Normalizing probabilities between zero and one breaks the rule of making impossible states unrepresentable. Negative or superunerary probabilites are impossible.
This normalization is the result of the frequentist interpretation. Bayesians should use numbers between negative and positive infinity. Zero means no prior knowledge. Negative infinity means total disinformation.
@BartoszMilewski yes but didactically and in some practical purposes log odds (etc) are harder to intuit. I do hold in my mind the vast chasm between eg actually impossible and very unlikely probabilities such as building collapse
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@drmakimber @BartoszMilewski Spiced with a "logarithm is just the number of zeroes" log-odds make quick takes rather easy.
@dpwiz @BartoszMilewski yeah, I felt there was a log odds of about -0.1 that somebody would say that ;)