I like the idea of your proposal—communicating how solidified one’s credences are should be helpful for quickly communicating on new topics (although I could imagine that one has to be quite good at dealing with probabilities for this to actually provide extra information).
Regarding your particular proposal “CR [ <probability of change>, <min size of change>, <time spent on question> }” is unintuitive to me:
In “80% CI [5,20]” the probability is denoted with %, while its “unit”-less in your notation
In “80% CI [5,20]”, the braces [] indicate an interval, while it is more of a tuple in your notation
A reformulation might be
80% CI [5,20] CR [0.1, 0.5, 1 day] --> 80% CI [5,20] ×10 % CR1d [0.5}
Things I dislike about this proposal:
The “CR1d” complicates notation. Possibly one could agree on a default time interval such as 1 day and only write the time range explicitly if it differs? Alternatively, “1 day CR” or “CR_1d” might be usable
the “[0.5]” still feels unintuitive as notation and is still not an interval. Maybe there is a related theoretically-motivated quantity which could be used? Possibly something like the ‘expected information gain’ can be translated into its influence on the [5,20] intervals (with some reasonable assumptions on the distribution)?
80% CI [5,20] ⋇0.5 @ 10 % CR1d might be an alternative, with the “\divideontimes” symbol being the ± of multiplication and hinting at the possible modification of the interval [5, 20]. For latex-free notation, “[5, 20] x0.5″ might be a suitable simplified version.
Overall, I don’t yet have a good intuition for how to think about expected information gain (especially if it is the expectation of someone else). Also, it would be nice if there was a theoretical argument that one of the given numbers is redundant—getting an impression of what all the 6 numbers mean exactly would take me sufficiently long that it is probably better to just have the whole sentence
My 80% confidence interval is 5-20. I think there’s 10% chance I’d change my upper or lower bound by more than 50% of the current value if I spent another ~day investigating this.
But this would of course be less of a problem with experience :)
I like the idea of your proposal—communicating how solidified one’s credences are should be helpful for quickly communicating on new topics (although I could imagine that one has to be quite good at dealing with probabilities for this to actually provide extra information).
Regarding your particular proposal “CR [ <probability of change>, <min size of change>, <time spent on question> }” is unintuitive to me:
In “80% CI [5,20]” the probability is denoted with %, while its “unit”-less in your notation
In “80% CI [5,20]”, the braces [] indicate an interval, while it is more of a tuple in your notation
A reformulation might be
80% CI [5,20] CR [0.1, 0.5, 1 day] --> 80% CI [5,20] ×10 % CR1d [0.5}
Things I dislike about this proposal:
The “CR1d” complicates notation. Possibly one could agree on a default time interval such as 1 day and only write the time range explicitly if it differs? Alternatively, “1 day CR” or “CR_1d” might be usable
the “[0.5]” still feels unintuitive as notation and is still not an interval. Maybe there is a related theoretically-motivated quantity which could be used? Possibly something like the ‘expected information gain’ can be translated into its influence on the [5,20] intervals (with some reasonable assumptions on the distribution)?
80% CI [5,20] ⋇0.5 @ 10 % CR1d might be an alternative, with the “\divideontimes” symbol being the ± of multiplication and hinting at the possible modification of the interval [5, 20]. For latex-free notation, “[5, 20] x0.5″ might be a suitable simplified version.
Overall, I don’t yet have a good intuition for how to think about expected information gain (especially if it is the expectation of someone else).
Also, it would be nice if there was a theoretical argument that one of the given numbers is redundant—getting an impression of what all the 6 numbers mean exactly would take me sufficiently long that it is probably better to just have the whole sentence
But this would of course be less of a problem with experience :)