The graph (via Tehran Bureau) looks pretty amaing; but in fact, as I explain, it’s pretty much what you’d expect real election data to look like.
One point there wasn’t room for in the piece; if you look carefully at the chart above, you’ll see that the folks at Tehran Bureau got the election returns to fit the line y = 0.5238x – 742642 very well. But in some sense that’s irrelevant, unless there’s some reasonable expectation that clerical powers-that-be would want faked election numbers to follow a funny line with a negative y-intercept. When R.A. Fisher went after Gregor Mendel, it wasn’t just because Mendel’s results looked suspiciously regular; it was because they looked suspiciously close to Mendel’s theoretical predictions. If Mendel shaded the data, consciously or not, that’s the direction it would go.
I mean, I can fit a really nice quadratic in x to the Iranian election data — or, for that matter, U.S. election data — but absent any reason to posit a vast parabola-loving conspiracy, it’s just not that suspicious.
Update: (June 18) Lots more material around the web about Iranian election stats. A preprint on the arXiv claims the official numbers violate Benford’s law, but Andrew Gelman says no. On the other hand, via Mark Blumenthal at Pollster, I learn that Walter Mebane at Michigan finds some suspicious-looking irregularities in the town-level data.