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@make(letterhead,Phone"497-4430",Who"John McCarthy", Logo, Old, Department CSD)
@style(indent 8)
@begin(address)
Prof. Doris Schattschneider, Editor
Mathematics Magazine
Moravian College,
Bethlehem, Pennsylvaia 18018
@end(address)
@greeting(To the Editor:)
@begin(body)
	James Ward's "Probability of Election Reversal"
@i[Mathematics Magazine], Vol. 54, No. 5, (November 1981) omits
an important consideration.

	The probability of reversal when an election is repeated
is very much larger than his estimates, because there can be
a change in circumstances between the original election and the
repeat election.  Voters may change their minds or people who
didn't think their votes would count for much in the first election
may decide to vote.

	If we knew a probability distribution of events that might
shift  @i[n] votes, we could compute the probability of
a shift of given size when an election is held.  I would conjecture
that the expected shift from an
 event
 influencing public
 opinion is ordinarily much larger than the expected shift from
an accidental bias on the part of voters casting invalid ballots.

	This makes holding repeat elections 
unfair to the winner of the original election if the
court or other body that may require the repeat may be biased in
favor of the original loser.  An extreme unfairness would occur
if the side favored by the election authorities could always
demand a revote if the results were at all close.  Such situations
have existed in undemocratically run organizations.  Even if the
election authority is unbiased, it may be thought to be biased, so
the above criteria also apply to the maintenance of confidence
in the electoral process.

	Therefore, there needs to be a fixed rule stated
before the election to determine how many
invalid ballots are needed to require a new election.
@end(body)
Sincerely



John McCarthy
Professor of Computer Science


@flushleft(cc. James Ward III)