 1974,

p. 14). It follows from this that, in the 1970s, Arrow cannot be regarded as a welfarist

even when he evaluates consequences of the market, because he uses non-welfaristic

10 Although Arrow recommends redistribution of goods to improve social welfare, Nozick opposes such consequentialism. Therefore, Arrow’s criticism seems to be misdirected. However, I refer to his criticism for the scope of this analysis.

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bases for evaluation, such as fairness and equality.

This conclusion raises the question of what the relationship between political decision

and justice is. In the next section, this point is examined by tracing Arrow’s theoretical

change from the 1950s to the 2000s.

3.2 Political decision and justice

3.2.1 Arrow during the 1950s–1960s

As previously noted, when Arrow published his theorem in the 1950s, he noted that

the evaluation of the collective decision process contributes to the evaluation of social

good. However, this opinion was criticized by Little. According to Little (1952), it is

unclear why an individual should obey social preference as the evaluation of social

good, especially when his/her preference is different from social preference.

After publishing the second edition of SCIV, Arrow replied to Little’s criticism of

why an individual accepts social preference as a value judgment when it stands in

opposition to individual preference. According to Arrow, the individual obeys social

preference as an obligation because this is better than not obeying and creating a lack of

consensus. The best situation for him/her is to become a dictator and decide to act by

himself/herself. Social preference then accords with his/her individual preference.

However, one cannot be a dictator in a democratic society. Hence, he/she adopts the

second-best measure: it is better to make a compromise with others than to decide on no

social action. Consequently, one agrees with social preference even if it opposes

individual preference. Once he/she agrees with it, he/she is obliged to obey a social

agreement. Society is perpetuated by people’s protection of such an agreement; however,

this agreement does not last, but can change with the environment and individual

preference (Arrow 1983, pp. 78-9).

In short, in the 1960s, Arrow insisted that consequences of political decision are

regarded as criteria of social welfare, and obeying social agreement is a moral

obligation. However, an individual need not obey social agreement if doing so does not

improve his/her welfare.

3.2.2 Arrow during the 1970s–1980s

In the 1970s, Arrow slightly modified his discourse, considering that obeying social

preference is a stricter moral obligation of individuals.

Arrow insists upon the necessity of agreement either through the political decision

process or tacitly for social stability. This is required for the following three reasons.

First, it is needed to improve social welfare. According to Arrow, one acts individually

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in the market but cannot deal with all socially necessary things by doing so. It is also

necessary to act collectively in various ways. The most typical example of collective

action is the state’s action. The state provides public services such as public goods that

the market cannot distribute to individuals. However, it is a mistake to consider state

action as a necessary collective action alone. More informal collective action includes

norms of social behavior and ethical or moral codes. Such social norms can also

compensate for market failure. In that case, society imposes social norms as a moral

code on the individual (Arrow 1974, Ch. 1).

Mutual agreement is necessary to execute such non-market, formal and informal

collective action. However, such an agreement and the persuasion of those who enter

society to accept it are costly. Voting is one way to form such an agreement, but the

voting mechanism has its difficulties and the larger its scale, the higher the costs. Hence,

as an alternative plan, society tacitly forms such an agreement by making it inherent to

individuals. By doing so, society cuts costs and can develop (Arrow 1974, p. 20). Either

way, some customs and norms, such as the ethical importance of a relationship of trust,

provide commodities that the price system cannot adopt, and which can improve the

economic efficiency of the market.

The second reason is that this agreement is required to harmonize individual desire

with social requirements in the individual’s conviction and to make society stable.

According to Arrow, individual desire always conflicts with social requirements.

Accordingly, it is essential to compromise with others who have different values and to

form an agreement that is an abstraction of common elements. Therefore, society

requires individuals to protect social rules. For example, law observance restricts

individual freedom from the standpoint of individual desire, but also protects the

freedom of others. This means that individuals should agree to restrict individual desire

in accordance with social requirements. The society cannot be stable without such an

agreement.

