I’d start with one of the simplest models possible: I’d put December and March into a simple hope function with a flat distribution over time periods http://www.gwern.net/docs/1994-falk The relevant short-run equation being:
To put it into the box terms: December is 1 box, January/February/March are 3 boxes, and there’s some probability l0 that his resignation is in any of these 4 boxes so n=4 (and l0-1 that there won’t be a resignation in March or before). We want to know our belief that the resignation will be in the first box, box 1, or i=1. I think most promises to resign are kept or accelerated in first world countries, so I’d give l0 around 90% that he will resign before or during March. With all that, my expectation that the resignation will be in the first of 4 boxes given a 90% belief that the resignation is in the boxes at all is 29%
(It’d be more different from 1⁄4 if we had opened more boxes, or if there were more boxes to begin with.)
Incidentally, was this inspired by Monti of Italy?
Your procedure gives a de novo probability, but I don’t quite see how to combine it with any preexisting information you might have.
I mentioned it was a uniform distribution, where each box is equal. If you had pre-existing information that December and February will be absolutely critical while January is less important, then you can move on to more complex versions. For example, here’s a calculation with a normal distribution instead: http://lesswrong.com/lw/5hq/an_inflection_point_for_probability_estimates_of/4291
I’d start with one of the simplest models possible: I’d put December and March into a simple hope function with a flat distribution over time periods http://www.gwern.net/docs/1994-falk The relevant short-run equation being:
To put it into the box terms: December is 1 box, January/February/March are 3 boxes, and there’s some probability l0 that his resignation is in any of these 4 boxes so n=4 (and l0-1 that there won’t be a resignation in March or before). We want to know our belief that the resignation will be in the first box, box 1, or i=1. I think most promises to resign are kept or accelerated in first world countries, so I’d give l0 around 90% that he will resign before or during March. With all that, my expectation that the resignation will be in the first of 4 boxes given a 90% belief that the resignation is in the boxes at all is 29%
(It’d be more different from 1⁄4 if we had opened more boxes, or if there were more boxes to begin with.)
Incidentally, was this inspired by Monti of Italy?
Monti, yes. :)
Your procedure gives a de novo probability, but I don’t quite see how to combine it with any preexisting information you might have.
I mentioned it was a uniform distribution, where each box is equal. If you had pre-existing information that December and February will be absolutely critical while January is less important, then you can move on to more complex versions. For example, here’s a calculation with a normal distribution instead: http://lesswrong.com/lw/5hq/an_inflection_point_for_probability_estimates_of/4291