Kenneth Arrow as a Political Philosopher

Social Choice Theory and The Necessity of Agreement and Consensus

As I’m writing the final words of my manuscript and – hopefully – would-be book tentatively titled “Social Choice and Public Reason,” I’ve been rereading some classics of social choice theory to find some material relevant for the general introduction. As the tentative title suggests, the broad idea is to connect two very different traditions, one in normative economics and the other in political philosophy. Social choice theory has a reputation for being a very technical field mostly interested in formal issues (i.e., establishing possibility or existence theorems) that, while in principle relevant to political philosophy, are treated in such a way that the field remains mostly esoteric for non-insiders. This reputation is probably deserved, but doesn’t mean that the field has nothing interesting to offer to political philosophers.

I’ve been for a while now convinced that in this perspective, one of the most interesting contributions of social choice theory is the seventh chapter of Kenneth Arrow’s Social Choice and Individual Values.[1] The chapter is titled “Similarity as the Basis of Social Welfare Judgments” and is a sketchy reflection on the possibility of collective choice-making in light of the impossibility results of his famous theorem. As a reminder, Arrow shows in the fifth chapter that there is no “social welfare function” (i.e., a mathematical function mapping a profile of individual preferences over social states onto an ordering of those states) that respects the conjunction of four compelling conditions: (1) the function is well-defined for all possible profiles of individual preferences; (2) the function respects unanimous individual preferences; (3) the (social) preference between two social states depends only on the individual preferences between those two states; and (4) the (social) ordering generated by the function is not identical to the individual preferences of one agent.[2] The sixth chapter shows that the impossibility result holds under the traditional (“individualistic) assumptions of welfare economics where social states correspond to bundles of commodities. It is in this chapter that Arrow claims that his result also applies to the so-called “Bergson-Samuelson social welfare functions,” a claim that sparked a long-lasting even if obscure controversy between Samuelson and Arrow.[3]

As the title of the seventh chapter indicates, Arrow seeks to ground that very possibility of making collective choices in the fact that in many circumstances we can expect individuals to share similar judgments and preferences. In some cases, “similarity of social attitudes” triggered by such values as “the desires for freedom, for national power, and for equality,” may lead to quasi-unanimity in social judgments.[4] Unanimity is arguably a special case that is not going to be often achieved in pluralistic societies where individuals entertain a large diversity of views about the good life, about what matters, and about the best ways to fulfill their goals. However, at least as far as the main concern is to escape the implications of the impossibility theorem, Arrow points out that unanimity is not needed; it is enough if individuals’ preferences over social states are “single-peaked.”[5] As it’s well-known, a few years before Arrow published his book, the economist Duncan Black showed that when the condition of single-peaked preferences holds, the majority rule will always deliver determinate results in a voting situation, provided that the number of voters is odd.[6] Moreover, provided that the number of social states over which individuals form their preferences is strictly finite, for any profile of individual preferences that satisfies the single-peaked condition, the majority rule will generate a transitive ordering of social states. In other words, thanks to Duncan Black, we know that if preferences are single-peaked, there is at least one decision rule (the majority rule) that guarantees that a well-defined social choice exists. Hence, the impossibility result is in this case circumvented.

The single-peaked preferences case is a variant of the similarity of judgments scenario. Though individuals may disagree on what is the best or the more just option, their preferences share a structural property that guarantee that a social choice satisfying some compelling conditions is possible. However, as for the stronger case of unanimity, very often it’s unclear why we should expect individuals’ judgments to exhibit this structural pattern. It requires that individuals share a common conceptual perception or representation of the decision problem such that, for instance, they agree that this political party is more to the left of the political spectrum than that other party. While it may hold in many electoral settings,[7] this is definitely not something to be expected to be the case for most social choice problems.[8] Even if this requirement is satisfied, there is no obvious reason why individuals’ preferences must in general be single-peaked. The prospects of grounding the possibility of social choice in a structural similarity of individuals’ preferences based on an agreement about the conceptual representation of the social choice problem are therefore bleak.

