Annals of heroic inference

This is Joseph.

Via Andrew Gelman, we get this gem:

One consequence of this is that the number of respondents who report that they are not citizens yet vote or are registered to vote is quite small in absolute terms: in 2010, for example, only 13 respondents — not 13 percent, but 13 out of 55,400 respondents — reported that they were not citizens, yet had voted. Given the ever-present possibility of respondent or coder error, it takes a bit of hubris to draw strong conclusions about the behavior of non-citizens from such small numbers.

Yes, it is very hard to determine characteristics of very rare groups.  For one thing, it's unlikely that you know much about the underlying source population.  So I think the authors are right that it is going to hard to say much about this group, given this instrument.