Such an agreement can change as individual preference changes because one obeys it

for his/her own sake. However, to form and modify such an agreement, even tacitly, is

costly. The cost of modification is particularly high because one obeys it tacitly. Even if

modification is necessary to compromise each individual’s interest, people sometimes

maintain the status quo. Some let people obey it by using the technical ethical code

advocated by philosophers for their sake. In other words, some use such codes as an

excuse for a monopoly or dictatorship (Arrow 1970, p. 20). Accordingly, we should

maintain our opposition to such a dictatorship and make a collective decision that is

open to all feasible alternatives. According to Arrow, social ordering is not only a

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consequence of voting, but also of such a tacit agreement. Ethics or morals are not

“technical ethical codes,” but mutual compromises to increase each individual’s interest

(i.e., social ordering).

Arrow goes a step further. The third reason is that obeying it is just. Arrow mentions

his utilitarianistic idea in his paper, criticizing Rawls’s A Theory of Justice as follows.

Rawls assumes that the individual has a moral personality. However, Arrow adopts a

more neutral position on individual preference. By accepting any pattern of individual

preference in his framework, Arrow can analyze a more general social decision process

than Rawls (Arrow 1983, p. 97).

Moreover, Arrow opposes Rawls’s idea that the will of the majority is not just. He

further insists that it is necessary to express individual will by voting; otherwise, a

public officer cannot know whether social policies contribute to the social good.

According to Arrow, maximizing social good is one aim of justice. Moreover, even if

individual preference differs from social preference, obeying the will of the majority is

itself a moral obligation. In Arrow’s words: “I would hold that the notion of voting

according to one’s own beliefs and then submitting to the will of the majority represents

a recognition of the essential autonomy and freedom of others. It recognizes that justice

is a pooling of irreducibly different individuals, not the carrying out of policies already

known in advance” (Arrow 1970, p. 109). Therefore, Arrow considers obeying social

preference to be a moral obligation, even if it is not one’s compromise plan. In sum,

Arrow believes that one should obey a social decision as a moral obligation even if one

does not want to do so, and even if it is good for him/her to not act socially.

In conclusion, in the 1970s, Arrow thought that obeying social preference, whether by

tacit consent or by vote, is a moral obligation for individuals and can stabilize society.

Arrow mentions that, although his theorem denies the existence of an ideal democratic

decision process, there is some agreement in real society and one should obey it.

3.2.3 Arrow in the 1990s

On the other hand, in the 1990s, Arrow shows a positive attitude toward liberalism, as

the position that does not assume the consequences of democratic decision to have

ethical value. He admits that social norms accept racial discrimination in some eras and

in some areas, although almost no philosopher in the 1990s supports this ethically.

Arrow also refutes it ethically. From this, it is clear that he was aware that real social

norms sometimes stand in opposition to intuitive morality. It is also clear that Arrow

became aware that technical ethics is not only an excuse used by some people to protect

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their interests, but also a fair tool to protect one’s dignity.11

In and after the 2000s, Arrow more clearly considered that obeying social preference

is not an ethical obligation. Arrow is becoming increasingly doubtful that democratic

decisions can produce ethical consequences.12

In short, in the 1970s, Arrow insisted that obeying social preference is a moral

obligation. However, in the 1990s, he left room to reject social preference ethically.13 In

other words, after publishing his theorem, Arrow admitted the moral obligation of

obeying social preference and that such social preference is not always objectively just.

3.3 Social welfare and right

Arrow also changed his perspective on right.

It is found from Arrow’s criticism against Nozick that Arrow admitted the violation of

one’s property rights and entitlement to improve social welfare in the 1970s. In another

paper, he criticized Amartya Sen’s liberal paradox and clearly showed his utilitarianistic

position (Kelly 1983).

However, Arrow does not admit the violation of one’s right in the market in the 1990s.

