Speaking about executive pay, German chancellor Angela Merkel was recently quoted by The Economist as saying that “exorbitance cannot be allowed in a free and socially minded society.” Margaret Thatcher, who died a month later, had often been blamed for her statement that “there is no such thing as society.”

One might take Merkel’s expression as a slip of tongue or just florid style—like if she had talked about, say, a “stony minded stone”—if her statement and Thatcher’s did not represent two profoundly different visions of society. Merkel seems to consider society as a thoughtful entity with a consistent preference set, just like an individual. Thatcher knew better.

The personification of collectives is common. Just consider a few examples: An environmental and anti-globalization activist declared that “[a] healthy society decides what it will export and import.” In democratic times, the collective persona is all of us: “we as a society,” “we as a nation,” “we as a country.” “As a nation, we have repeatedly passed up the opportunity to address this issue,” declared the husband of Rep. Gabrielle Giffords about gun control. “We as a country” killed bin Laden, boasted president Barack Obama.

If we decide and do things “as a society” or “as a nation,” then “we” must have some collective preferences that allow us to choose what to do. Society must have preferences, socially minded or not. Few people seem to wonder where such social preferences come from, despite a long strand of scientific inquiry proving that they are of the same reality as unicorns.

Consider the dilemma: On the one hand, society’s preferences cannot be totally independent of the preferences of the individuals who compose it. A society made of only non–socially minded individuals could not itself be socially minded. For social preferences to be totally distinct from the preferences of society’s individual members, we have to imagine society as a sort of biological organism with its own distinct mind. Many people do seem to think this. Just one hot example: writing about the recent Boston Marathon bombing and the failure of imposing more gun controls (something that Europeans have deep problems understanding), the American correspondent of The Economist ranted about the British “national conscience” and the American “national psyche.” Friedrich Hayek reminded us that social organicist theory is not only without scientific foundations, but “has almost invariably been used in support of hierarchic and authoritarian views.” So society’s preferences cannot be independent of the preferences of individual society members.

On the other hand, social preferences cannot correspond exactly to individual preferences either, if only because the latter vary from one individual to the next. Some function is needed to transform individual preferences into social preferences. Economists call this mapping a “social welfare function.”

Preference aggregation problem | Welcome to the problem of preference aggregation. People who talk of “we as a society” or of an X-minded society (e.g., open-minded, high-minded, God-minded) assume that society has its own preferences that can be aggregated in some way from individual preferences. But how do you do this? How do you add together the preferences of different individuals—say, some socially minded and other non–socially minded individuals? The answer provided by the academic literature on preference aggregation is that you cannot.

Paul Samuelson, the winner of the 1970 Nobel Prize in economics, showed that society cannot have, like an individual, consistent preferences between baskets of goods and services (say between different combinations of guns and butter). The social welfare function is meant to represent society’s welfare just as individual utility functions describe individual utility, but Samuelson demonstrated that such a social welfare function is impossible to define (in goods space).

The reason is simple, although the full demonstration requires some technical analysis. For society (if you allow me to speak like Merkel for a moment), any given basket of goods and services will lie on a different social indifference curve—meaning a different level of social welfare—depending on how it is distributed among the members of society. For example, whether the basket composed of one million houses and 500,000 cars is preferred to a basket of 500,000 houses and one million cars depends on how the houses and cars are distributed among individuals. If this were not true, the preferences of individuals about distribution, including crucially what an individual gets for himself, would not be taken into account. Consequently, the only social welfare function that can be assigned to society must be defined in utility space: it must be concerned with distribution among individuals.

This sort of social welfare function came to be known as a Bergson-Samuelson social welfare function. It expresses society’s preferences over the distribution of utility among individuals. The most enlightened among its users knew that it did not actually aggregate individual preferences: as Francis Bator, a Harvard University economist, put it haughtily in a famous 1957 article, the social welfare function “could be yours, mine, or Mossadegh’s.” (“Mossadegh” might have been a reference to Mohammad Mossadegh, the progressive prime minister of Iran who was overthrown in 1953, or Bator’s way of saying “Joe Smith.”)

Arrow’s theorem | Samuelson’s demonstration was in fact a special case of the more general Arrow Impossibility Theorem. In 1951, just a few years before Samuelson’s and Bator’s articles, Kenneth Arrow (1972 Nobel Prize in economics) published his seminal work Social Choice and Individual Values. In the book, he mathematically demonstrated that aggregation of individual preferences into a social welfare function—even in utility space—is impossible unless one is willing to violate some conditions that seem axiomatically obvious. To simplify and reformulate, the main conditions are:

  • The social preferences must be as consistent as individual preferences are. That is, if A is preferred to B, and B to C, then A must be preferred to C.
  • The social welfare function must not be dictatorial in any way. That is, the preferences of some individuals for some social outcome must not win all the time, whatever the other individuals want.

