When you heard the Supreme Court’s 5-4 decision to remove a piece of the Voting Rights Act, you may have been surprised. But the most mathematically minded Americans should have been surprised for an entirely different reason—the decision did not come down 9-0. The justices are all intelligent and heard the same facts, so how did they not reach the same conclusion?
This seems patently absurd. Anyone passively familiar with the court knows we receive 5-4 decisions all the time, and every one of us has long-standing political disagreements with friends we consider to be rational-minded. Disagreement is the lifeblood of intellectual debate.
Enter the mathematicians. Robert Aumann, a Nobel laureate with a Gandalf beard and a genial grin, has spent most of his career studying knot theory and correlated equilibrium in non-cooperative games. But in 1976, he published a brief, three-page paper called “Agreeing to Disagree,” which has gradually become his most-cited work. In it he proves what is now known as Aumann’s agreement theorem: Two rational people with the same information can’t disagree.
In what may seem like a coy bit of self-reference, you cannot disagree with this theorem. It is derived from incontrovertible axioms using sound steps of logic. If you take issue with it, you must also take issue with the core tenets of mathematics.
The argument leading to this conclusion is so simple that Aumann all but apologizes for publishing it. “Once one has the appropriate framework,” he writes, “it is mathematically trivial.” He proceeds to break down the statement into mathematical formalisms, but his reasoning can be likened to a young child who has just learned the power of the question, “Why?”
For example: “I believe New York is safer now than it was in 1980.” “Why?” “The murder rate is lower now, and lower murder rates make a city safer.” “Why is your first statement true?” “There were 2,228 murders in 1980, and 414 murders in 2012, and 414 is a lower murder rate than 2,228.” “Why are your first two statement true?” “The New York Times reports those numbers, and what the New York Times reports is generally true.” “Why is your second statement true?” And so forth.
To disagree with a conclusion, you must disagree with an assumption, which can be broken up into more basic assumptions. This process continues until you reach an unbreakable atom of information, and we assumed everyone has the same information.
Aumann’s theorem, you will not be shocked to hear, does not translate well from paper to podium. Politics cannot be atomized as easily as mathematics, so the notion of two people truly having the “same information” is an approximation at best. And more importantly, people are not rational in the way theorists imagine they are—we like our current beliefs, and we will shape new information in light of them. And we really don’t like being wrong.
Imagine the blowback if, mid-debate, Romney had conceded that perhaps he ought to read up a bit on military spending cuts before criticizing Obama’s actions. Imagine the ridicule if, after reading enough op-eds , the president announced his conclusion that perhaps Obamacare wasn’t such a good idea after all and endorsed the motion toward its repeal. These scenarios are comically unthinkable, and yet they would be the norm if the world were inhabited by the rational beings we read about in economics textbooks.
The tenured justices of the Supreme Court may do better than most to seek honest results, but their 5-4 disagreements, often along partisan lines, betray their inability to distance themselves from the culture of political adversarialism. Fortunately, we needn’t let the improprieties of public discourse infect the halls of academia. My hope is that, knowing rational disagreement is impossible, you may temper your convictions and actively attempt to be convinced. There are smart people who disagree with you—if an omniscient referee were called in, would you bet your beliefs?
The aforementioned ruling on the Voting Rights Act has led to new voter ID laws, which are presently being both hailed as commonsense and censured for racism. Today, make an effort to discard your preexisting conviction. Do some research and gather relevant information. Build a modest conclusion built directly from obvious assumptions. Submit to peer review by finding a friend who takes issue with your verdict. Have her identify the assumption with which she disagrees, and break it down further.
You will undoubtedly find it difficult to defend claims you thought were safe. As you struggle, do your best to remember Aumann’s gospel: You don’t win a debate when your opponent is convinced; you win a debate when all parties reach the truth.
Milo B. Beckman ’15, a Crimson editorial comper, is a government concentrator in Eliot House.