Arrow refers to child trafficking as an example, insisting that this violates the rights of a

child. According to Margaret Radin (1996), the market should not set any price on

goods related to the violation of an individual’s personality. Nevertheless, it sometimes

sets the price of such goods, such as child trafficking and prostitution. Such goods

“contest” the setting of any price and this is a market failure (Arrow 1997). Arrow partly

agrees with this opinion but does not clarify the reason. It can, however, be interpreted

that he considered that there are two types of goods, only one of which can be

purchased in the market. Individuals and the market sometimes confuse the two.

This opinion is different from his opinion in the 1970s. At that time, when Arrow

took up a controversial issue, stating that we can deal with some goods (e.g.,

commercial blood transfusion) in the market, he protected the justification of the market

mechanism (Arrow 1972).

Second, Arrow insists that the consequence of a vote cannot violate certain individual

rights. The individual mistakenly prefers a social state that sells goods that should not

be sold to another state that does not do so. He/she may form his/her individual

preference as such. Therefore, social preference, which is an aggregation of individual 11 Arrow did not argue whether people should obey social norms, such as racial discrimination, as a moral obligation. 12 For example, he criticized Donald Trump (Arrow 2016, pp. 180-181). 13 Arrow notes the possibility of civil disobedience against the will of the majority (Arrow 1974).

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preferences, like the market, is not always considered as having an ethical meaning.

As mentioned before, in the 1960s and 1970s, Arrow accepted the condition of

unrestricted domain and regarded the consequences of social decision as ethical

judgments. Therefore, if most individuals judge child trafficking to be ethically

acceptable, Arrow may have admitted this ethical judgment. However, in and after the

1990s Arrow rejected some types of individual preference on ethical grounds. In

Arrow’s words, “[j]udicial decisions and votes are not to go to the highest bidder.

Individuals cannot waive certain legal rights” (Arrow 1997, p. 765).

Arrow is well aware that this perspective is incompatible with his previous idea that

the consequences of the democratic decision process have moral meaning. He noted that

he has a contradictory idea. On the one hand, he trusted the ethical meaning of the

consequences of the democratic decision process for a long time. On the other hand, he

now doubts it and wants to protect one’s right against it. He stated in his interview, “I

don’t have a consistent answer” (Arrow 2016, p. 112).

This makes it clear that, in the 1990s, Arrow believed that if the consequences of the

market or a vote go against one’s rights, they should become null and one should not

obey them. In short, Arrow changes his opinion and considers that one’s right is

superior to social welfare. He therefore becomes a non-welfarist.

4. Criteria of justice

Finally, the aim of this section is to clarify Arrow’s criterion of justice.

4.1 Rawls’s original position

In 1985 Arrow raised the question “What are the standards of justice?” (Arrow 1985,

p. 136). This paper lies between Arrow’s populistic view on democracy and his liberal

view.

First, according to Arrow, Rawls’s theory of justice affirms the redistribution of goods.

Arrow agrees with Rawls’s fundamental assumption, although he criticizes him on

many points. Rawls’s fundamental assumption is that “justice values both liberty and

equality” (Arrow 1985, p. 136). Freedom means free choice and equality means the

equality of income and power. Accordingly, Arrow recommends correcting an

imbalance and equalizing income to some extent by the redistribution of goods.

According to Arrow, freedom and equality do not conflict with each other; instead,

one cannot be achieved without the other. The biggest restriction on an individual’s free

choice and action in the market is the scale of his/her budget. Consequently, his/her

income decides his/her free choice regarding consumption type and occupation.

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Therefore, inequality of income means that many people are restricted from getting a

job and only a few enjoy freedom. However, respect for one’s freedom as justice means

equal respect for everyone’s freedom. The consequence of the market cannot provide a

just distribution of income because poverty restricts freedom.14

Moreover, according to Arrow, “income inequality also constrains freedom in

dimensions other than economics,” such as political freedom. Some resources are

necessary to exercise political freedom, especially freedom of expression and

publication. Since the rich tend to provide extra money to help public officials operate

the market politically and receive special political advantages in return, “an equalization

of income will increase the political freedom of the lower-income groups” (Arrow 1985,

p. 137).

Along with income equalization, the equalization of power is essential to promote

freedom. Power means the authority to make a collective decision. For example, China

and Cuba have achieved equality of income to some extent, but they are not ideal equal

societies, because only a few people have the authority to make collective decisions in

these countries.