Arrow showed that these two conditions cannot hold at the same time: social preferences aggregated from individual preferences must be either inconsistent (intransitive) or dictatorial—the dictator or dictators imposing some of their preferences on others.

One of the fascinating aspects of this story is that another special case of Arrow’s theorem, called the paradox of voting, had been discovered in the 18th century by a French mathematician and philosopher, the Marquis de Condorcet, and again in the 19th century by mathematician Charles Dodgson (better known by his literary nom de plume, Lewis Caroll), and independently once again by economist Duncan Black a bit before Arrow developed his theorem. Condorcet, Dogson, and Black found that voting, which is one of the ways to aggregate individual preferences, could lead to inconsistency, also called “cycling” because the majority could choose A over B, and later B over C, but then choose C over A.

When he realized that an electorate composed of all consistent voters may be utterly inconsistent, Black was deeply upset: “On finding that the arithmetic was correct and the intransitivity persisted,” he later explained, “my stomach revolted in something akin to physical sickness.” Arrow extended the nausea to all economists and political scientists who study the issue.

This mathematical feature of voting and other preference-aggregating mechanisms may explain, when ignorance does not suffice, the inconsistencies often exhibited by majority opinion. For example, an opinion poll taken in April (after the Boston bombing) shows that a majority of Americans both support expanded background checks for gun purchases and give a higher approval rating to the National Rifle Association than to congressional Democrats. The intuitive explanation of such inconsistencies is that different majorities support different alternatives, and some voters have, compared to the majority, distorted views of the relations between the different alternatives. They have not only different opinions, but also divergent outlooks on the world.

Condorcet, who was a classical liberal, was arrested under the French Terror and died in his jail cell on March 29, 1794. His tragic end had nothing to do with his discovery of the voting paradox—or perhaps it indirectly did, so momentous are the implications of the inescapable alternative between irrational and dictatorial political choices. If the decisions of the French revolutionary authorities were not imposed by a few radicals, they could very well have been inconsistent.

Collectivist language | Arrow’s theorem has generated a vast literature. Although the theorem was never proven false (a theorem is a matter of logic), some of its conditions were criticized—arguably without challenging its central insight. From a political economy, less technical viewpoint, Gordon Tullock argued that social and political institutions mitigate the possible inconsistencies of voting choices, rendering Arrow’s theorem irrelevant. James Buchanan, on the contrary, welcomed cycles, since they prevent one majority from consistently exploiting the same minority. Another criticism, perhaps more conservative and closer to Tullock and possibly to Hayek, would see in traditional rules of conduct a way to prevent too much social heterogeneity and thus keep inconsistent preferences at bay. Consistency is purchased at the price of imposing traditions on everybody.

We may safely conclude that society does not have preferences on the basis of which it makes choices like an individual does. Further, the entity that makes political choices (in a generally irrational way) is the state, not society as such. There are real individuals who are steamrolled. There can’t be an X-minded society, except if X is mutable or is imposed by some on others. Speaking of an X-minded society does not make scientific sense. Speaking of a socially minded one is even more absurd, as it implies a self-referential process unique to the individual mind. Similarly, “we as a society” means nothing consistent, or else it means “we who force others in the mold of our own preferences.”

Perhaps Merkel was just speaking carelessly. Since she is not an economist, she has probably never heard of Condorcet, Dodgson, Black, or Arrow (in fact, many economists only have a vague clue themselves). Perhaps she was just another unconscious victim of what Hayek called “our poisoned language.” “Though abuse of the word ‘social’ is international,” wrote Hayek, “it has taken perhaps its most extreme forms in Germany where the constitution of 1949 employed the expression sociazialer Rechtsstaat (social rule of law).” This collectivist language is dangerous because it provides implicit support for the discriminatory-minded state to impose the preferences of some individuals on others. The fact that Merkel lived much of her life in East Germany did not provide the best antidote. At any rate, Thatcher was right: in the sense of a thinking and acting entity, there is no such thing as society.

Readings

  • Law, Legislation and Liberty, Vol. 1: Rules and Order, by Friedrich A. Hayek. University of Chicago Press, 1973.
  • “Public Choice: Politics Without Romance,” by James M. Buchanan. Policy, Vol. 19, No. 3 (Spring 2003).
  • Social Choice and Individual Values, 2nd ed., by Kenneth J. Arrow. Yale University Press, 1951.
  • “Social Indifference Curves,” by Paul A. Samuelson. Quarterly Journal of Economics, Vol. 70, No. 1 (February 1956).
  • The Fatal Conceit: The Errors of Socialism, by Friedrich A. Hayek. University of Chicago Press, 1988.
  • “The General Irrelevance of the General Impossibility Theorem,” by Gordon Tullock. Quarterly Journal of Economics, Vol. 81, No. 2 (May 1967).
  • “The Simple Analytics of Welfare Maximization,” by Francis M. Bator. American Economic Review, Vol. 47, No. 1 (March 1957).