I don't see how that is possible

> but it does not salvage statistics.

Statistics does not need salvaging.

> Originally i claimed that what happens is it becomes game theory. That was a bit of a simplification, but it is illustrated by your example.

My cheating statistics example is a counter-example that defeats your argument.

> In this case, statistical methods cannot positively identify no cheating,

That is the entire point of cheating statistical analysis, to determine if cheating occurred. If cheating is not statistically identified, then the analysis shows "positively" that cheating hasn't occurred.

> and the extent to which they can identify instances of cheating, it is because the observed party was not acting adversarially.

Statistical analysis of cheating does not involve direct observation, and any cheater is adversarial by definition.

> The algorithm i presented anove for gerrymandering is very general.

On the contrary, it is not only specific, it does not support your argument. Politicians are not statisticians, and the depth of statistical analysis is notably shallow and has a single factor, party affiliation.

Statistics is a very old and complex discipline. It is technically a branch of mathematics. In advancing the argument that a biased statistician can produce incorrect results, or that statistics can not accurately study adversarial subjects, the underlying fallacy to these arguments is hasty generalization. As laymen, we can not invalidate an entire discipline or even speculate the limits of such a discipline based on such very specific and synthetic circumstances.