Next, Arrow considers that one should choose a redistributive policy to achieve such

freedom and equality through the social decision process. To clarify this point, he notes

the relationship between social choice and distributive justice.

Social choice theory provides a normative judgment of interpersonal relationships. In

other words, it can provide the criterion of justice. For example, this theory can adopt

Rawls’s theory of justice, which it can interpret as the problem of social choice and an

attempt to deduce “state x is more just than state y” from “state x is better than y for

individuals” (Arrow 1985, p. 142).

However, economists, especially social choice theorists, have tried to achieve an

objective criterion of distributive justice, but have not succeeded. It is necessary to

clarify the criterion of social good to realize the fair distribution of income because one

aim of distributive justice is achieving the appropriate social good. This criterion can be

identified by aggregating individual value judgments. Consequently, it is necessary to

observe one’s choice in the market and vote to clarify it. However, there are many

difficulties in this respect.

First, as previously mentioned, even if social preference can be formed successfully,

this is not always just. It may be difficult to create a criterion of justice by collecting

14 According to Arrow, it has been pointed out in general equilibrium theory that equal distribution is not efficient. However, the theory has made it clear that perfect employment solves the conflict between equality and efficiency.

15

individual preference.

Second, individual desire and values are incommensurable and mutual

communication is imperfect. What we can do is only analyze individual observable

actions, which may not stem from all of an individual’s emotions (Arrow 1974, p. 19).

For example, we cannot judge whether observable actions are based on an individual’s

true individual preference.

Third, a paradox exists when one tries to aggregate individual preferences to form

social preference, as Arrow’s theorem proves. Although scholars try to overcome

Arrow’s theorem, many other impossibility theorems exist in social choice theory. It

cannot be affirmed that an objective and just criterion of distribution exists (Arrow

1974).

Nevertheless, Arrow believes that justice is not independent from the problem of

social choice. He only questions whether its real consequence achieves justice.

Accordingly, he insists that rational choice in Rawls and Harsanyi’s original position is

a desirable procedure to deduce a justice criterion. According to this position, parties do

not know their characteristics, belongings, or their entire lives. Such a position is

desirable because it provides an impersonal decision process.

According to Arrow, justice is not specific to some individuals, and it adapts equally

to any individual. It is universal and impersonal. Moreover, mutual respect is essential

for society. No one can ethically defend a distributive policy unless it benefits everyone

equally. Rawls and Harsanyi’s original position provided the procedure that satisfies the

requirement of justice (i.e., impersonality and mutual respect).

According to this position, risk-averse rational agents prefer equal distribution. In

Arrow’s words, “the original-position argument shows that the impersonality that

characterizes moral judgment implies that the content of that judgement is an

equalization of outcomes” (Arrow 1985, p. 145). Moreover, “[w]e may similarly

presume that in the original position, where the uncertainties are the whole outcomes of

a life, the individuals would find it prudent and desirable to enter into a mutual

insurance agreement, to redistribute the incomes they would subsequently receive to

make them more nearly equal” (Arrow 1985, p. 145).

The consequences of rational choice are just because the prudent and selfish

judgment in the original position conforms to just judgment in reality, because it

achieves impersonality and mutual respect. Arrow believes that the problem of

consistency between justice and goodness can be solved by this idea. Additionally,

Arrow, as an economist, could deal with the problem of justice without giving up his

commitment to rationality.

16

As explained previously, Arrow identifies Rawls’s original position in A Theory of

Justice with Harsanyi’s and supports it as a fair procedure. According to Arrow, it is true

that Rawls’s original position differed in character from Harsanyi’s. However, the two

scholars also had something in common in that both sought fair and equal distribution.

This similarity is more noteworthy than their differences (Arrow 1985, p. 145).

