I spent some time in Alaska and was informed that as it is a very "Rich" and indeed sparsely populated State it pays a bounty to new arrivals and financial bonuses to families with young children in teh hope that they will settle there and improve/increase the populace. American Service personel can choose to take advantage of this by registering as Alaskans and therefore paying Alaskan State Taxes (or not) rather than higher taxes elsewhere. Or words to that effect
