New Empirical Estimates of the Biases of the Electoral College for the 1980s

• Author: James D. Dana,Lawrence D. Longley
• DOI: 10.1177/106591298403700111
• Published date: 01 March 1984
• Date: 01 March 1984
• Subject Matter: Articles

NEW
EMPIRICAL ESTIMATES OF THE BIASES
OF THE ELECTORAL COLLEGE FOR THE 1980s
LAWRENCE D. LONGLEY, Lawrence University
and
JAMES D. DANA, JR., Massachusetts Institute of Technology
VER
the course of the past decade, there has been considerable
~ ~ interest in the empirical analysis of the electoral college (for
0
recent surveys of empirical research on the electoral college, see:
Longley 1980a, 1980b, 1982; and Peirce and Longley 1981). Many of
these efforts have addressed themselves to the assessment of the biases
alleged, in conventional wisdom, to be contained in the electoral college.
Among the structural features of the electoral college frequently cited as
giving rise to biases are (1) the constant two constitutional allocation of two
electoral votes to every state regardless of size (corresponding to its Senate
representation) in addition to electoral votes equal to its number of
congressmen; (2) the unit rule extraconstitutional provision (sometimes
termed the &dquo;winner-take-all&dquo; feature) that the candidate who receives a
plurality of votes in a state wins all that state’s electoral votes; (3) the
assignment of electoral votes (other than the &dquo;constant two&dquo;) to states on
the basis of population rather than voter turnout; and (4) the assignment
of electoral votes on the basis of census population figures, which reflect
population shifts only at ten-year intervals (Longley and Yunker 1971:
1-2; Yunker and Longley 1973: 173-74); Longley and Braun 1972 and
1975: 95-96); and Longley 1974: 68). These features ensure that the
electoral college will always provide an imperfect reflection of the popular
vote for President. To say that the electoral college introduces random
distortions into the election of the President is, however, only a half-truth,
for it also contains a variety of systematic biases conferring advantages on
some voters and imposing disadvantages on others.
Much of this decade-long research into the biases of the electoral
college has used what is called the &dquo;voting power&dquo; approach (defined
below) to estimate the biases of the electoral college and major alternative
reform plans. Initial research (Longley and Yunker 1971; Longley and
Braun 1972; and Yunker and Longley 1973) elaborated on and expanded
upon the voting power analysis of Banzhaf (1968), especially in going
beyond Banzhaf’s state data to derive the biases of the electoral college for
various demographic and geographical groups. Later research (Longley
and Yunker 1973; Longley and Braun 1975; Yunker and Longley 1976;
Longley 1977a, 1977b, 1980a, 1980b, 1982; and Peirce and Longley 1981)
NOTE: This research was made possible by a Lawrence University Faculty Research Grant
and by an NSF-CAUSE Grant to Lawrence University. Appreciation for various forms
of assistance in this project is expressed to Professors David Cook, James Evans, and
Michael Hittle of Lawrence University, and Mr. John Yunker, formerly of the Univer-
sity of Minnesota.