Of course, many differences exist between Arrow’s position and that of Rawls. First,

Arrow criticizes Rawls’s way of deducing the difference principle, noting that rational

agency with a risk-averse tendency in the original position supports the choice of the

principle of average utility. However, if one’s risk-averse tendency reaches the limit,

he/she will choose the difference principle. Therefore, the two principles are not

qualitatively different from each other as Rawls argues (Arrow 1983, pp. 107-108). This

is why Arrow does not agree with Rawls’s criticism of utilitarianism and instead

supports utilitarianism. For Arrow, Rawls and utilitarianism are not so different from

each other.

Second, Arrow considers that an object that parties in their original position choose is

not a principle of justice, but social preference. For Arrow, a criterion of justice is a

social preference that satisfies mutual respect and impersonality. It can be assumed that

such a social preference is a criterion of justice because it leads to a just social condition.

This condition is considered to include non-welfaristic aspects (i.e., equal distribution of

freedom of choice and power). Arrow’s idea is different from that of Rawls, who

considers that parties choose a principle of justice.

Third, Arrow did not clearly answer the question, “Equality of what?” Arrow agrees

with the equalization of income and power. However, Rawls considers that these are just

elements of social primary goods and fundamental freedoms. Arrow respects the

equality of social position and dignity in dealing with the problem of racial

discrimination and child trafficking. However, the nature of the relationship between his

opinion and his idea of justice is unclear. Moreover, Arrow respects free choice, which

is also one element of Rawls’s idea of fundamental freedoms.

Fourth, Arrow’s view of one’s talent differs from that of Rawls. Rawls considers that

one’s talent is a common asset of society. Arrow does not adopt the assumption that

one’s talent is either equal or a common asset of society, stating instead that it is unequal

and belongs to the individual (Arrow 1985, p. 146). On that point, he agrees with

libertarianism. He simply believes that a person with great talent has an obligation to

contribute to society by using it.

Fifth, Arrow places importance upon the problem of incentive. According to him,

maintaining one’s incentive can conflict with promoting equality. However, this does

17

not make it necessary to reject the redistribution of goods. A certain method of

redistribution can be compatible with the problem of incentive. It is true that providing

incentive is important; however, one may display his/her ability without reward.

Moreover, it is clear that some inequality is necessary to incentivize workers; one need

not, however, acquire all rewards in accordance with the productivity principle (Arrow

1985, p. 147).15

Many differences exist between Arrow and Rawls. However, it is clear that Arrow

considers that rational choice in the original position deduces a criterion of justice

because of its impersonal character. He believes that the consequences of real social

decisions are not always just, but that the problems of justice and social choice are

related.

We can characterize Arrow’s idea as proceduralism because he regards social states as

just not because they consequently optimize social welfare, but because they are

deduced by a fair process. This means that Arrow has a non-welfaristic aspect. On the

other hand, we can also say that Arrow maintains his consequentialistic aspect because

he mentions that consequences of such fair process are standards of true social good. As

mentioned before, Arrow wanted justice to be consistent with good. In other words,

Arrow wanted proceduralism to be consistent with consequentialism.16

4.2 Doubts about the intrinsic value of freedom: Criticism of Sen’s approach

In the previous section, we reviewed Arrow’s non-welfaristic aspects. However, in

another paper Arrow expresses his doubt about the intrinsic value of freedom. He takes

up Sen’s study as an outstanding study that values freedom intrinsically. Arrow notes

that Sen’s study expands the interpretation of preferences. In Sen’s study, one’s

preference is not only for goods, but also for freedom, or opportunity sets.

After mentioning this point, Arrow criticizes Sen’s study of ranking of opportunity

sets and of “the pairs (x, A), where A is the set from which the choice is to be made

(‘menu’ in Sen’s terminology) and x belongs to A” (Arrow 2006, p. 54) as follows. On

the one hand, Sen considers that opportunity sets can be ranked by the number of

elements then contain. On the other hand, Some of Sen’s criteria to evaluate opportunity

sets constitute consequentialism. Arrow takes up “One criterion, called Elementary 15 Moreover, Arrow does not argue the difference between social choice and social contract theories. Conversely, Amartya Sen argues this difference in An Idea of Justice (Sen 2009). According to Sen, social choice theory can compare relatively different social states, and the social contract theory can define the best and ideal social state. Sen insists that the former has more relevance than the latter. However, Arrow does not note this difference, and he considers the former able to deal with the latter. 16 See Suzumura’s interview (Bossert and Fleurbaey 2014).

