[FoRK] Agreeing to agree

Jeff Bone <jbone at place.org> on Tue Aug 21 19:53:52 PDT 2007

> As always, all of the above is only my opinion.  Please, do NOT use  
> this
> blindly to drive your investment or life choices.  Intelligent  
> people can,
> and do, disagree!

Perhaps, but it is perhaps impossible for truly rational people with  
equivalent information to disagree.  The ever-insightful Hal Finney  


Agreeing to Agree

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. [1] 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. This  
combination of elegance and parsimony of proof combined with the  
totally unexpected nature of the result is part of what makes this  
area so fascinating to me.

Aumann's proof, although elegant, is opaque unless you are familiar  
with the formalism. Tyler Cowan and Robin Hanson translate Aumann's  
proof into English on pages 7-9 of their paper, Are Disagreements  
Honest? [2] Some other papers that touch on the same result include  
Geanakoplos & Polemarchakis' We Can't Disagree Forever, [3] which  
discusses the sequence of events as two rational debaters come to  
agreement; and various "no bet" theorems such as the classic by  
Milgrom & Stokey, [4] showing that rational people will not  
participate in betting markets, since the mere fact that someone is  
willing to take your bet is evidence that you are wrong. Robin has  
several other papers in this area available from his web site. [5]


[1] http://www.ma.huji.ac.il/%7Eraumann/pdf/Agreeing%20to%20Disagree.pdf
[2] http://hanson.gmu.edu/deceive.pdf
[3] http://cowles.econ.yale.edu/P/cp/p05b/p0552.pdf
[4] http://www.kellogg.northwestern.edu/research/math/papers/377.pdf
[5] http://hanson.gmu.edu/vita.html

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