What should a good carbon pricing scheme look like? It makes sense to be clear about what we want before we look at whether a tax or a cap and trade system should be used.
A good policy has to meet technical and political criteria. I would suggest starting with the following criteria.
1) Effective: This is obviously the first requirement.
2) Easy and quick to implement: delays matter more and more,
3) Quick to take effect, since delays matter
4) Reasonably complete coverage of all fossil fuels:
5) Reasonably complete coverage quickly:
6) Cheap to run: We want to minimize transaction costs. They could be very large.
7) Politically and technically easy to raise the price
8) Minimizes leakage
9) Robust to changing political regimes
10) Easy to understand
11) Provides stable prices: this makes it easier to plan investments
12) Provides precise contol of quantities
When I go through this list it is clear that a carbon tax is superior on almost all points. Cap and trade might be in the game on items 8 and 12. On cost, item 6, cap and trade gets toally skunked, and it loses badly on items 1-5.
We could argue about whether to add other criteria, and we could argue about the order of the list.
It is important to realize that these requirements are all about a pricing mechanism. Any pricing system will also raise revenue unless politicians are extremely stupid. I suspect much of the disagreement is around using the revenue from charging a price.
When talk about what to do with the revenue, we are not talking about the pricing system. Once there is money to spread around, a lot of other goals are put on the table. The other goals include encouraging research or technology adoption, improving income redistribution, protecting favoured industries and reducing taxes. Many of these make sense, but there is a danger as we try to get money for our favorite projects we will end up making serious compromises on the price system.