If the larger percentages are in the larger precincts, i.e., the data points that pull up the average tend to occur toward the end of the sequence, then it won't flatten out. It's only going to flatten out if you get to a point where the prior average is (roughly) the overall average, and the remaining precincts average out to the overall average ... but that's not the case if there's a correlation between the precinct ordering and the vote percentage.
What the non-flattening graphs show, in a convoluted way, is that there IS a correlation between precinct size and vote percentage. If there is such a correlation, the graph won't be flat, and the stronger the correlation the less flat it will be.
Look at it this way. Assume there's a correlation between precinct size and vote percentage and for this example, assume it's increasing. If we look at some midpoint in the sorted sequence, then the correlation means that the points to the right will have a higher average than the points to the left. But the cumulative average is obviously the average of the points to the left, so points to the right will cause the cumulative average to continue rising as we continue accumulating them. So the correlation means that the curve is not flat. Fraud or no fraud, it's just the effect of sorting by a non-independent variable.
The statistical argument assumes that the precinct size and vote percentage are independent variables. If there's a correlation between precinct size and vote percentage, then the statistical argument is incorrect.



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