AFAIK Canada does this by giving everyone a fixed amount of tax credit to offset the tax. That way poor people aren't taxed more but everyone are still incentivized to reduce their emissions

The best way is to take all the carbon tax collected, divide it by the number of people in the country, and distribute it evenly to everyone.

That way, if you use less than the average amount of carbon, you actually make money.

That's essentially what Canada has done, except on a subnational level (as it only applies in individual provinces that don't have their own emissions reduction mechanisms with at least equivalent effects)

Poor people will still pay in the form of higher prices that bake in the coat of the carbon tax.

1. that's how the tax would be collected for most peope. ie. you'll pay $x/gal more at the gas pump, rather than declaring how much tons of carbon you emitted on your tax return.

2. whether they pay or not is irrelevant. what actually matters is whether they end up paying more or less in net. for a scheme that taxes people according to their consumption but gives everyone the same amount of tax credits in return, poor people would be expected to come out ahead because they consume less on average.

Poor people are also the most exposed and suffer the most from carbon emissions.

Progressive taxes on carbon emissions will discourage economies of scale. This means for the same amount of co2 produced you have less production (good things for society) which is pretty bad. Ideally the co2 should be taxed at exactly the cost to reduce it to an easily stored or safe molecule.

carbon dividend.