Civil Discourse, Humility, and Aumann’s Agreement Theorem
Our national political climate is intensely volatile. The recent and tragic shooting at the practice for the Congressional baseball game can be understood as an isolated event, or as symptomatic of the seemingly intractable divisiveness that somehow encourages extreme behaviors among fringe members of the electorate. Our thoughts and prayers must be with the victims of this horrible shooting, including Representative and Majority Whip, Steve Scalise (R.LA.), and the officers injured in the line of duty. Of course, it is mistaken to ascribe causation, in any legal sense of the term, for the planned mass shooting by a deranged man to the failings of our public discourse. And yes, listening to Kellyanne Conway cast blame on political leaders on the left for creating a hostile political climate, see here, is not entirely unlike ingesting ipecac syrup. There is almost no doubt in my mind that neither this tragedy, nor any other, is going to perceptibly improve our political climate. If the Newtown, Connecticut massacre, which involved the tragic deaths of twenty-six people, including twenty children, could not soften extreme views on the Second Amendment, this more recent tragedy certainly will not accomplish a more general softening. Asking why our politics has broken down to the point of dysfunction is a bit like asking why Hamlet is depressed; the causes are overdetermined. Even so, it is important to identify elements, or strands, knowing that any account is necessarily incomplete. That’s especially appropriate for a post offered to praise humility and to lament hubris.
Humility not only counsels crediting others for accomplishments one could not have achieved without their help, see here; it also counsels trying to understand the point of view of those with whom we disagree, even if, and perhaps especially if, we know deep in our soul that those views are profoundly mistaken. Most people do not strive to be wrong. Instead of seeking to understand why so many persist in holding demonstrably false beliefs, we cast aspersions, and we don’t limit ourselves to arguing down the merits of a contrary position. We go further. Within our political culture, it’s somehow inadequate to disagree; we must demonstrate that our opponents are stupid. I don’t have data on this, but my strong intuition is that this tendency, although not new, has greatly intensified over the last decade.
The Israeli-American Professor of Mathematics and Nobel Laureate in Economics, Robert Aumann, see here, posed what is known as the Aumann Agreement Theorem. The theorem posits that under specified conditions reasonable persons cannot "agree to disagree." (More formally, two Bayesian rationalists with common priors, and with shared knowledge of their posterior probabilities, will have their posterior probabilities align. See here.) Setting aside the technical jargon, the intuition is straightforward enough: If two people disagree respecting a verifiable truth, the person holding the false belief is either (1) not a Bayesian rationalist (meaning he is unwilling or unable to reassess claimed predictions based on informed experience), or (2) unwilling to benefit from the other person’s better-informed knowledge and experience. Subject to the specified conditions, for persons able and willing to learn from their own experience and to internalize the learning and experience of others, disagreements should, in theory, eliminate. Alice and Barbara can rightly disagree over which flavor ice cream is “best,” but they cannot disagree on which flavor ice cream Chelsea Clinton or Ivanka Trump, or for that matter, each other, deems best. The former is a matter of opinion; the latter is the product of acquired and verifiable knowledge.
Certainly, Aumann is not claiming that actual persons do not disagree or that the disagreements dissipate with conversation. Such a belief would ironically remove Aumann from the category of Bayesian rationalist. As with all theorems, the true meaning is as much in the interpretation as in the formulation. If we disagree about how long it takes to make a hard-boiled egg, and if I say twenty minutes in boiling water, and you say ten, a Google search will prove me right (benefitting from the posterior probabilities of countless bloggers). Failing that, you can try it on your own (updating your own posterior probabilities). In public discourse, however, disagreements are rarely so trivial, and the rightness of one person’s view, is almost never so easily confirmed. Instead, disagreements arise because people not only differently interpret data (sometimes in ways that are verifiably false), but also because they disagree on how issues are framed. Sharing posterior probabilities is generally more helpful respecting the first sort of error than the second.
Consider the following hypothetical argument: I express disdain that Donald Trump is pulling the US out of the Paris Climate Accords by positing the critical importance of countering global warming. A Trump supporter responds that the evidence supports a fairly modest likely impact if we remain in. I defend my position by saying that the real issue isn’t the projected temperature impact, although that is a great concern, but rather, it is the importance of signaling US global leadership on an issue so vital, and the hope for more ambitious global targets moving forward. The Trump supporter defends by claiming that Barack Obama failed to demonstrate true political leadership by failing to achieve Senate ratification. I respond that the Republican Senate made this an impossibility despite the high stakes, and that past presidents, including Republicans, have undertaken comparable unilateral executive actions. The Trump supporter defends by claiming that Democrats have themselves engaged in obstructionist tactics, for example, during the Bush II administration.
And the volleys continue. My point is not to resolve any of the specific steps in the argument. Rather, it is to demonstrate that this (not entirely) hypothetical conversation is unlikely to be resolved by either side sharing posterior probabilities with the other respecting any given point of contention. Instead, each volley reframes the conversation, thereby shifting, over and over again, the dimensionality of the issues in dispute as a way to maintain originally held positions. In doing so, each side avoids responding to the merits of the opposing argument. We increasingly speak past one another, failing to move toward consensus or even to advance common understanding, as anyone who watches CNN’s never-ending panel of experts routinely observes.
Aumann’s conditions better describe machine than human learning. Computers aren’t embarrassed by error, and they won’t seek to “rescue” Baysian priors along a separate analytical dimension, despite, or upon, learning another’s contrary posterior probabilities. A programming error is just that, and once corrected, the outlier program, or machine, comes back into the fold. We humans, by contrast, are not programmable machines. Our minds seem infinitely capable of framing and reframing. This capacity, which is so central to who we are, see here and here, allows us to improve our depth of knowledge. The problem is that too often in the heat of political discourse we no longer seek to move the ball forward in ways that advance collective understanding. Instead, we seek to be right, and that demands salvaging our priors, often without actually defending them.
I don’t have any easy solution to these problems. I do think it is important to admit the limits of our framings and knowledge. I wish those engaged in high profile political discourse and debate would sometimes do just that. I’m not asking anyone to suddenly compromise core principles or lock arms with those on the other side and sing Kumbaya. But I think that it is wise, even virtuous, to be humble enough to say “We seem to view this problem differently, but you have raised a point worth thinking more about.” No one likes being treated as if they are stupid, and politicians don’t like to appear weak. But humility isn’t weakness; rigid insistence on being right no matter what is in front of you is a true weakness, and its consequences can be dire. If we allow ourselves to consider how our opponents frame the issues that lead them to another place and encourage them to stay there, then just maybe, every once and a while, our posterior probabilities might align.
As always, your comments are most welcome.