Politics. Morality. Religion. Relationships. Even science. These are examples of the many categories in which you will find disagreements. These debates occur just as much with intelligent people as they do with those of lesser mental aptitudes.

When people get frustrated with another's reasoning in such heated discussions, you will often hear the phrase "we'll have to agree to disagree." It means that one party will tolerate the other party's position while simultaneously rejecting it.

But according to Bayesians, rational people shouldn't agree to disagree... because it's not rational. Mutual awareness of opinions requires that you agree.

The idea is effectively this: if you both have the same information, it should be impossible to disagree. It's not simply a matter of another's opinion - it's a matter of calculating where the error is in the objective logic. The error likely comes from some psychological bias, whereby someone disregards information that is unpleasant to them or that doesn't conform to what they know. This is known as a cognitive bias (one of the more infamous ones being the Dunning-Kruger effect).

Granted, there are some hard assumptions in this idea. For example, the people debating must have the same information (aka "common priors"). But it's rare to find that disagreeing people have the exact same information. The idea could also be considered circular: rational people agree that they shouldn't disagree. You don't agree with that theory. Therefore, you are acting irrationally. Thus, the idea is sound.

One of the goals of rational people should be to trace differences in information to identify where relevant facts are missing and where subjective content is entering into the argument. If you and the person you are debating are honest, truth-seeking people, you should each strive to obtain, at minimum, a complete set of facts. To find and eliminate the biases, especially as they apply to relevance, you must explore the details of your influences and potential self-deception. What is objectively true should never be a disagreement among rational people. Unlike politics, facts should change our beliefs.

When people disagree, how do you determine if the disagreement is rational? Would we gain more agreement if we identified our favored positions or biases as part of the discussions? As Sextus Empiricus has suggested, should we suspend judgment about virtually all beliefs and be skeptics of everything? How much of a rational argument can be subjective and still considered rational? How do you know if someone's beliefs are derived through reason? What are the standards for rationality?

It's been mentioned a few times already, but I want to draw attention to what is IMO probably the most interesting, surprising and challenging result in the field of human bias: that mutually respectful, honest and rational debaters cannot disagree on any factual matter once they know each other's opinions. They cannot "agree to disagree", they can only agree to agree.

This result goes back to Nobel Prize winner Robert Aumann in the 1970s: Agreeing to Disagree. Unfortunately Aumann's proof is quite static and formal, building on a possible-world semantics formalism so powerful that Aumann apologizes: "We publish this note with some diffidence, since once one has the appropriate framework, it is mathematically trivial." It's ironic that a result so counter-intuitive and controversial can be described in such terms...

There is much that can be said on this topic but I'll focus on two aspects here. The result can be seen in either normative terms, telling us what we should do as rational thinkers, or positive terms, describing how rational humans behave. In the positive sense, it is obvious that the theorem is not a good description of human behavior. People do disagree persistently, and when they "agree to disagree" it is taken as a sign of respect rather than mutual contempt. It's possible that this is mere politeness, though, and that we recognize at some level that such failures to reach agreement indicate a certain lack of good faith among the participants...

Normatively what I find most striking is the variation in how people respond upon learning of this result. Many people have a strong intuitive opposition to it, and seek out loopholes and exceptions which will allow them to justify their persistent disagreements. Indeed, such loopholes do exist, the most notable being the assumption that the debaters are acting as Bayesian reasoners with common priors. However as Tyler and Robin note in their paper, a number of extensions and relaxations of Aumann's original result over the years have increased its scope and made it harder to appeal to these exceptions as a justification for ignoring the results.

Agreeing to Agree

DISCUSS!

Original posting by Braincrave Second Life staff on Jul 29, 2011 at http://www.braincrave.com/viewblog.php?id=610