That Arrow realized this is suggested by the fact that he also considers in some details a third form of similarity-based agreement allowing to escape the impossibility theorem. Referring to what he calls the “idealist school” of Rousseau, Kant, and T.H. Green, Arrow contemplates the possibility that a “general will” transcending the mutually conflicting individual wills. In this perspective, Arrow recasts the idealist position in the framework of social choice theory:[9]

“The idealist doctrine then may be summed up by saying that each individual has two orderings, one which governs him in his everyday actions and one which would be relevant under some ideal conditions and which is in some sense truer than the first ordering. It is the latter which is considered relevant to social choice, and it is assumed that there is complete unanimity with regard to the truer individual ordering.”

There are at least two remarkable points worth insisting on here. First, Arrow is here anticipating (or at least reformulating in the language of normative economics) an idea that will get traction a few years after he wrote these lines at the beginning of the 1950s. Arrow indeed suggests that to identify individuals’ “truer” orderings, we should ask what their judgments would be in “ideal conditions” that radically differ from the conditions that give rise to overt preferences as individuals express and reveal them. Though Arrow does not give any indication about what these ideal conditions could be, there is an obvious connection with the notions of the “original position” and the “veil of ignorance” that John Harsanyi[10] and John Rawls[11] have independently developed from the 1950s onward. Harsanyi, in particular, will develop an account of the original position that formalizes the dual orderings idea Arrow alludes to. Hence, Arrow anticipates the idea that, if any form of agreement can exist at all, it must be found in the fact that individuals can take a distinct point of view that shells them from the contingencies of their everyday experience.

Second, Arrow explicitly states that “there must be some sort of consensus on the ends of society, or social welfare function can be formed.”[12] It follows that the economic and political institutions of society must be defined and evaluated in light of the necessity of agreement and consensus. More specifically, the choice of social choice mechanisms must be governed by the imperious consideration that their primary social function is to foster agreement and consensus in society.[13] Arrow suggests that the case for democracy precisely rests on this consideration but also that acknowledging this view implies that the market mechanism cannot pretend to be more than a limited instrument in the quest for agreement because market participants, in general, do not exhibit the kind of motives needed to secure the consensus:[14]

“Any view which depends on consensus as the basis for social action certainly implies that the market mechanism cannot be taken as the social welfare function since that mechanism cannot take account of the altruistic motives which must be present to secure that consensus. If, in particular, the consensus in question is that of moral imperatives, the case is even worse since the market can certainly express only pragmatic imperatives. This does not deny the possibility of a limited use of the market as an instrument for achieving certain parts of the social optimum, especially if it is deliberately manipulated to make behavior under pragmatic imperatives coincide with that which would exist under moral ones.”

This is a very interesting claim, one that could be viewed as a partial response to the provocative idea that the functioning of markets is akin to a “daily plebiscite,” that Eric Schliesser has recently traced back in the writings of (neo) liberals economists and philosophers. As Eric writes in his essay, “there is, lurking in this neoliberal tradition, an intrinsic defense of markets rooted in ideas of consent and democracy. The significance of this is that it is wrong to think of neoliberalism as always inimical to or highly skeptical of democracy. In some of its most salient guises it appeals to democracy to legitimate markets.” Arrow explicitly argues against the idea of “market democracy” as a basis for the required consensus, precisely because within the market there is no reason to expect that individuals’ preferences will have the kind of similarity needed to overcome the impossibility result.

Now, obviously, this claim entirely relies on the postulate that market processes can be interpreted as social choice mechanisms, something that liberal/libertarian economists have been prone to reject.[15] If indeed, market processes are not appropriately conceived as social welfare functions, then there is no reason to think that the conditions imposed by Arrow on them are relevant, starting with the requirement that social (“market”) preferences should be well-ordered. As James Buchanan, it would be then mistaken to require from market processes a form of “social” or “collective” rationality:[16]

“By the very nature of free markets, however, the only entity required to compare two social alternatives when a choice is actually made is the individual. And, since individual orderings are assumed to be connected and transitive, the market mechanism does provide a means of making consistent choices as long as individual values remain unchanged. If, given this constancy in individual tastes (values), the economic environment is allowed to change, consistency requires only that the same social state result always from similar environmental changes. Of course, there is no way of telling what a market-determined result will be (even if we know the individual orderings) except to wait and see what the market produces. The market exists as a means by which the social group is able to move from one social state to another as a result of a change in environment without the necessity of making a collective choice. The consistency of the market arises from what Professor Polanyi has called the system of "spontaneous order" embodied in the free enterprise economy. The order "originates in the independent actions of individuals." And, since the order or consistency does originate in the choice process itself, it is meaningless to attempt to construct the ordering. We should not expect to be told in advance what the market will choose. it will choose what it will choose.”

