A CO2 offset usually means paying someone else to reduce greenhouse gases (beyond what they would have done anyway) and claiming it as your own reduction. The fallacy is that it usually involves double-counting, where both you and they (or their country) claim the same reduction.
For example you join with others (usually through a nonprofit) and:
In any of these examples, suppose you pay 10% of the cost, so you claim credit for reducing emissions by 40,000 pounds per year. You then continue to emit 44,000 pounds per year, but say your net emissions are only 4,000 pounds per year.
However the power, landfill, and farm customers also can look at the new lower emissions by their power, landfill and farm, and they too claim they are emitting 400,000 pounds per year less than before. The only way to avoid double-counting is to pretend they are still emitting the same old high levels. But all the CO2 reports and goals around the world look at actual emissions, not what the emissions would have been if you hadn't paid to reduce them.
Furthermore, your personal reduction only makes sense as part of a worldwide reduction to the sustainable level of 3,700 pounds CO2 equivalent per person per year. Most of those power, landfill and farm customers themselves emit far more than this goal, and have to reduce to that level for a sustainable earth, so you are claiming reductions which they needed to make anyway.
The farm example is a proposal by Michigan State University to reduce fertilizer slightly, from the upper to lower bounds of recommended ranges in the Midwest, expecting no decrease in yields. If there really is no decrease in yield the farmers would do it anyway to save fertilizer cost. If it decreases yields, other land has to be cleared or fertilized more to grow the missing food. The Midwestern farmers and their customers already emit far more CO2e than a sustainable level, so selling an offset means they pay themselves to continue emitting unsustainably. Furthermore the authors acknowledge (p.202) that it would take expensive accurate testing (emitting CO2) to measure nitrogen levels in soil or plants, to be sure the farmers did not add more fertilizer anyway, to increase yields.
The poor country example (D) is different. These savings really would help us get closer to a global goal. But you are unlikely to find people willing or able to reduce their emissions so low. Just making and maintaining the solar cookers uses up some of the CO2 savings. What can they buy with the money you pay them without using up even more of the CO2 savings? As they develop (you want them to develop, right?) it will be hard enough for them to keep emissions under 3,700 pounds per person per year, let alone 1,700. Then consider the ethics and instability of such drastic inequality in CO2 output. It involves 20 people living at a destitute level of CO2 for every one person staying at the current US level.
China is often able to sell offsets, since it has companies ready and willing to reduce emissions from old manufacturing methods. However China, like richer countries, already emits more than the sustainable level of CO2 per person, so it needs its own reductions, and counting them elsewhere is double-counting.
The tropical forest example (E) does capture CO2 in years when you expand the forest and reduce demand for land. There are several issues to remember.
All the discussion above about paying others to reduce CO2 emissions is a version of the "cap and trade" method of limiting emissions. That is a term used when governments cap CO2 emissions, and allow emitters who can go below their cap to sell the savings to emitters who can't cut so easily and stay above the cap. Overall the caps would be met. On a long term world scale, people would have a cap, such as 3,700 pounds CO2 emissions per year, and people above the cap would have to buy emission rights from people below the cap. Buying from people above the cap, who have no unused emission rights to sell, doesn't get you anywhere. In fact, as mentioned on the Goals page, the 3,700 pound limit per person will have to drop even lower in the future as world population rises, to keep world emissions at or below 32 trillion pounds CO2 per year, which in turn is necessary to hold the temperature down.
A landfill like example (B) above was the subject of a controversy between Business Week and Terrapass over CO2 offsets claimed by the 2007 Academy Awards ceremony. Supporting the landfill purportedly let the stars offset the CO2 emitted by their celebrity lifestyles. However that controversy only addressed whether current regulations would have forced the methane to be captured anyway. Regardless of old regulations, the earth does require both methane capture and CO2 cutbacks in our lifestyles. It is not a choice. It is both, and much more.
UK consumer group's overview of offsets with helpful ratings and links
Friends of the Earth statement against offsets
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