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Stuart_Armstrong comments on How should negative externalities be handled? (Warning: politics) - Less Wrong Discussion
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Cap and trade means the government can fix the right figure for carbon emissions (at least somewhat plausible). Carbon taxes means the government can fix the right price to get the right figure for carbon emissions (very implausible).
There is no intrinsic right figure for carbon emissions. There is a cost that's incurred by carbon emissions. The more you emit, the higher the cost. The right figure is when the cost to emit more is equal to the benefit. You could find out the variables you need and solve the equations, or you can just work out the cost, charge people that much, and let the market deal with it.
Estimating the costs of carbon emissions involves estimating the temperature rises AND the effects of these on agriculture and other parts of the economy AND the likely costs of disasters AND the potential benefits AND the effects on the natural world AND how we should price these effects (which no-one would agree on). And also implement these calculations properly within a political system.
If we want to stabilise temperature rises at a particular point (which would be "good enough" according to most preference systems), you only need to estimate and implement the first term.
(ok, technically you need to be reasonably sure that temperature rises would be a net negative and keep an eye on carbon credits in case their prices get extraordinarily high, but these require muuuuuch less work than a proper pricing; the second thing will happen naturally within the political system anyway)
If there's an approximately linear cost for carbon emissions, then estimating a good enough value will be worse than estimating the cost. You have all the original error from guessing the cost of emissions, and now you're guessing the demand curve for emissions licenses as well.
If there is a point that will cause sudden problems, then capping and trading would work better, assuming you know where that point is. As you've pointed out, it's hard to tell. As such, it's better to treat it as a linearly increasing probability of hitting that point.
That doesn't seem to be a reasonable assumption at all - expected damage seems to escalate faster at the extreme end.
In any particular area, the cost will be approximately linear. If all you're looking at is the emissions in one state caused by one group of things (like power plants) over the course of one year, then it's approximately linear. Also, depending on how accurately you can guess at what the market equilibrium will be, you can narrow it down further so the linear approximation is still more accurate.