Kenneth Arrow‘s impossibility theorem, a pillar of neoclassical economic theory, argues that under certain “seemingly reasonable” conditions, no social welfare function can adequately represent the preferences of society’s members. A social welfare function is a mathematical formula that combines individual preferences in some manner to reflect societal preferences. The impossibility theorem is sometimes colloquially understood as implying that aggregating individual preferences to form a social preference ordering is impossible. However, the restrictions Arrow placed for his theory to hold are far from reasonable, undermining the validity of his theorem.

Let’s take a closer look. One of the constraints Arrow includes in his theorem is the “independence of irrelevant alternatives” (IIA). This supposes that a person’s preference between two options shouldn’t be influenced by other choices. Essentially, it posits that preferences shouldn’t be dependent on any other alternatives becoming available.

Some economists have likened the IIA assumption to choosing amongst flavors of ice cream. Whether I prefer chocolate to vanilla ice cream shouldn’t depend on whether strawberry is available, or so it is argued. The ice cream metaphor is a poor one, however, given the trivial nature of the alternatives. So let’s break down the IIA assumption with another, more appropriate, example.

Suppose you’re torn between going out to party tonight and staying home to study for an exam. At face value, partying appears to be the more enjoyable option. However, a third option, like “getting into a good college,” may depend on your decision. Clearly, this third choice—the future consequence—ranks higher among your preferred alternatives than the immediate option to party. This is despite the fact that partying, when taken independently of future consequences, seems to be the preferred choice over studying.

Herein lies the problem with Arrow’s impossibility theorem: it overlooks long-term consequences and focuses too much on immediate gratification. This is troubling because much of today’s welfare analysis, including cost-benefit analysis, is based, at least indirectly, on Arrow’s theorem, leading economic theory broadly and public policy specifically to take a short-sighted approach.

Rejecting Arrow’s theorem shouldn’t be controversial. Nor should it be a politically divisive issue. Many from the political left already contest Arrow’s theorem and its rigid IIA assumption. However, those on the political right have been slower to disavow it, perhaps because of a natural skepticism toward a social planner dictating societal values through a social welfare function.

This is a mistake. Ironically, rejecting the use of any social welfare function at all, as some libertarians do, also implies rejecting the market process—which itself is guided by a social welfare function of sorts. Arrow himself acknowledges as much in his book that presents the impossibility theorem, Social Choice and Individual Values, when he concludes that “the market mechanism does not create a rational social choice.” Strangely, most libertarians have failed to heed the lesson.

Without the IIA condition, the impossibility theorem falls apart. The key takeaway here is that economists need to revisit some of their foundational theories. Indeed, much of modern welfare economics needs a fresh look and reevaluation. The mid-20th century, sometimes regarded as a golden age of economic theory, may well have been a breeding ground for economic errors. We need to rectify these, and a good starting point would be to revisit Arrow’s impossibility theorem.


James Broughel is a Senior Fellow at the Competitive Enterprise Institute with a focus on innovation and dynamism.