I think it would be unwise to use random sampling theory, with or
without the finite population correction, to infer what the percentage
of Bush and Gore votes would be among the non-machine counted votes.
There were several analyses published in the press about who would
have won a recount, based on the recounts in Broward, Palm Beach and
Miami-Dade county. All of these models presented in the press
predicted Bush would have won a state-wide recount. These models appear
to have assumed that the uncounted votes were randomly drawn from the
same population as the counted votes (i.e., determine on a
precinct-by-prencinct basis the Bush-Gore votes, add a yield rate for
the % of uncounted votes for which voter intent can be discerned,
incorporate an error rate, and predict Bush v. Gore among the uncounted
votes with an error rate).
It appears that the non-machine-counted votes are anything but a
random sample of the total vote. In Broward County, with punchcards,
the undervote was significantly more pro-Bush (34%) than the machine
vote (31%). This week, the Orlando Sentinel evaluated 6000 overvotes in
the highly GOP Lake County. Many overvotes result from GOP and DEM
voters voting for Bush or Gore and then confirming their choice by
checking the write-in box and then writing in the same choice. They
were trying to avoid any ambiguity, perhaps thinking back to earlier
days of written ballots, and these voters got their ballots thrown out.
These votes were being counted as per the Florida Supreme Court
decision, but counting stopped with the SCOTUS decision. The Orlando
Sentinel anlayzed the unambiguous votes and determined that Gore picked
would have picked up 130 votes. A model based on a yield rate, an error
rate multiplied by % of Bush-Gore votes, would be unlikely to have
predicted that Gore would have picked up votes in heavily GOP counties.
The take-home message is that an election should be viewed as a
complete census and calculations of margins of error to the larger
non-voting population are irrelevant. Sampling statistics might be used
to infer the likely outcome of the non-machine counted vote, but
indications are that these votes are not merely random draws from the
larger pool of voters.
Sampling statistics could play and did play a role in this election.
Judge Sauls ruled that the Gore legal team did not present sufficient
statistical evidence that a recount presented had a reasonable
probability of altering the election outcome. I'm sure that there is a
dissertation topic or two out there to develop statistical models that
will past muster with a future Judge Sauls.
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