![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png) simont |
Wed 2005-11-16 15:43 |
| This is beginning to come close to the sort of thing I was trying for in my failed attempt. It was clear that for probabilities near zero "twice as likely" meant roughly doubling the probability, and clear that for probabilities near one, "twice as unlikely" meant roughly getting twice as far away from one; and then it occurred to me that a layperson might naively expect "twice as likely" and "twice as unlikely" to be inverses under composition (so that "twice as likely" as 0.99 would be around 0.995). So I searched for a function which had gradient 2 near zero and gradient 1/2 near 1, and then I generalised to "k times as likely" and searched for a family of such functions, so that f_k had gradient k at zero and gradient 1/k at 1, and such that f_k composed with f_m was f_(km). |
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