The title of Aumann’s paper is just a pithy slogan. What the slogan means as the title of his paper is the actual mathematical result that he proves. This is that if two agents have the same priors, but have made different observations, then if they share only their posteriors, and each properly updates on the other’s posterior, and repeat, then they will approach agreement without ever having to share the observations themselves. In other papers there are theorems placing practical bounds on the number of iterations required.
In actual human interaction, there is a large number of ways in which disagreements among us may fall outside the scope of this theorem. Inaccuracy of observation. All the imperfections of rationality that may lead us to process observations incorrectly. Non-common priors. Inability to articulate numerical priors. Inability to articulate our observations in numerical terms. The effort required may exceed our need for a resolution. Lack of good faith. Lack of common knowledge of our good faith.
Notice that these are all imperfections. The mathematical ideal remains. How to act in accordance with the eternal truths of mathematical theorems when we lack the means to satisfy their hypotheses is the theme of a large part of the Sequences.
The title of Aumann’s paper is just a pithy slogan. What the slogan means as the title of his paper is the actual mathematical result that he proves. This is that if two agents have the same priors, but have made different observations, then if they share only their posteriors, and each properly updates on the other’s posterior, and repeat, then they will approach agreement without ever having to share the observations themselves. In other papers there are theorems placing practical bounds on the number of iterations required.
In actual human interaction, there is a large number of ways in which disagreements among us may fall outside the scope of this theorem. Inaccuracy of observation. All the imperfections of rationality that may lead us to process observations incorrectly. Non-common priors. Inability to articulate numerical priors. Inability to articulate our observations in numerical terms. The effort required may exceed our need for a resolution. Lack of good faith. Lack of common knowledge of our good faith.
Notice that these are all imperfections. The mathematical ideal remains. How to act in accordance with the eternal truths of mathematical theorems when we lack the means to satisfy their hypotheses is the theme of a large part of the Sequences.