Better to just rebate a fixed amount to everyone so that you preserve the incentives for cutting back any marginal unit of fossil fuel consumption, while mitigating the overall income effect.

How do you know what to rebate people? The carbon tax will hit more than their electric bill. Also, some people have greener electricity than others. Here's how electricity is generated by state:

https://www.washingtonpost.com/graphics/national/power-plant...

If it affects the poor, it would make the most sense to rebate purely on income level, equally based on income level.

If the idea is to just give it back to the people that paid into it, that completelt defeats the entire purpose.

So, someone who lives in a state with green electricity, and buys products from "green companies", will get the same as someone from a coal state, like West Virginia?

The question is why are you giving rebates to people who are mostly using green energy?

Because they aren't dumping as much carbon into the atmosphere. Thats the entire point of it all! Those who are dumping carbon into the atmosphere are free loading on the rest of society, expecting others to pay for their externalities.

And it's not "giving rebate" it's returning tax revenues to those that can least afford them.

But there are many other sources of carbon than poorly planned electrical systems. Driving, flying, and industry.

The poor person in West Virginia getting his electricity from dirty coal and driving a 10 year old F150 is getting the same rebate. He's buying stuff from Walmart that's shipped from China.

Are you rewarding people for using less carbon or is the rebate to help offset the cost past through from companies passing on the extra tax onto consumers? Two different claims are being made.

They may be getting the same rebate, but they aren't paying the same tax. If the rebate is the same for all, then those who use less will make a profit, considering the $rebate - $tax amounts, while those using more will pay more tax than they get in rebates. (This is assuming a revenue neutral arrangement).

I havn't looked into it in detail, but I was under the impression that it wasn't so much to affect consumer choices directly, as commercial behavior.

That is, putting a price on carbon will result in businesses either putting up prices, or choosing lower emission production options. All other things being equal, this should result in having lower emission companies having a pricing edge, and then consumers picking those products.