Agreement Theorem
That doesn`t mean that mathematicians and scientists get it wrong when they change tables when they feel the urge. But other areas are not necessarily wrong to maintain their differences, because differences of opinion and diversity of opinions are useful cognitive resources that should not be abandoned at the same time. Very nice contribution! Here are some remarks: I first wrote an essay on Aumann: Science, Beliefs and Knowledge: A Personal Reflection on Robert J. Aumann`s Approach. Which mention some of Aumann`s work and a long and specific disagreement between the two of us. Indeed, despite Aumann`s sentence, we do not agree and we often agree not to agree. When we found out that we agreed on a specific political matter! We were so surprised to share the same opinion that we decided to write a “letter to the editor” that contains our position on this subject. When we got to the fine details, it was impossible to accept “agree.” Second, two reasons (among several) are the reasons why Aumann`s sentence and associated insights fail in reality, the difficulty of assigning probabilities to events, and sensitivity to noise. This is true for the very simple application of pronciples bayes and certainly for repetitive recursive applications, z.B. if we need to reach detailed priors (also based on our accessories based on the possibility that I`m another person, etc.). Indeed, some savings based on such Bavarian and Aumannian discoveries are in favour of a change in the judicial system allowing jurors to obtain and weigh all information, including the accused`s background, lawyers` recordings, press opinion, etc.
They claim that a Bayesian process based on all available information will provide optimal results. One can be skeptical of this advice and argue that the “noise sensitivity” of a complex Bavarian process will render the results insignificant. Aumann`s approval sentence states that two persons who act rationally (in a specific sense) and who have a general knowledge of the other`s convictions cannot agree to object. Specifically, if two people are true Bavarian rationalists with common priors, and if they all have a common knowledge of their individual rear probabilities, then their buttocks must be equal. [1] This sentence also applies when the different faces of man are based on different observations of information about the world. It is easy to know that another officer has observed certain information and has come to the respective conclusion, will force everyone to review their convictions, which will ultimately lead to a total agreement on the right behind. Thus, two rational Bayess officers must agree with the same priors who know each other. Update: There turns out that there is a moving piece of Oliver Sacks`s NYT that tells, among other things, his experience with his cousin, the auman of Aumann`s sentence. As one commentator said in advance, these relatively rare points of disagreement are interesting and important because they underlie the relationship of status and strength.
In science, careers are based on winning arguments by publishing a better back hypothesis than the next guy in every round of “negotiation.” When and if an agreement is finally reached, what contribution was the most important? So if we share all these results, we will have a clear idea of what rational divergences should be: they should follow impartial random walks until they end sooner or later in the general knowledge of total convergence. We are faced with a small conundrum, because few differences of opinion in the history of the world have ever been. So, what`s going on? I go through the details like (2) and (3) allow the escape of Aumann`s sentence in a document that came out recently in the verification of symbolic logic.