Kenneth Arrow’s Theory on Why Fair Voting is Impossible

In America, the election cycle is elevated to a level that is nearly sacred. The sanctity of the ballet box relies on our ability to trust that we are voting independent of the influence of others. However, fair voting goes one step further: requiring that voters derive sensible results with ample choice. Why this holds true is rather complex, but in practice, it’s correlated with reality. Here, we attempt to explain Arrow’s theorem.

The Problem is Options

Arrow’s theory states that one cannot choose between more than two options without establishing cyclic preferences, which is to say preferences that cannot be ranked from best to worst. You’ve probably heard this expressed as a third party candidate who was able to split the vote, as Ross Perot was able to do in 1992 between George H.W. Bush and Bill Clinton.

Fair voting would take the true majority of the country into account, but this example shows that in some cases, people vote for the lesser of two evils or they vote for someone else entirely because they see no hope in other candidates or care about alternative issues.

The practice of holding an election isn’t as simple as everyone writing names on a slip of paper, putting those names into a box and tallying votes. The primary concern in modern elections is freedom from what is known as “irrelevant alternatives”. A third party candidate can be considered an irrelevant alternative when he or she speaks on and gains significant traction for issues that are not relevant to the general electorate. We could make things simple and exclude third party candidates entirely, but this would present the dictatorship paradox.

Credit LA Cicero, 11/4/1996, color neg. Kenneth J. Arrow, professor emeritus in economics, Nobel Laureate
Credit LA Cicero, 11/4/1996, color neg.
Kenneth J. Arrow, professor emeritus in economics, Nobel Laureate
By Phineas Upham

About the Author: Phineas Upham is an investor at a family office/ hedgefund, where he focuses on special situation illiquid investing. Before this position, Phin Upham was working at Morgan Stanley in the Media and Telecom group. You may contact Phin on his Phineas Upham website or Facebook page.