In a comment to this post from the Citizens about the Minnesota senate race:
I'm not a statistician, but "margin of error" refers to the likelihood of a survey not accurately reflecting the population the survey is taken from.
Since the votes are what decide the election (we don't care what the population who doesn't vote thinks), the vote is a census, not a survey, and doesn't have any margin of error in the statistical sense.
But, as Florida 2000 demonstrated, you are right in thinking there will be "a different tally every time they are tallied." This isn't a mathematical issue, but a practical one. Out of three million ballots, some are going to be weird, subject to interpretation, of imperfect provenance, etc.
I _think_ the error rate associated with this sort of thing varies a lot based on the exact situation. Different voting machine types (and different voting machines) will produce ambiguous results at different rates; different jurisdictions will have different judges who consider different proportions of provisional ballots to fall into the category of "subject to legal interpretation."
If, after the error-checking of the recount, the difference is still only a couple hundred, the chances are good that there's enough "fuzziness" in some of the votes that the result will come down to luck -- who has the higher tally when the courts (or the election laws) say "enough". But not necessarily -- it's possible that even a very small margin is demonstrably genuine in the eyes of the law, if the voting machines are so good they don't produce many ambiguous results. (This is the point of electronic voting machines, although optical scanning offers a clearer paper trail to check results against.)
I say "in the eyes of the law" because there's no way to determine beyond the shadow of <i>any</i> doubt that every voter's intent has really been accurately captured. This boils down to the impossibility of absolute certainty -- at some point we draw the line and say "yes, it's possible that this electronic voting machine switched the vote of every 10,000th voter and we didn't happen to catch it with comparison to exit poll data, but that possibility isn't worth pursuing."
I'm not a statistician, but "margin of error" refers to the likelihood of a survey not accurately reflecting the population the survey is taken from.
Since the votes are what decide the election (we don't care what the population who doesn't vote thinks), the vote is a census, not a survey, and doesn't have any margin of error in the statistical sense.
But, as Florida 2000 demonstrated, you are right in thinking there will be "a different tally every time they are tallied." This isn't a mathematical issue, but a practical one. Out of three million ballots, some are going to be weird, subject to interpretation, of imperfect provenance, etc.
I _think_ the error rate associated with this sort of thing varies a lot based on the exact situation. Different voting machine types (and different voting machines) will produce ambiguous results at different rates; different jurisdictions will have different judges who consider different proportions of provisional ballots to fall into the category of "subject to legal interpretation."
If, after the error-checking of the recount, the difference is still only a couple hundred, the chances are good that there's enough "fuzziness" in some of the votes that the result will come down to luck -- who has the higher tally when the courts (or the election laws) say "enough". But not necessarily -- it's possible that even a very small margin is demonstrably genuine in the eyes of the law, if the voting machines are so good they don't produce many ambiguous results. (This is the point of electronic voting machines, although optical scanning offers a clearer paper trail to check results against.)
I say "in the eyes of the law" because there's no way to determine beyond the shadow of <i>any</i> doubt that every voter's intent has really been accurately captured. This boils down to the impossibility of absolute certainty -- at some point we draw the line and say "yes, it's possible that this electronic voting machine switched the vote of every 10,000th voter and we didn't happen to catch it with comparison to exit poll data, but that possibility isn't worth pursuing."
