CS Liu-final presentaion-information cascades

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  • ~How to Decide more Ra0onally~

    Cheng-Shu Liu

  • We are Made of What We Have Decided

    2

  • 3

  • A Decision to Make

    Make the Decision Sequen0ally

    Own a Private Informa0on

    Observe What Others Do

    4

  • 5

  • 6

  • 1 2 3 4 5 6

    MB/MR

    Ball

    7

  • 8

  • 9

  • 10

  • 11

  • 12

  • AB

    A

    B

    Pr A B!" #$=Pr AB[ ]Pr B[ ]

    Pr B A!" #$=Pr BA[ ]Pr A[ ]

    =Pr AB[ ]Pr A[ ]

    Pr A B!" #$=Pr A[ ] Pr B A!" #$

    Pr B[ ]

    Pr A B!" #$Pr B[ ] = Pr AB[ ] = Pr B A!" #$Pr A[ ]

    Pr A[ ]Pr B[ ]

    13

  • 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!" #$= 0.8Pr report =Y[ ] = Pr true =Y[ ] Pr report =Y true =Y!" #$+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

    14

  • 15

  • 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

    16

  • 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

    17

  • 18

  • 19

  • ~Thanks for Listening~

  • 22