The result Eliezer is referring to is P(Conclusion)=P(Conclusion|Positive Test)P(Positive Test)+P(Conclusion|Negative Test)P(Negative Test)=E(P(Conclusion|Test Result))
If you know what you’ll believe after the test (i.e. your expected belief after the test), then that is your current belief.
The result Eliezer is referring to is P(Conclusion)=P(Conclusion|Positive Test)P(Positive Test)+P(Conclusion|Negative Test)P(Negative Test)=E(P(Conclusion|Test Result))
If you know what you’ll believe after the test (i.e. your expected belief after the test), then that is your current belief.