They count the spending in different places in these two cases, but it's the same idea.

You spend X on something that gets stolen. X counts towards GDP.

The government steals Y from you and spends it themselves. Y counts towards GDP.

It's conceptually the same mistake. X and Y weren't acquired voluntarily by their ultimate consumer, so we can't say that the consumption was worth X or Y.

Undisciplined

But there is a zero sum effect with crime. One person benefits at the expense of the victim. It’s not a voluntary transaction 


Bell_curve

econ

Is GDP an Accurate Measure of Reality?

An interesting note on this is that they are actually consistent in how regular crime is treated. 

They don't subtract the monetary value of stolen goods, because they assume the thief gains just as much utility as the rightful owner would have, which is exactly the same assumption they're making with government spending.