Rational Agreement Theorem

by admin on April 11th, 2021

There is a lot to be said for that, but I will focus here on two aspects. The result can be seen either in normative terms that tell us what we should do as rational thinkers, or positive terms that describe how rationally people behave. In a positive sense, it is obvious that the sentence is not a good description of human behavior. People are stubbornly divided, and if they “agree,” it is more a sign of respect than of mutual contempt. However, it may be just courtesy and we may recognize, at some level, that such breaches of agreement reflect a certain lack of good faith among the participants. I would be curious to see how others perceive this kind of situation. Philosophers like to discuss Sherlock Holmes and Professor Moriarty, who meet in a train station, and Moriarty said, “I knew you`d be here,” and Holmes said, “I knew you knew I`d be there,” and Moriarty said, “I knew you knew I`d be there” etc. But real people tend not to be able to think reliably on three or four levels in the hierarchy of knowledge. (In context, you may have heard of the game, where everyone guesses a number between 0 and 100, and the winner is that is the number closest to 2/3 of the average of all numbers. If this game is played by completely rational people who know they are all perfectly rational, and know they know, etc., then they need to guess all 0 – exercise for you to see why. However, experiments show that if you really want to win this game against average people, you should guess about 20. People seem to start at 50 or something like that, iterate the multiplication operation with 2/3 a couple of times, then stop.) In a way, all this talk of rationality reminded me of this gem of Seth Lloyd`s writings: “Ironically, it is customary to associate our own predictable behavior and that of others with rationality: we are to be rational, we think the world is more predictable. In fact, it is precisely when we behave rationally and move logically from one stage to another like a computer that our behavior becomes unpredictable.

Rationality combines with selfishness to make our action in itself paradoxical and uncertain. Ian #7: Yes, absolutely, general knowledge of rationality and honesty is one of the basic assumptions – something that was mentioned in the mail, but should have been more explicit. IIRC, is there literature on variants of Aumann`s theorem where you can relax this assumption (anyone else wants to give references? If I won`t try it later). But the simplest interpretation is, in turn, that these results have a desirable meaning: they describe what conversations between two people whose honesty and rationality are so strong that the other does not doubt it, and the other does not doubt that they doubt it, etc. Geanacoplos – Polemarchakis[2] prove that if the information is finished, it can be extended to a communication environment, even without general knowledge (although they still adopt common priors). Scott Aaronson[3] sharpens this sentence by deleting the common precedent and limiting the number of messages communicated. In particular, the parties can, in ε with probably at least 1 – δ with an exchange of 1/2) messages (read how, in the duration of the entire existence of the universe). Aumann`s agreement phrase[1] is the result of Robert Aumanns, winner of the 2005 National Bank of Sweden Economics Prize in memory of Alfred Nobel, a revolutionary discovery in 1976 that a sufficiently respected game theorist can bring everything in a journal evaluated by experts. 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.

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