Review: Arrow's Social Choice and Individual Values

Kenneth J. Arrow's Social Choice and Individual Values (1951, 1963, second edition, Yale University Press) is rightly considered essential reading for English-speaking political philosophers. I do not claim to understand Arrow's proofs--I did not advance past basic symbolic logic in college--but I will share a general overview. 

Let us assume all democratic systems are flawed because they lead to factions seeking aggrandizement. Once a faction has achieved a majority, compromise becomes unnecessary, even if 49% of the citizenry will be disadvantaged or unhappy. Given such obvious flaws, how can we promote a government that protects liberty and diversity while preserving unity? A representative republican system incorporating two legislative bodies with different apportionment formulas should have mitigated nepotism and extremism; however, America's current political climate indicates representative republicanism is not necessarily more robust than pure democracy. 

Arrow does not claim to have solved political gridlock: "The notion of a 'democratic paralysis,' a failure to act due not to a desire for inaction by an inability to agree on the proper action" deserves further study. (pp. 120) Nevertheless, his paradigm intends to maximize individual agency while preserving collective goodwill: "Collective rationality in the social choice mechanism is not then merely an illegitimate transfer from the individual to society, but an important attribute of a genuinely democratic system capable of full adaptation to varying environments." (pp. 120) In a nutshell, Arrow rejects a hedonistic form of libertarian governance; and attempts to elicit observable preferences from which compromise leading to a defined consensus can be consistently achieved.

To his credit, Arrow openly highlights problems. First, his path towards a clearly defined consensus assumes, a priori, social cohesion: "it must be demanded that there be some sort of consensus on the ends of society, or no social welfare function can be formed." (pp. 83) We "may expect that social welfare judgments can usually be made when there is both a widespread agreement on the decision process and a widespread agreement on the desirability of everyday decisions." (pp. 91)

Arrow further assumes the act of voting "is not a device whereby each individual expresses his personal interests, but rather where each individual gives his opinion of the general will." (pp. 85) If a country is already blessed with a majority of citizens more apt to think of others than themselves, one sees a flaw immediately: Arrow's formulations rely on a pre-existing collective already primed to succeed under any political system. Yet, the flaw is not fatal, as one can also assume most citizens desire to vote/act in ways promoting the general will but thus far have been unable to agree on the best or most consistent way of effectuating their desires.

Think of Arrow as taking Kant's categorical imperative and making it practical: "A group of individuals, each rationally obeying the moral imperative, constitutes a 'kingdom of ends'--in our terminology, a society with a satisfactory social welfare function." (pp. 82) Arrow targets a practical medium between Plato's "objective social good defined independently of individual desires" and Jeremy Bentham's morally-subjective utilitarianism. (pp. 22) Ergo, we may assume the possibility of a unanimously accepted scenario in which everybody is better off (more precisely, everybody is at least as well off and one person better off) in one social state over another according to individual tastes; and "a universally accepted ordering of different possible welfare distributions in any given situation." (pp. 71) Such a possibility, if implemented, "may find the desired agreement in the moral imperatives of various members of... society." (pp. 83) So far, Arrow is guilty of idealism but not impossibility. 

A second criticism is whether a collective can be rational, or whether rationality presupposes individually-tailored agency. (i.e., Is "collective rationality" an oxymoron?) This argument seems overly academic and not worth examining. Obviously, an individual within a society of other individuals assumes, whether explicitly or implicitly, some set of agreed-upon rules. Arrow is not devising a system for hermits.

A third criticism is apt. What about the truth? Some persons in a society are surely more skilled than others in locating and parsing data, and Arrow's formula does not assign such persons proper weight. In contrast, Plato called "for a small specialized group of guardians to make the social choices." (pp. 86) Here, Arrow is naive. He argues "different opinions on social issues arise from lack of knowledge and can be removed by discovering the truth and letting it be widely known." (p. 88) Every government in the world in 2021 would laugh at the prior statement, and of course Arrow's book was published before mobile phones, the internet, and social media. Arrow's response could be updated by assuming an independent, widely trusted watchdog or a nonprofit news outlet, but such a scenario would incorporate too much Plato for Arrow's tastes.

A fourth criticism--which I am not sure applies--is that Arrow's approach may require resolving taste conflicts by paying off dissatisfied members, despite his claim that "the actual distribution of welfare dictated by the second value judgment cannot be stated simply in money terms." (pp. 72) In his defense, Arrow differentiates values from tastes, stating, "All individuals are assumed to have the same values at any given instant in time, but the values held by any one individual will vary with variations in the tastes of all." (pp. 71) From my perspective, once Arrow accepts that any financial or in-kind benefit will accrue to some members of his ideal society but not others, he risks his entire paradigm. A loud, aggrieved minority may not always be correct, but attempts to bribe away his or her dissatisfaction may alter the formula's effects to the detriment of all. Arrow would respond that my criticism is simplistic and his forms of "payment" involve meticulously-studied subsidies or taxes promoting equilibrium. (pp. 71)

Overall, Arrow's book provides plenty to think about and is well-worth to one or two hours of reading required to understand everything but his propositional formulas. 

© Matthew Mehdi Rafat (2021)

Bonus: the following sentence contains the most accessible interpretation of Arrow's ordering formula: "The information which enables us to assert that individual A prefers x to y more strongly than B prefers y to z must be based on comparisons by A and B of x and y not only to each other but also to other alternatives." (pp. 112)