> Well, I agree mostly with you, except that I'm not a probabilist.
Good enough for me. :-) (Aumann's agreement theorem notwithstanding, I have to recognise the capacity for actual humans to agree is limited.)
> I'm definitely going to read [Jayne's book]!
I have yet to read it all, but the foundations are laid out early. The preface mostly explains where the author is coming from, chapter 1 and 2 do most of the justifications. The rest focuses more on applications of probability theory. My general impression was like:
Matches my intuitions,
solid theoretical foundations,
works in practice...
...case closed I guess.
> On the evaluative side we have thought experiments like Spectrum Cases (Temkin, Rachels): Suppose A gives you extremely high pleasure for a month, B gives you a little bit less pleasure than A (barely noticeable) for 3 months, C gives you a little bit less pleasure than B (barely noticeable) for 9 months, and so on.
Hmm, that's a hard one. Depending on the value I attach to pleasure, there should be 3 possibilities: A is best, Z (or whatever is the last iteration) is best, or there's a sweet spot in between. I get the circular preference, and would likely fall prey to it if the circle is hidden to me. But stuff like that is like a big warning sign that most probably requires more thought than a quick intuitive judgement.
> Couldn't you just say that any heuristics are permissible in certain circumstances as shortcuts that - under these circumstances - are conducive to adequate probability approximations?
I could. I didn't because once we start making shortcuts, evaluating the impact on the shortcut on the final assessment is very difficult. Probabilities are non-linear, it's very easy for a seemingly innocuous approximation to translate to snowball into a huge error. But if careful, it often can (and does) work.
It's a bit like floating point approximations. The ideal math on real numbers is correct, floating points only introduce small errors, but some operations (like a division close to zero) can magnify those errors from "approximate" to "utterly wrong". Special care is typically taken to ensure that does not happen.
> Anyway, it was nice chatting with you!
For me as well. I'll keep your references in mind, and thank you for your patience.
Good enough for me. :-) (Aumann's agreement theorem notwithstanding, I have to recognise the capacity for actual humans to agree is limited.)
> I'm definitely going to read [Jayne's book]!
I have yet to read it all, but the foundations are laid out early. The preface mostly explains where the author is coming from, chapter 1 and 2 do most of the justifications. The rest focuses more on applications of probability theory. My general impression was like:
> On the evaluative side we have thought experiments like Spectrum Cases (Temkin, Rachels): Suppose A gives you extremely high pleasure for a month, B gives you a little bit less pleasure than A (barely noticeable) for 3 months, C gives you a little bit less pleasure than B (barely noticeable) for 9 months, and so on.Hmm, that's a hard one. Depending on the value I attach to pleasure, there should be 3 possibilities: A is best, Z (or whatever is the last iteration) is best, or there's a sweet spot in between. I get the circular preference, and would likely fall prey to it if the circle is hidden to me. But stuff like that is like a big warning sign that most probably requires more thought than a quick intuitive judgement.
> Couldn't you just say that any heuristics are permissible in certain circumstances as shortcuts that - under these circumstances - are conducive to adequate probability approximations?
I could. I didn't because once we start making shortcuts, evaluating the impact on the shortcut on the final assessment is very difficult. Probabilities are non-linear, it's very easy for a seemingly innocuous approximation to translate to snowball into a huge error. But if careful, it often can (and does) work.
It's a bit like floating point approximations. The ideal math on real numbers is correct, floating points only introduce small errors, but some operations (like a division close to zero) can magnify those errors from "approximate" to "utterly wrong". Special care is typically taken to ensure that does not happen.
> Anyway, it was nice chatting with you!
For me as well. I'll keep your references in mind, and thank you for your patience.