1. ~How
to
Decide
more
Ra0onally~
Cheng-­‐Shu
Liu

2. We
are
Made
of
What
We
Have
Decided
2

3. 3

4. A
Decision
to
Make
Make
the
Decision
Sequen0ally
Own
a
Private
Informa0on
Observe
What
Others
Do
4

5. 5

6. 6

7. 1
2
3
4
5
6
MB/
MR
Ball
7

8. 8

9. 9

10. 10

11. 11

12. 12

13. 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[ ] 13

14. 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⋅0.8
0.32
= 0.5
14

15. 15

16. Pr majority − blue blue# $%=
Pr majority − blue[ ]⋅Pr blue majority − blue#$ %
Pr blue[ ]
numerator =
1
2
⋅
2
3
=
1
3
Pr blue[ ]= Pr majority − blue[ ]⋅Pr blue majority − blue#$ %+
Pr majority −red[ ]⋅Pr blue majority −red#$ %=
1
2
⋅
2
3
+
1
2
⋅
1
3
=
1
2
Pr majority − blue blue#$ %=
1
3
1
2
=
2
3
16

17. 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# $%=
2
3
⋅
2
3
⋅
1
3
=
4
27
Pr blue,blue,red[ ]= Pr majority−blue[ ]⋅Pr blue,blue,red majority−blue#$ %+
Pr majority−red[ ]⋅Pr blue,blue,red majority−red#$ %=
1
2
⋅
2
3
⋅
2
3
⋅
1
3
+
1
2
⋅
1
3
⋅
1
3
⋅
2
3
=
6
54
=
1
9
Pr majority−blue blue,blue,red#$ %=
4
27
⋅
1
2
1
9
=
2
3
17

18. 18

19. 19

20. ~Thanks
for
Listening~

22. 22