Reply #31: OK

[Febble]

Let's take, for the sake of argument, DC in 2004. Kerry one the EC vote. If we want to ensure that Bush was not the victim of pro-Kerry fraud, we postulate that to overturn a true Bush win, the pro-Kerry fraudsters would have had to have stolen about 180,000 votes. To do this, they would have had to have stolen votes in a large number of precincts. An audit sample size needs to be large enough to detect a small percentage of corrupt precincts with a high degree of confidence. So, clearly, if the minimum proportion of corrupt precincts required to overturn the vote is large (as in a state with a large official margin for one candidate) then for a given degree of confidence, the sample size needs to be smaller than in a state where the margin was small, and a larger minimum proportion of corrupt precincts would have been required to overturn the result.

However, the other danger is that the fraudsters did not concentrate their fraud in a small number of precincts, but actually spread it thinly over a large number. This is why, to my mind, audit protocols that require an full recount of the audited sample of precincts (or machines) have the edge, because the tolerances in such a recount can be very tight. Not only that, but even if every single precinct or machine that was recounted came to within a vote or two of the initial count (and within the specified tolerance of the machine) then you could still apply a chi square or a sign test to find out whether the errors were significantly (to your required confidence level) more likely to benefit one candidate rather than the other. If not, you would suspect fraud, and start prosecutions, even if the size of the effect was insufficient to overturn the result.

Prosecutions should follow whatever the margin. The margin merely tells you how the minimum proportion of precincts required to overturn the race.