Reply #18: And to quote what I said further on in that post:

[Febble]

One reason for this nonsense, could, I agree, be fraud. However, I see two alternative explanations that I find plausible, though I respect your right to disagree.

One is that no-one knows whether the weightings were correctly applied - my guess is that they would be optimized to constraints more binding (like gender) than past vote, as past vote is a notoriously unreliable measure. However, there are almost certainly multiple solutions to the possible weights that could be applied to match the poll data to the count data (and I agree - who could not? - that they were matched: they were designed to be matched) and some may give a more veridical match to the Gore/Bush proportions. So the final Gore/Bush proportions may simply be wrong, even though the estimate of the vote count now matches the vote count. Weighting solutions may exist that do a better job of approximating the actual Gore/Bush proportion.

But secondly, I do not believe the Gore/Bush raw responses are necessarily accurate. I find it plausible that the initial proportions of Gore/Bush respondents only coincidentally matched reality. I am not saying this is so, just that it could be so. In other words it is possible that the final table tells you something real about what people who voted for Bush in 2004 wanted to think about they way that they had voted in 2004. And that some Bush voters in 2004 wanted to think they had voted for Bush in 2000, whether they had in fact voted for him, or whether in fact they had voted at all. We know, from good research, that people do this.

However, I do not think this is necessarily the case. I think it may simply be an artefact of the way the weighting was done.

But it means that although I follow your mathematical reasoning, I cannot agree that Gore/Bush proportions in the final table are incontrovertible proof of fraud, particularly in the light of evidence that bias was greater where random sampling protocol was most likely to be compromised, for example, where interviewing rate - the rate at which voters are selected for interview - was low.

And I think to assert that it is incontrovertible proof is misleading. It is contingent on a notoriously unreliable measure of past voting behaviour from a minority subsample of the participants in the poll, and moreover, the final Bush/Gore proportions diverge from what is possible in exactly the way that one would expect - that people like to report have previously voting for the person they are currently voting for. I think it is known as the "consistency bias".

However, these are behavioural arguments, not mathematical. I do not dispute your math.