Imagine there are spoiled Thune votes in those three counties in the amounts of 1800, 900, and 600 respectively. Then Thune vote would be running approximately 0.3 of registered, Johnson vote 0.4 of registered, and turnout relatively constant at 0.7 of registered - right at the statewide average figure. That matches the performance on the other reservations, with minor statistical dispersion, just as you would expect.
The likely fraud signature, therefore, is pro-Thune ballots not counted (or spoiled) in Shannon, Todd, and Dewey counties. The amounts might be around 1500, 1000, 500 or around 25% of votes cast, and together would make up enough to eliminate the margin of 2800 that Thune possessed early in the reporting.
That is the spot the statistics suggest should be put under a microscope, and the method to look for is not double voting or votes by non-existent people, but non-recording or spoiling of pro-Thune votes in reservation areas where precinct workers consider such votes "incorrect".
Now, a potential statistical confirmation of the thesis is past turnout and vote split behavior, D vs. R, in those three counties. It is less the credible on its face that Johnson just happened to get his highest % of the vote in the lowest % turnout Indian areas, always getting 0.4 of the vote, while Thune got dramatically less than the 0.3 of reservation votes he pulled elsewhere, in exactly the lowest turnout reservation areas.
The Libertarian candidate received > 0.35% in every county {usally around 0.5 - 1.0%}
Except:
0.20% - Shannon
0.25% - Clay
0.34% - Todd
Hmmmmmmmmmmm