~How to Decide more Ra0onally~�
Cheng-‐Shu Liu�
We are Made of What We Have Decided�
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A Decision to Make
Make the Decision Sequen0ally
Own a Private Informa0on
Observe What Others Do
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MB/MR�
Ball�
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A∩B
A
B
Pr A B!" #$=Pr A∩B[ ]Pr B[ ]
Pr B A!" #$=Pr B∩A[ ]Pr A[ ]
=Pr A∩B[ ]Pr A[ ]
Pr A B!" #$=Pr A[ ] ⋅Pr B A!" #$
Pr B[ ]
Pr A B!" #$⋅Pr B[ ] = Pr A∩B[ ] = Pr B A!" #$⋅Pr A[ ]
Pr A[ ]Pr B[ ]
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Pr true =Y report =Y!" #$=Pr true =Y[ ] ⋅Pr report =Y true =Y!" #$
Pr report =Y[ ]Pr true =Y[ ] = 0.2;Pr report =Y true =Y!" #$= 0.8
Pr report =Y[ ] = Pr true =Y[ ] ⋅Pr report =Y true =Y!" #$+Pr true = B[ ] ⋅Pr report =Y true = B!" #$= 0.2 ⋅0.8+ 0.8 ⋅0.2 = 0.32
Pr true =Y report =Y!" #$=Pr true =Y[ ] ⋅Pr report =Y true =Y!" #$
Pr report =Y[ ]=0.2 ⋅0.80.32
= 0.5
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Pr majority− blue blue"# $%=Pr majority− blue[ ] ⋅Pr blue majority− blue#$ %&
Pr blue[ ]
numerator = 12⋅23=13
Pr blue[ ] = Pr majority− blue[ ] ⋅Pr blue majority− blue#$ %&+
Pr majority− red[ ] ⋅Pr blue majority− red#$ %&=12⋅23+12⋅13=12
Pr majority− blue blue#$ %&=1312=23
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Pr majority− blue blue,blue, red"# $%=Pr majority− blue[ ] ⋅Pr blue,blue, red majority− blue#$ %&
Pr blue,blue, red[ ]
Pr blue,blue, red majority− blue"# $%=23⋅23⋅13=427
Pr blue,blue, red[ ] = Pr majority− blue[ ] ⋅Pr blue,blue, red majority− blue#$ %&+
Pr majority− red[ ] ⋅Pr blue,blue, red majority− red#$ %&=12⋅23⋅23⋅13+12⋅13⋅13⋅23=654
=19
Pr majority− blue blue,blue, red#$ %&=
427⋅12
19
=23
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~Thanks for Listening~�
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