Picture a democracy where every citizen’s voice is heard, each vote carries equal weight, and collective decisions flawlessly reflect the will of the people. The institutions are free from bias, manipulation, and corruption. Leaders represent the interests of the majority, policies serve the common good, and no individual or group holds disproportionate power. This is the ideal that all democracies have sought for centuries through political evolution and reforms. These efforts include global measures like the formation of the United Nations, national milestones like the Emancipation Proclamation, and local measures like knocking door-to-door to ensure maximum voter turnout. However, not a single country has been able to successfully implement this ideal. This is no coincidence.
Kenneth Arrow was an American economist, mathematician, and political theorist who served on the economics faculties of the University of Chicago, Harvard, and Stanford. He received the Nobel Prize 1972 for his pioneering contributions to general equilibrium theory and welfare theory. The most significant of these was Arrow’s Impossibility Theorem also known as “The General Impossibility Theorem” or “Arrow’s Paradox.” Here, he examines the mechanisms governing the conversion of a combination of individuals’ preferences, welfare, and opinions to community decisions. This theorem sparked a re-evaluation of how democratic decision-making procedures arrive at representative expressions of individuals’ preferences and, at a larger scale, are used to challenge the concept of “the public” as a meaningful social entity. In essence, Arrow claims that, in a ranked voting system with more than two options, it is impossible to reach a fair conclusion solely by collecting and converting individuals’ preference orders.
A crucial step in unpacking this theory is to define what Arrow considered a “fair election.” First, the election needs to consider multiple voters, ensuring “non-dictatorship.” Second, is “unrestricted domain” which requires the preferences of all citizens to be counted. Third, the “independence of irrelevant conditions” warrants consistency and rationality in the choice of individuals. The fourth condition is of a technical nature that requires voters to be able to order their choices in connected relations, like from best to worst. Lastly, and most importantly, the voting system should respect the preferences of the individuals. In an extreme case, this may look like the populace unanimously voting for Candidate A but the system granting Candidate B the win. Generally, these conditions are realistic criteria for the idea of a fair election.
It is important to note that this theory applies only to systems where voters rank candidates in order of preference without measuring the intensity of the preference, like the plurality voting system in the U.S. Conversely, Arrow’s Theorem does not apply to a cardinal voting system that considers intensity of preference of candidate. For context, the national elections of every democracy uses a ranked voting system, making Arrow’s Theorem universally applicable.
Arrow has set plausible and realistic guidelines for his version of fair elections and developed a theory that applies to the federal elections of every single country and more.
Arrow showed that it is impossible to construct a procedure that meets the above conditions. In general, there can be no institution that results in a collectively rational expression of individual desires. This matches our intuition, since, logically, a perfect democracy would require every citizen to vote on every decision. This would eventually result in mob rule that may represent the manifestation of the principles of democracy, but would be ineffective for governance. By extension, this makes it impossible to define basic needs or universal criteria that collective decision-making should recognize, such as minimal nutrition standards or human rights.
We realize the applications of this theorem everyday through the necessary trade-offs elected officials engage in to further policies. For example, in parliamentary systems, like that used in India, coalition-building is necessary to ensure stability of government. However, this leads to policy compromises that do not completely align with voter preferences. Similarly, the U.S. Senate’s equal representation structure is an example of disproportionate power. However, the Great Compromise was crucial in persuading the smaller states to ratify the U.S. Constitution and safeguarding them from the influence of larger states.
While this may sound grim, the pursuit of order is, at its core, a reflection of human nature mirroring our desire for stability, fairness and predictability.
Every idea has its drawbacks and while this may sound grim, the pursuit of order is, at its core, a reflection of human nature mirroring our desire for stability, fairness, and predictability. We often fail to acknowledge that legal systems and political institutions are separate from human thought and influence. It is vital to realize that, since they were created by imperfect humans, at its core, they too will be flawed. They too will resemble the imperfections, contradictions, and struggles that define the very existence of humanity. More broadly, this means that the order various groups strive for is not an absolute truth or universally accepted ideal but rather a subjective illusion.
In conclusion, Kenneth Arrow defined the essence through a political science lens, showing that order is not a rigid and absolute concept, but rather a dynamic and adaptable mechanism.
Husain Master ‘27 studies in the College of Arts & Sciences. He can be reached at h.a.master@wustl.edu.