Note that the closer the probability of something to 0 or to 1, the harder it is evaluate accurately. A simple example: starting with a fair coin and observing a sequence of N heads in a row, what is an unbiased estimate of the coin’s bias? Log odds of N heads are -N when starting with a point estimate of a fair coin, which matches the Bayesian updates, so it is reasonable to conclude that the probability of heads is 1-2^(-N), but at the level small enough there are so many other factors that can interfere, the calculation ceases being accurate. Maybe the coin has heads on both sides? Maybe your brain makes you see heads when the coin flip outcome is actually tails? Maybe you are only hallucinating the coin flips? So, if you finally get a tail, reducing the estimated probability of heads, you are able to reject multiple other unlikely possibilities, as well, and it makes sense that one would need less evidence when moving from -N to -N+1 for large N than for small N.
Note that the closer the probability of something to 0 or to 1, the harder it is evaluate accurately. A simple example: starting with a fair coin and observing a sequence of N heads in a row, what is an unbiased estimate of the coin’s bias? Log odds of N heads are -N when starting with a point estimate of a fair coin, which matches the Bayesian updates, so it is reasonable to conclude that the probability of heads is 1-2^(-N), but at the level small enough there are so many other factors that can interfere, the calculation ceases being accurate. Maybe the coin has heads on both sides? Maybe your brain makes you see heads when the coin flip outcome is actually tails? Maybe you are only hallucinating the coin flips? So, if you finally get a tail, reducing the estimated probability of heads, you are able to reject multiple other unlikely possibilities, as well, and it makes sense that one would need less evidence when moving from -N to -N+1 for large N than for small N.
Yes—and this is equivalent to saying that evidence about probability provides Bayesian metric evidence—you need to transform it.
Could you explain your point further?