18

Option Superiority” as an example. When one wants to compare two opportunity sets, S

and T, this criterion “simply says that S is at least good as T if there exists an element, x,

in S such that x is at least good as y for every element y in T” (Arrow 2006, p. 55).

However, S may have fewer elements than T has. This is inconsistent with the previous

criterion. In other words, Sen sometimes values opportunity sets because they express

freedom, and sometimes values them by their outcomes. In short, Sen’s idea comprises

both the intrinsic value of freedom and consequentialism. This also means that he does

not fully abandon the consequentialistic view.

Arrow also has doubts about the intrinsic value of freedom, for three reasons. First,

there is some historical evidence that people want to abandon freedom. For example,

Adolf Hitler was elected by a majority. Second, it is sometimes said that freedom is very

important because people can die for it. People, however, can die not only for freedom,

but also many other things. Third, as Erich From argued, people sometimes want to

escape from freedom because freedom implies responsibility and they consider it a

burden (Arrow 2006, 58-60).

Apparently, this idea is inconsistent with his previous idea of respect of freedom and

equality. However, we can infer that Arrow merely criticizes the idea that only freedom

is important and we do not have to consider other things (e.g., social good or the

majority will). He seems to take the balance between freedom and other valuable things

seriously.

Furthermore, Sen’s capability approach developed because of criticism of both an

idea of Rawls’s primary good and the allocation of goods in the market. Arrow mentions

that his task is simply to modify the system of the market a little and not to provide an

alternative idea (Arrow 2016).

In conclusion, in and after the 1990s, compared to the 1950s-60s, Arrow distinguishes

political decision-making from economic decision-making and distinguishes justice

from both of them, but he still attaches importance to the market mechanism. Although

Arrow has non-welfaristic aspects, he does not respect only such aspects as freedom and

equality. He instead considers how they are compatible with welfaristic values, such as

social welfare or social good, or the appropriate balance of such values.

Concluding remarks

In summary, the argument of this paper is as follow. In the 1950s–1960s, Arrow

admitted that social preference is a criterion of social welfare. Moreover, he insisted in

the 1970s that one should obey it as a moral obligation. However, in the 1980s–2000s

he changed his position and insisted that social preference is not always just. Arrow

19

considered that impersonal and hypothetical rational choice in the original position, as

opposed to real social choice, can deduce a criterion of justice.

After understanding this theoretical change, we consider Arrow’s idea of justice from

the viewpoint of welfarism. Welfarism is defined as focusing on welfare only as the

informational foundation by which to evaluate social states. Because welfare is defined

as the happiness which individuals achieve, welfarism is the equivalent of welfaristic

consequentialism. Moreover, welfarism can be divided into two classes. One is ordinal

welfarism and the other is cardinal welfarism. They can be classified into comparability

and non-comparability of welfare.

In SCIV, Arrow regards non-comparable and ordinal individual welfare judgment as

the informational foundation. He regards social preference as a criterion of social

welfare. Conversely, after the 1970s-1980s, Arrow came to believe that the

consequences of both market and social choice are not always just from a

non-welfaristic point of view. He also gradually came to believe that we must protect

one’s rights, no matter how society violates it. Instead, he considered that it is collective

choice under a veil of ignorance that can deduce a criterion of justice, because its

informational foundation is the individual welfare judgment that eliminates subjective

viewpoints and such a procedure satisfies both mutual respect and impersonality.17 A

criterion of justice also includes non-welfaristic aspects (e.g., equal distribution of

power and opportunity of choice and correction of inequality). Therefore, we can say

that Arrow has non-welfaristic aspects. However, it must be noted that Arrow wants

such non-welfarism to be compatible with the welfarism that Arrow displayed from the

beginning.

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