My understanding is there are two somewhat separate issues, one being the improper use of uniform priors and the other being a failure to give estimates that take all evidence (GCMs, recent temperatures, paleoclimate, etc) into account, with probability distributions from mostly-independent evidence sometimes having wrongly been taken as confirmation of the same uncertainty range instead of being combined into a narrower one. Do the estimates that you’re eyeballing update on every line of evidence? Annan and Hargreaves under some assumptions find numbers like a 95% upper probability bound of 3.6 degrees, which would imply virtually no risk of ECS>5. (Structural uncertainty may, of course, weaken such conclusions.)
As you explain in your writeup, the 7 degrees here represents an eventual temperature increase that will only be attained in centuries, and the increase over the 21st century would be significantly less (though still major), which makes the scenario less extreme than it sounds.
Your writeup uses Wagner and Weitzman’s interpretation of the IPCC’s uncertainty range for sensitivity. If I remember correctly, AR5 does discuss the issues of priors and combined evidence, but bases the 1.5-4.5 degree range on subjective judgment, so it’s hard for me to be sure that bad Bayesianism is what’s causing this interval to be as wide as it is, but Annan seems to think people aren’t taking his points into account enough.
I’ve found it hard to find good information on the questions most directly relevant to estimating the pdf of the size of the effects of climate change (with your writeup as one of the main exceptions) and may be getting things wrong.
If the claims made here from p.13 on are true, it seems like the model can’t be reliable. This also disagrees. In general, it seems intuitively like it would be extremely hard to do this kind of statistics and extrapolate to the future with any serious confidence or rely on it for an estimate without a lot more thought. (I haven’t tried to look for critiques of the critiques and don’t claim to have a rigorous argument.)
I was thinking if climate has effects on growth rate, companies may not be capturing the full costs/benefits from that. My intuition that it could be extremely effective was something like “if an extremely blunt tool like global average temperature can have big effects on growth through improving local temperature in more places than it worsens local temperature, you can probably get much bigger effects by optimizing local temperature in a fine grained way through changing the locations of things.” Maybe that’s wrong, I don’t know.