The root of the different feel for your estimates is that you’re comparing two different kinds of probability. You can only ever test The Ancient Life on Mars proposition once, whereas you can test the die a sufficient number of times to determine that the probability of rolling a 6 on any given throw is 1⁄6.
Let’s say that after you make your predictions your interrogator puts a gun to your head and asks, “We can either roll this die or determine whether there was Ancient Life on Mars, both will take the same amount of time. If you choose to roll the die and it’s a 6 we shoot you. If you choose to bet on Ancient Life on Mars and there was ancient life, we shoot you. Which do you choose?” In this scenario if you feel inclined to choose one option over the other (for want of not getting shot) then you don’t in truth agree with your 1⁄6 probability estimate for at least one of the options. You should feel the same about two different 1⁄6 probabilistic estimates when they’ve each been reduced to a one-shot, unreproducible test.
The root of the different feel for your estimates is that you’re comparing two different kinds of probability. You can only ever test The Ancient Life on Mars proposition once, whereas you can test the die a sufficient number of times to determine that the probability of rolling a 6 on any given throw is 1⁄6.
Let’s say that after you make your predictions your interrogator puts a gun to your head and asks, “We can either roll this die or determine whether there was Ancient Life on Mars, both will take the same amount of time. If you choose to roll the die and it’s a 6 we shoot you. If you choose to bet on Ancient Life on Mars and there was ancient life, we shoot you. Which do you choose?” In this scenario if you feel inclined to choose one option over the other (for want of not getting shot) then you don’t in truth agree with your 1⁄6 probability estimate for at least one of the options. You should feel the same about two different 1⁄6 probabilistic estimates when they’ve each been reduced to a one-shot, unreproducible test.