You’re reading it correctly, but I disagree with your conclusion. If Mayne says p=.7, and Szymborski says p=.8, and their estimates are independent—remember, my classifiers are not human experts, they are not correlated—then the final result must be greater than .8. You already thought p=.8 after hearing Szymborski. Mayne’s additional opinion says Joe is more-likely than average to hit more than 10 home runs, and is based on completely different information than Szymborski’s, so it should make Joe’s chances increase, not decrease.
remember, my classifiers are not human experts, they are not correlated
Is that necessarily true? It seems that it should depend on whether they have underlying similarities (eg a similar systematic bias) in their algorithms.
You’re reading it correctly, but I disagree with your conclusion. If Mayne says p=.7, and Szymborski says p=.8, and their estimates are independent—remember, my classifiers are not human experts, they are not correlated—then the final result must be greater than .8. You already thought p=.8 after hearing Szymborski. Mayne’s additional opinion says Joe is more-likely than average to hit more than 10 home runs, and is based on completely different information than Szymborski’s, so it should make Joe’s chances increase, not decrease.
Is that necessarily true? It seems that it should depend on whether they have underlying similarities (eg a similar systematic bias) in their algorithms.