---

158
built upon these earlier efforts in two ways: by correcting and re-
calculating the original 1968 Banzhaf figures for the electoral college in
the 1960s and by presenting new data measuring the biases of the elec-
toral college as apportioned for the presidential elections of the 19’70s.1
The research presented here builds on this preceding work by
analyzing, for the first time, the biases of the electoral college for the
presidential elections of the 1980s (those of 1984 and 1988), reflecting the
electoral vote apportionments and population distributions among the
states resulting from the 1980 census, and by contrasting these biases over
a three-decade period with those for the electoral college in the 1960s and
1970s. Comparable data are also briefly presented for various frequently
discussed reform alternative plans.
Most of the above cited research has concerned itself with more than
just questions of state advantages and disadvantages under the electoral
college and alternative plans. Conventional wisdom concerning the elec-
toral college asserts that various groups and interests are advantaged or
disadvantaged under the present mechanism for electing the President.
Among the voters often seen as advantaged are urban and ethnic voters,
inhabitants of &dquo;swing&dquo; states, metropolitan areas, the South, and minority
groups -
in particular black voters. (See especially Longley 1980b, 1982;
and Peirce and Longley 1981.) For the most part, arguments dealing with
these demographic groups have been based on the premise that either
large states or small states have an advantage and a particular group or
interest concentrated in those states has a corresponding advantage.
Consequently, these interpretations have been subject to much the same
controversy surrounding the big-state, small-state debate concerning who
is really advantaged by the electoral college.
In the analysis that follows, we not only discuss the state-by-state
advantages and disadvantages resulting from the electoral college as
apportioned for the presidential elections of the 1980s (those of 1984 and
1988), we also analyze the biases of the electoral college in the 1980s for a
number of demographic groups, and contrast these biases with compara-
ble figures for the electoral college in the 1960s and the 1970s. Part I of
this paper briefly reviews the voting power approach to the analysis of the
electoral college. Part II presents the state biases for the 1980s of, respec-
tively, the present electoral college and, more briefly, the proportional,
district, and direct vote reform plans. This section also mentions several
different methods of determining voting power, including approaches
utilizing vote turnout data instead of state population data, and ap-
proaches based on alternative definitions of pivotal voting power. Part III
I
’ The " 1960s" refers to the electoral college apportionments based on the 1960 census and in
effect for the presidential elections of 1964 and 1968. The " 1970s" refers to the electoral
college apportionments based on the 1970 census and in effect for the presidential
elections of 1972, 1976, and 1980. The "1980s" refers to the electoral college appor-
tionments based on the 1980 census and in effect for the presidential elections of 1984
and 1988. It is a curious feature of the electoral college that any population shifts or
increases after 1980 will not affect the electoral college until the presidential election of
1992.

---

159
discusses the regional and group biases in the 1980s of the electoral
college and the same three proposed reforms. Both Parts II and III also
contrast these biases estimates with those for the 1960 and 1970 electoral
college. A summary of the major findings concludes the paper.2
2
I. THE VOTING POWER APPROACH
Until the last decade, there was no sophisticated means of analyzing
the actual influence of states and their citizens on the electoral college. In
addition, there was no reliable means of determining how the various
reform alternatives would affect the influence of states and individual
citizens in selecting the President. Advances in game theory and the
mathematical analysis of voting power have, however, made possible the
development of techniques allowing for a reasonably sophisticated de-
termination of the relative influence of the states and their citizens in the
election of the President. The inquiry into the electoral consequences of
the present electoral college has been conducted on two levels. On the one
hand, determinations of the relative power of the states in the present
electoral college were made by Mann and Shapley (1962 and 1964). On
the other hand, Banzhaf ( 1968) calculated the relative power of individual
citizen-voters within each state in the present electoral college and in
various alternative systems. The work of Riker and Shapley (1966) served
as a valuable transition between these works.
The Mann and Shapley Studies
The first of these efforts, the Mann and Shapley studies, developed a
&dquo;51-person, weighted majority game&dquo; to evaluate the electoral college.
From it, they concluded that there is a slight systematic bias in favor of the
large states in the present electoral college as a result of the unit rule, but
one not exceeding a 10 percent varation in power per electoral vote
among the various states. This bias, in their opinion, was meaningful,
though &dquo;not very important in the total consequences of the electoral
college.&dquo; However, in a footnote to their conclusions, Mann and Shapley
suggested that in a multi-million-person game, taking the individual
voters as the players, the voters in the large states actually might be
favored with a bias that &dquo;quantitatively might be as much as double the one
seen by treating the states as players&dquo; (Mann and Shapley 1964: 9, 154).
The
reason for this apparent contradiction is that Mann
and Shapley (and
later Riker and Shapley) felt that a citizen’s voting power was inversely
proportional to the square root of his constitutency’s population.
2
A technical appendix is available which considers a number of specific problems including
the complexities introduced by Maine’s use of the district plan starting with the 1972
election (the analysis in this article assumes that Maine determines its electoral votes
under the same winner-take-all rule as all other states — as it has, in effect, done since its
1972 change), and the questions raised by the calculation of the variances of the prob-
abilities...