Do I use half as much "double concentrated" tomato paste?

I would not change the amount.

Tomato products are graded as following:

• pureed tomatoes (passata di pomodoro), up to 10% dry mass
• tomato paste (concentrato di pomodoro) single, 14 to 22% dry mass
• tomato paste double, 28 to 30% dry mass
• tomato paste triple, 36 to 40% dry mass.

These are German numbers. Other countries use somewhat different prescriptions, but are in roughly the same range. There are higher concentrations of tomato paste too, but they are not commonly sold in supermarkets.

My first reason to not use it is that singly concentrated tomato paste is rarely sold. So I would assume that whoever wrote your recipe intended to use either doubly or triply concentrated paste. It is unlikely that, by changing the amount, you will get closer to what the recipe author used. You may even be already on the low side of tomatoes (if the author uses triple), so you'd make it even less authentic if you try to compensate.

Second, as you see, this is not some simple mathematical doubling of everything. Not even the dry mass jumps exactly double as much, and a tomato is not simply dry mass. If you really wanted to be closer to the recipe (if it has been designed for singly concentrated), you would have to reduce by less than half. And even then, you cannot be completely the same in taste, since the heat/pressure concentration process changes more than just the amount of water.

Third, tomato paste is an ingredient that is used when you want your dish to have lots of tomato flavor and little water. If this was not the case, the author would probably be suggesting the use of tomato puree or canned tomato pieces. Even if the recipe was originally developed for singly concentrated paste, it is rarely wrong to add more tomato flavor by using doubly concentrated. So just throw the whole amount in and see what happens - chances are, you'll like it.

Tomato paste is used as a thickener for sauces. Use the same amount the recipe calls for. if the recipe is too thick, adjust it with a bit of water until you get the desired consistancy.