I think I can make sense of this. If you believe there’s some underlying exponential distribution on when some event will occur, but you don’t know the annual probability, then an exponential distribution is not a good model for your beliefs about when the event will occur, because a weighted average of exponential distributions with different annual probabilities is not an exponential distribution. This is because if time has gone by without the event occurring, this is evidence in favor of hypotheses with a low annual probability, so an average of exponential distributions should have its annual probability decrease over time.
An exponential distribution seems like the sort of probability distribution that I expect to be appropriate when the mechanism determining when the event occurs is well-understood, so different experts shouldn’t disagree on what the annual probability is. If the true annual rate is unknown, then good experts should account for their uncertainty and not report an exponential distribution. Or, in the case where the experts are explicit models and you believe one of the models is roughly correct, then the experts would report exponential distributions, but the average of these distributions is not an exponential distribution, for good reason.
I think I can make sense of this. If you believe there’s some underlying exponential distribution on when some event will occur, but you don’t know the annual probability, then an exponential distribution is not a good model for your beliefs about when the event will occur, because a weighted average of exponential distributions with different annual probabilities is not an exponential distribution. This is because if time has gone by without the event occurring, this is evidence in favor of hypotheses with a low annual probability, so an average of exponential distributions should have its annual probability decrease over time.
An exponential distribution seems like the sort of probability distribution that I expect to be appropriate when the mechanism determining when the event occurs is well-understood, so different experts shouldn’t disagree on what the annual probability is. If the true annual rate is unknown, then good experts should account for their uncertainty and not report an exponential distribution. Or, in the case where the experts are explicit models and you believe one of the models is roughly correct, then the experts would report exponential distributions, but the average of these distributions is not an exponential distribution, for good reason.