This is clearly a huge debate and I will not expand further on it. The point that remains however is that Arrow identifies desirable properties that social choice mechanisms must have and conditions under which these properties are likely to obtain. In the last part of the chapter, Arrow suggests that those conditions are more likely to obtain in case the social choice procedure attempts to order “social ends” rather than “social decisions.” The main reason is that the former depends on individuals’ ultimate ends that have a “biological and cultural basis” that makes them more likely to be similar than the preferences over means (e.g., tax or antimonopoly policies) to reach those ends. Here, Arrow is expressing a fairly common view that is typical of what I have called elsewhere the “technocratic scheme” according to which democratic politics is mainly about choosing ends that policies, determined by experts and technocrats, are deemed to pursue. This is confirmed by Arrow’s statement that “the social ordering of social decisions should be based on the social ordering of social ends plus the use of scientific and statistical methods to limit the amount of ignorance in passing from decisions to ends and to limit the effects of the remaining ignorance.”[17]

Arrow ends the chapter with sketchy considerations on a related topic. If establishing a consensus is one of the considerations that should determine which collective choice mechanism to adopt, it is not necessarily the only one. The collective decision process is also valuable in itself and therefore, the choice of collective choice mechanisms should be responsive to a range of values beyond the mere establishment of a consensus. Obviously, the choice of a collective choice mechanisms is also a social choice problem and all the points that Arrow has mentioned before also applies. To avoid an infinite regress, Arrow concludes that unanimity is needed at some point. We are thus back to square one, which is clearly not satisfactory.[18] My own conclusion is that social choice theory, while a powerful tool for thinking about collective decision problems, is not enough to establish the possibility of making social choices that are justified and legitimate. This provides the main motivation to look somewhere else – in my case, public reason liberalism – to address this limitation. But this is another story.   

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[1] Kenneth Joseph Arrow, Social Choice & Individual Values (Yale University Press, 1963). The seventh chapter is the last one of the original 1951 edition and the penultimate one of the second edition published in 1963.

[2] In Arrow’s terminology, (1) is called the unrestricted domain condition, (2) the (weak) Pareto principle, (3) the independence of irrelevant alternatives condition, and (4) the non-dictatorship condition.

[3] My colleague Herrade Igersheim has a very interesting paper on the history of this controversy, Herrade Igersheim, “The Death of Welfare Economics: History of a Controversy,” History of Political Economy 51, no. 5 (October 1, 2019): 827–65.

[4] Arrow, Social Choice & Individual Values, pp. 74-5.

[5] For a definition and a discussion of the single-peaked assumption, see this previous essay of mine. Formally, the preferences of the members of a group are single-peaked if and only if it is possible to order the social states (i.e., the options over which individuals form preferences) along a (horizontal) axis such that, for any individual, any state that is at the right (left) of her preferred option is preferred to any option that is even further on the right (left).

[6] Duncan Black, “On the Rationale of Group Decision-Making,” Journal of Political Economy 56, no. 1 (February 1948): 23–34, https://doi.org/10.1086/256633.

[7] Though current political affairs in many Western countries suggest that this may no longer be the case.

[8] Indeed, as I shall discuss at length in Chapter 9, the rule seems rather to be the pervasiveness of “perspectival disagreement.”

[9] Arrow, Social Choice & Individual Values, pp. 82-3.

[10] John C. Harsanyi, “Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility,” Journal of Political Economy 63, no. 4 (1955): 309–21.

[11] John Rawls, “Justice as Fairness,” The Philosophical Review 67, no. 2 (April 1958): 164.

[12] Arrow, Social Choice & Individual Values, p. 83.

[13] Ibid., p. 85.

[14] Ibid. p. 86.

[15] See, in particular, James M. Buchanan, “Social Choice, Democracy, and Free Markets,” Journal of Political Economy 62, no. 2 (1954): 114–23.

[16] Ibid., p. 122.

[17] Arrow, Social Choice & Individual Values, p. 88.

[18] I’ve discussed in more details this section of Arrow’s seventh chapter here.