pinyaka comments on Bayesian Adjustment Does Not Defeat Existential Risk Charity

pinyaka 18 Mar 2013 19:35 UTC
0 points
I got a different updated value ratio in part 2. If my calculations are wrong, would someone correct me?

V = Value; A = Analysis predicted value

Prior Probabilities:
```
P(V=0)=0.4999
P(V=1)=0.5
P(V=100)=0.0001
```
Analysis Result Probabilities:
```
P(A=0)=(0.5*0.4999)+((1/3)*0.5*1)=0.4166
(half the ones that are zero plus a third of the half where the test fails)
P(A=1)=0.4167
P(A=100)=0.1667
```
Accurate analysis results:
```
P(A=0|V=0)=P(A=1|V=1)=P(A=100|V=100)=(1/2)+(1/3)=2/3
(the half when the analysis works and reports accurately plus
the third when it fails but gives the correct value anyway) 
```
Inaccurate analysis results:
```
P(A=0|V=1)=P(A=0|V=100)=P(A=1|V=0)=P(A=1|V=100)=P(A=100|V=0)=P(A=100|V=1)=(1/2)*(1/3) = 1/6
```
Posterior Probabilities:
```
P(V=0|A=0)=P(A=0|V=0)*P(V=0)/P(A=0) = (2/3)*0.4999/0.4166 = 0.8000
P(V=1|A=1)=0.7999
P(V=100|A=100)=0.0004
P(V=0|A=1)=0.2000
P(V=0|A=100)=0.4998
P(V=1|A=0)=0.2000
P(V=1|A=100)=0.4999
P(V=100|A=0)=4E-5
P(V=100|A=1)=4E-5
```
So,

=\sum_{N=0,1,100}P(V=N%7CA=x)*N)
```
EV(A=0)=0.800*0+0.2000*1+4E-5*100=0.2040
EV(A=1)=0.8039
EV(A=100)=0.5399
```
So the ratio goes from 50:1 to 80:54 unless I’m off somewhere. I’m just starting to learn this stuff so any feedback will be welcome.

EDIT: formatting

DOUBLE EDIT: I realize this isn’t the point of the article and has no bearing on the conclusion. This was an exercise in how to update an EV for me.
- pengvado 19 Mar 2013 1:20 UTC
  0 points
  Parent
  “50:4” in the post refers to “P(V=1|A=100)*1 : P(V=100|A=100)*100″, not “EV(A=1) : EV(A=100)”. EV(A=1) is irrelevant, since we know that A is in fact 100.
  - pinyaka 19 Mar 2013 1:52 UTC
    0 points
    Parent
    I think this confused me:
    
    So the ratio of the expected value contributions changes from 50:1 to 50:4.
    
    I see that. Thanks.