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army1987 comments on 2012 Survey Results - Less Wrong
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The mean was 1768, the median 1780, and the mode 1800. Only 169 of 1006 people who answered the question got an answer within 20 years of 1701. Moreover, the three people that admitted to looking it up (and therefore didn't give a calibration) all gave incorrect answers: 1750, 1759, and 1850. So it seems like your first explanation can't be right.
After trying a bunch of modifications to the data, it seems like the best explanation is that the poor calibration happened because people didn't think about the error margin carefully enough. If we change the error margin to 80 years instead of 20, then the responses seem to look roughly like the untrained example from the graph in Yvain's analysis.
Another observation is that after we drop the 45 people who gave confidence levels >85% (and in fact, 89% of them were right), the remaining data is absolutely abysmal: the remaining answers are essentially uncorrelated with the confidence levels.
This suggests that there were a few pretty knowledgeable people who got the answer right and that was that. Everyone else just guessed and didn't know how to calibrate; this may correspond to your second explanation.
Another thing I have noticed is that I tend to pigeonhole stuff into centuries; for example, once in a TV quiz there was a question “which of these pairs of people could have met” (i.e. their lives overlapped), I immediately thought “It can't be Picasso and van Gogh: Picasso lived in the 20th century, whereas van Gogh lived in the 19th century.” I was wrong. Picasso was born in 1881 and van Gogh died in 1890. If other people also have this bias, this can help explain why so many more people answered 17xx than 16xx, thereby causing the median answer to be much later than the correct answer.
I hate the nth century convention because it doesn't match up with the numbers used for the dates, so I always refer to the dates.... but that actually tends to confuse people.
I was going to say “the 1700s”, but that's ambiguous as in principle it could refer either to a century or to its first decade. (OTOH, it would be more accurate, as my mental pigeonholes lump the year 1700 together with the following 99 years, not with the previous.)