Responding to my posting below:
>> .... I concluded that one would expect the division to be *closer* to
>> 1/2 each than for the clearly marked ballots. If you mix a certain
>> number of valid ballots with 1/3 - 2/3 proportions with another group
>> of invalid ballots, in which votes have been assigned randomly, in
>> 1/2 - 1/2 proportions, the proportions for the whole group will not
>> be 1/3 - 2/3, but rather will have shifted toward 1/2 - 1/2.
Tom Robertson <[EMAIL PROTECTED]> said:
> True, but irrelevant. What is a better basis for estimating how the
> invalid ballots are distributed than by how the valid ballots were
> distributed?
And Virgil <[EMAIL PROTECTED]> said:
>You make my point for me. You conclude that the "invalid" ballots will
>be split nearer half and half than the valid ballots. Why?
>
>The most reasonable assumption is that the same proprtion of the votes
>for each candidate would be declared invalid. In this case, if those
>invalid votes show any marks of intention at all, they should be split
>in the same proportions as the valid votes.
>
>The only case for a more nearly 50-50 split might be if totally
>indeterminant ballots had to be assigned to someone. Even then
>statistics indicates that they should be split in the same propotions as
>the valid ballots.
Let me try one more time:
1) A certain number of ballots will have been filled out by people
who HAD NO INTENTION OF VOTING FOR PRESIDENT. In a manual recount,
a certain number of these will nevertheless be assigned to some
presidential candidate. If they are so assigned in an unbiased
manner, they should split evenly. Furthermore, there is good reason
to think that such spurious assignments of votes will be more frequent
in the manual recount of ballots rejected by machine than in the machine
count of ballots that were regarded by the machine as unambiguous.
2) Among those ballots filled out by voters who DID intend to vote
for president, some will be more ambiguous than others. The
manual recount will not succeed in assigning 100% of the most
ambiguous ballots to the candidate whom the voter actually intended
to vote for. There is again reason to think that the error rate
for the manual recount of questionable ballots will be greater
than for the machine count of ballots that the machine regarded
as unambiguous. If the process is unbiased, those ballots where
it is not really possible to tell the voter intent, but where a
vote was nevertheless assigned, should split evenly.
Both (1) and (2) should result in the proportions of votes assigned in
the manual recount being shifted toward more equal proportions than
was the case for the machine count of ballots the machine didn't
reject, provided the manual recount is not biased. This assumes that
the degree of ambiguity in the ballot is not related to who the voter
intended to vote for (in cases where they intended to vote for
anyone). This might not be true, but that doesn't seem to be what the
responders to my post are concerned about.
It would be interesting to know whether the recount is looking at
ballots selected by some criterion that doesn't relate to whether it
seemed like it might be a vote for Bush or Gore, rather than for some
third-party candidate. If so, one could look at the vote counts for
the third-party candidates in the manual recount. If the proportion
of such third-part votes has gone up, that might give an indication of
how many essentially undecipherable ballots are being assigned
randomly, if you assume that the process is unbaised (not only between
Bush and Gore, but among all candidates). However, I wouldn't be
surprised if the proportion of third-party candidates has gone down,
reflecting a tendency for the manual recounters to not consider the
possibility of such an "irrelevant" vote.
----------------------------------------------------------------------------
Radford M. Neal [EMAIL PROTECTED]
Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED]
University of Toronto http://www.cs.utoronto.ca/~radford
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