TOM DOWNS,
DENNIS C. GILLILAND, and LEO KATZ
Elementary probability models can sometimes be used to
analyze the results of an election where irregularities have occurred. In this
article we give an illustrative example by considering the 1975 mayoral
election in the city of Flint, Michigan. True vote is esti- mated with an
estimator which is used in randomized response models.
KEY WORDS: Election challenge; True vote estimation;
Random- ized response model.
INTRODUCTION
The
result of a close election may be challenged on the basis of irregularities and
the outcome may ultimately be decided by the courts. A given court may uphold
the result, reverse the result, invalidate the entire election, or offer any of
a number of remedies. (For a comprehensive review of election law including
postelection remedies, see "Developments in the Law-Elections"
(1975).) In general, an election will not be overturned on the basis of a mere
mathe- matical possibility that the results would be reversed in the absence of
irregularities. Being reluctant to unjustly disenfranchise the valid electors,
the courts have sometimes required that a challenger establish a probability
that the result would be reversed in the absence of irregularities.
Sometimes
the evidence consists of proof that a certain number of persons voted who were
not quali- fied, with no evidence as to how these persons voted. Finkelstein
and Robbins (1973) compute the probability of reversal under random removal of
a number of votes equal to the number of illegal votes. They point out that
this is a neutral and proper measure of probability of reversal in cases where
there is no evidence to indicate that one candidate or another benefited from
the illegal votes.
In
this article we give the facts associated with the contested mayoral election
in the city of Flint, Michi- gan, on November 4, 1975. The irregularity in this
election is not a common one; however, the problem it created provided a
situation where an elementary probability model could be used to quantify the
probability of reversal.
THE FACTS
CONCERNING THE FLINT ELECTION
The
city of Flint, Michigan, held an election on November 4, 1975 for the office of
Mayor, wherein a mayor was to be elected for the first time under a new city
charter. The vote for mayor after recount is shown in Table 1. The breakdown
for Precincts 51 and 52 is given because these vote totals were disputed due to
a mixup in ballot assemblies in these precincts. The vote totals from the other
143 precincts and absentee voters were not disputed. The recorded vote shows
Rutherford the winner with a margin of 206 votes. However, due to the errors in
ballot assemblies in the two precincts and the closeness of the vote, the
decision by the Board of Canvassers to declare James Rutherford the winner over
Floyd McCree was chal- lenged in the courts.
Those
who voted in person used punch-card devices in the following manner. The
individual voter was given a punch-card to insert in a ballot assembly. The
ballot assembly is part of the voting device and is a book with the names of
candidates printed on the pages with a hole beside the name of each candidate.
The in- dividual voted for the candidate of his choice by punching through the
hole with a stylus. This re- moved a square from the punch card. The computer
used to tabulate the vote was programmed to know the correspondence between
squares on the punch card and votes for specific candidates.
The
ballot assemblies were arranged among pre- cincts so that neither candidate
would always be listed first or second. The computer was programmed and the
individual cards coordinated to take the rotation into account. Precincts 51
and 52 had five and four voting devices, respectively. The ballot assemblies
were to be rotated between the two precincts so that the candidate whose name
was first in Precinct 51 was second in Precinct 52.
By
mistake, the election officials placed one ballot assembly in Precinct 51 that
should have been in Precinct 52, and one ballot assembly in Precinct 52 that
should have been in Precinct 51. The result was that a voter using the device
with the wrong assembly in either precinct would have his vote recorded for the
other candidate.
The
error in ballot assemblies was discovered after the polls had closed and the
voting devices were dis- assembled. The commingling of all punch-cards from
voting devices within a precinct made it impossible to distinguish which or how
many votes were improperly recorded (reversed) within Precincts 51 and 52.
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