Along these lines, in Probability Theory: The Logic of Science Jaynes suggests thinking in decibels (which are just log probabilities). Here are some excerpts o

Along these lines, in Probability Theory: The Logic of Science Jaynes suggests thinking in decibels (which are just log probabilities). Here are some excerpts of this: "... it is very cogent to give evidence in decibels. When probabilities approach one or zero, our intuition doesn't work very well. Does the difference between the probability of 0.999 and 0.9999 mean a great deal to you? It certainly doesn't to the writer. But after living with this for only a short while, the difference between evidence of plus 30 db and plus 40 db does have a clear meaning to us. It's now in a scale which our minds comprehend naturally... In the original acoustical applications, it was introduced so that a 1 db change perceptible to our ears. With a little familiarity and a little introspection, we think that the reader will agree that a 1 db change in evidence is about the smallest increment of plausibility that is perceptible to our intuition." "... What probability would you assign to the hypothesis that Mr Smith has perfect extrasensory perception? ... To say zero is too dogmatic. According to our theory, this means that we are never going to allow [our] mind to be changed by any amount of evidence, and we don't really want that. But where is our strength of belief in a proposition like this? "... We have an intuitive feeling for plausibility only when it's not too far from 0db. We get fairly definite feelings that something is more than likely to be so or less likely to be so. So the trick is to imagine an experiment. How much evidence would it take to bring your state of belief up to the place where you felt very perplexed and unsure about it? Not to the place where you believed it -- that would overshoot the mark, and again we'd lose our resolving power. How much evidence would it take to bring you just up to the point where you were beginning to consider the possibility seriously? "So, we consider Mr Smith, who says he has ESP, and we will write down some numbers from one to ten on a piece of paper and ask him to guess which numbers we've written down. We'll take the usual precautions to make sure against other ways of finding out. If he guesses the first number correctly, of course we will all say 'you're a very lucky person, but I don't believe you have ESP'. And if he guesses two numbers correctly, we'll still say 'you're a very lucky person, but I still don't believe you have ESP'. By the time he's guessed four numbers correctly -- well, I still wouldn't believe it. So my state of belief is certainly lower than -40 db. "How many numbers would he have to guess correctly before you would really seriously consider the hypothesis that he has extrasensory perception? In my own case, I think somewhere around ten. My personal state of belief is, therefore, about -100 db. You could talk me into a +-10db change, and perhaps as much as +-30 db, but not much more than that."