Esther Inglis-Arkell gives a good definition of scope neglect (or scope insensitivity) but relies on a study that conflates the issue so badly as to be nearly meaningless. That's not her fault... almost every link I've found about scope neglect mentions the same study. So what does the study show?
How much would you pay to save 2,000 sad, oily birds from death? How much would you pay to save 20,000 birds of equal sadness and oleaginousness? How about 200,000? According to one study, your preferred amounts are $80, $78, and $88 respectively. (Perhaps more if you saw pictures of the birds while a Sarah McLachlan song was playing.)
You'll notice something strange there. First of all, people will only pay about $8 more to save 198,000 more birds. More importantly, judging by the $80 and the $78, it looks like people are actually willing to pay money to kill 18,000 birds. We wouldn't pay as much to save many birds as we would to save a few.
First, the difference between $80 and $78 is certainly insignificant, and the difference between $80 and $88 is pretty small as well. It's completely fallacious to infer from these numbers that people (on average) want to spend $2 to kill 18,000 birds.
Second, I think it's hard to infer anything about scope neglect from the thought experiment this study is based on. The amount that people are willing to spend is probably based more on their wealth than on the number of birds. Even though the number of birds changes, the wealth reference point of each respondent stays the same. An average person is willing to donate about $80 to clean up oily birds, and if you've got more birds then you need to find more donors.
Third, to illustrate the absurdity of the thought experiment, how much would a person give to save two billion birds? Or two quadrillion? Obviously at some point the limiting factor will be the resources available to the giver. My contention is that the donation level is resource-limited way below the 2,000-bird level. I personally wouldn't use this bird thought experiment at all, but if the researchers wanted to stick with birds they should have tried much smaller numbers. I doubt the answers for two, 20, or 200 birds would all have been $80.